Parent Directory
| 
Revision Log
Revision 2645 - (view) (download)
| 1 : | jj | 455 | # Comments start with # |
| 2 : | # The first line of a new text is TitleText | ||
| 3 : | # Edition and Author must be there too | ||
| 4 : | # Blank lines are only for decoration | ||
| 5 : | |||
| 6 : | TitleText('Financial Mathematics') | ||
| 7 : | EditionText('1') | ||
| 8 : | AuthorText('Holt') | ||
| 9 : | |||
| 10 : | 1 >>> Introduction to Interest | ||
| 11 : | jjholt | 528 | 1.0 >>> Algebra Prerequisites |
| 12 : | jj | 455 | 1.1 >>> Simple Interest |
| 13 : | 1.2 >>> Compound Interest | ||
| 14 : | 1.3 >>> Effective and Nominal Rates of Interest | ||
| 15 : | 1.4 >>> Present and Future Value | ||
| 16 : | |||
| 17 : | 2 >>> Equations of Value | ||
| 18 : | 2.1 >>> Time Value of Money | ||
| 19 : | 2.2 >>> Unknown Time and Logarithms | ||
| 20 : | 2.3 >>> Dollar Weighted Rate of Return | ||
| 21 : | 2.4 >>> Time Weighted Rate of Return | ||
| 22 : | |||
| 23 : | 3 >>> Annuities | ||
| 24 : | 3.1 >>> Geometric Sums | ||
| 25 : | 3.2 >>> Annuities | ||
| 26 : | 3.3 >>> Loans | ||
| 27 : | 3.4 >>> Sinking Funds | ||
| 28 : | 3.5 >>> Varying Payments | ||
| 29 : | 3.6 >>> Perpetuities | ||
| 30 : | |||
| 31 : | 4 >>> Bonds | ||
| 32 : | 4.1 >>> Yield Rates | ||
| 33 : | 4.2 >>> Bonds | ||
| 34 : | 4.3 >>> Book Value | ||
| 35 : | 4.4 >>> Other Bonds | ||
| 36 : | |||
| 37 : | 5 >>> Probability and Contingent Payments | ||
| 38 : | 5.1 >>> Introduction to Probability | ||
| 39 : | 5.2 >>> Expected Values | ||
| 40 : | 5.3 >>> Contingent Payments | ||
| 41 : | |||
| 42 : | 6 >>> Options | ||
| 43 : | 6.1 >>> Introduction to Options | ||
| 44 : | 6.2 >>> Hedging Strategies | ||
| 45 : | 6.3 >>> Binomial Trees | ||
| 46 : | |||
| 47 : | jj | 467 | TitleText('Mathematical Statistics') |
| 48 : | EditionText('6') | ||
| 49 : | AuthorText('Wackerly, Mendenhall, Scheaffer') | ||
| 50 : | |||
| 51 : | 1 >>> What Is Statistics? | ||
| 52 : | 1.1 >>> Introduction | ||
| 53 : | 1.2 >>> Characterizing a Set of Measurements: Graphical Methods | ||
| 54 : | 1.3 >>> Characterizing a Set of Measurements: Numerical Methods | ||
| 55 : | 1.4 >>> How Inferences Are Made | ||
| 56 : | 1.5 >>> Theory and Reality | ||
| 57 : | 1.6 >>> Summary | ||
| 58 : | jj | 468 | |
| 59 : | jj | 467 | 2 >>> Probability |
| 60 : | 2.1 >>> Introduction | ||
| 61 : | 2.2 >>> Probability and Inference | ||
| 62 : | 2.3 >>> A Review of Set Notation | ||
| 63 : | 2.4 >>> A Probabilistic Model for an Experiment: The Discrete Case | ||
| 64 : | 2.5 >>> Calculating the Probability of an Event: The Sample-Point Method | ||
| 65 : | 2.6 >>> Tools for Counting Sample Points | ||
| 66 : | 2.7 >>> Conditional Probability and the Independence of Events | ||
| 67 : | 2.8 >>> Two Laws of Probability | ||
| 68 : | 2.9 >>> Calculating the Probability of an Event: The Event-Composition Methods | ||
| 69 : | 2.10 >>> The Law of Total Probability and Bayes's Rule | ||
| 70 : | 2.11 >>> Numerical Events and Random Variables | ||
| 71 : | 2.12 >>> Random Sampling | ||
| 72 : | 2.13 >>> Summary | ||
| 73 : | jj | 468 | |
| 74 : | jj | 467 | 3 >>> Discrete Random Variables and Their Probability Distributions |
| 75 : | 3.1 >>> Basic Definition | ||
| 76 : | 3.2 >>> The Probability Distribution for Discrete Random Variable | ||
| 77 : | 3.3 >>> The Expected Value of Random Variable or a Function of Random Variable | ||
| 78 : | 3.4 >>> The Binomial Probability Distribution | ||
| 79 : | 3.5 >>> The Geometric Probability Distribution | ||
| 80 : | 3.6 >>> The Negative Binomial Probability Distribution | ||
| 81 : | 3.7 >>> The Hypergeometric Probability Distribution | ||
| 82 : | 3.8 >>> Moments and Moment-Generating Functions | ||
| 83 : | 3.9 >>> Probability-Generating Functions | ||
| 84 : | 3.10 >>> Tchebysheff's Theorem | ||
| 85 : | 3.11 >>> Summary | ||
| 86 : | jj | 468 | |
| 87 : | jj | 467 | 4 >>> Continuous Random Variables and Their Probability Distributions |
| 88 : | 4.1 >>> Introduction | ||
| 89 : | 4.2 >>> The Probability Distribution for Continuous Random Variable | ||
| 90 : | 4.3 >>> The Expected Value for Continuous Random Variable | ||
| 91 : | 4.4 >>> The Uniform Probability Distribution | ||
| 92 : | 4.5 >>> The Normal Probability Distribution | ||
| 93 : | 4.6 >>> The Gamma Probability Distribution | ||
| 94 : | 4.7 >>> The Beta Probability Distribution | ||
| 95 : | 4.8 >>> Some General Comments | ||
| 96 : | 4.9 >>> Other Expected Values | ||
| 97 : | 4.10 >>> Tchebysheff's Theorem | ||
| 98 : | 4.11 >>> Expectations of Discontinuous Functions and Mixed Probability Distributions | ||
| 99 : | 4.12 >>> Summary | ||
| 100 : | jj | 468 | |
| 101 : | jj | 467 | 5 >>> Multivariate Probability Distributions |
| 102 : | 5.1 >>> Introduction | ||
| 103 : | 5.2 >>> Bivariate and Multivariate Probability Distributions | ||
| 104 : | 5.3 >>> Independent Random Variables | ||
| 105 : | 5.4 >>> The Expected Value of a Function of Random Variables | ||
| 106 : | 5.5 >>> Special Theorems | ||
| 107 : | 5.6 >>> The Covariance of Two Random Variables | ||
| 108 : | 5.7 >>> The Expected Value and Variance of Linear Functions of Random Variables | ||
| 109 : | 5.8 >>> The Multinomial Probability Distribution | ||
| 110 : | 5.9 >>> The Bivariate Normal Distribution | ||
| 111 : | 5.10 >>> Conditional Expectations | ||
| 112 : | 5.11 >>> Summary | ||
| 113 : | jj | 468 | |
| 114 : | jj | 467 | 6 >>> Functions of Random Variables |
| 115 : | 6.1 >>> Introductions | ||
| 116 : | 6.2 >>> Finding the Probability Distribution of a Function of Random Variables | ||
| 117 : | 6.3 >>> The Method of Distribution Functions | ||
| 118 : | 6.4 >>> The Methods of Transformations | ||
| 119 : | 6.5 >>> Multivariable Transformations Using Jacobians | ||
| 120 : | 6.6 >>> Order Statistics | ||
| 121 : | 6.7 >>> Summary | ||
| 122 : | jj | 468 | |
| 123 : | jj | 467 | 7 >>> Sampling Distributions and the Central Limit Theorem |
| 124 : | 7.1 >>> Introduction | ||
| 125 : | 7.2 >>> Sampling Distributions Related to the Normal Distribution | ||
| 126 : | 7.3 >>> The Central Limit Theorem | ||
| 127 : | 7.4 >>> A Proof of the Central Limit Theorem | ||
| 128 : | 7.5 >>> The Normal Approximation to the Binomial Distributions | ||
| 129 : | 7.6 >>> Summary | ||
| 130 : | jj | 468 | |
| 131 : | jj | 467 | 8 >>> Estimation |
| 132 : | 8.1 >>> Introduction | ||
| 133 : | 8.2 >>> The Bias and Mean Square Error of Point Estimators | ||
| 134 : | 8.3 >>> Some Common Unbiased Point Estimators | ||
| 135 : | 8.4 >>> Evaluating the Goodness of Point Estimator | ||
| 136 : | 8.5 >>> Confidence Intervals | ||
| 137 : | 8.6 >>> Large-Sample Confidence Intervals Selecting the Sample Size | ||
| 138 : | 8.7 >>> Small-Sample Confidence Intervals for u and u1-u2 | ||
| 139 : | 8.8 >>> Confidence Intervals for o2 | ||
| 140 : | 8.9 >>> Summary | ||
| 141 : | jj | 468 | |
| 142 : | jj | 467 | 9 >>> Properties of Point Estimators and Methods of Estimation |
| 143 : | 9.1 >>> Introduction | ||
| 144 : | 9.2 >>> Relative Efficiency | ||
| 145 : | 9.3 >>> Consistency | ||
| 146 : | 9.4 >>> Sufficiency | ||
| 147 : | 9.5 >>> The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation | ||
| 148 : | 9.6 >>> The Method of Moments | ||
| 149 : | 9.7 >>> The Method of Maximum Likelihood | ||
| 150 : | 9.8 >>> Some Large-Sample Properties of MLEs | ||
| 151 : | 9.9 >>> Summary | ||
| 152 : | jj | 468 | |
| 153 : | jj | 467 | 10 >>> Hypothesis Testing |
| 154 : | 10.1 >>> Introduction | ||
| 155 : | 10.2 >>> Elements of a Statistical Test | ||
| 156 : | 10.3 >>> Common Large-Sample Tests | ||
| 157 : | 10.4 >>> Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test | ||
| 158 : | 10.5 >>> Relationships Between Hypothesis Testing Procedures and Confidence Intervals | ||
| 159 : | 10.6 >>> Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values | ||
| 160 : | 10.7 >>> Some Comments on the Theory of Hypothesis Testing | ||
| 161 : | 10.8 >>> Small-Sample Hypothesis Testing for u and u1-u2 | ||
| 162 : | 10.9 >>> Testing Hypotheses Concerning Variances | ||
| 163 : | 10.10 >>> Power of Test and the Neyman-Pearson Lemma | ||
| 164 : | 10.11 >>> Likelihood Ration Test | ||
| 165 : | 10.12 >>> Summary | ||
| 166 : | jj | 468 | |
| 167 : | jj | 467 | 11 >>> Linear Models and Estimation by Least Squares |
| 168 : | 11.1 >>> Introduction | ||
| 169 : | 11.2 >>> Linear Statistical Models | ||
| 170 : | 11.3 >>> The Method of Least Squares | ||
| 171 : | 11.4 >>> Properties of the Least Squares Estimators for the Simple Linear Regression Model | ||
| 172 : | 11.5 >>> Inference Concerning the Parameters BI | ||
| 173 : | 11.6 >>> Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression | ||
| 174 : | 11.7 >>> Predicting a Particular Value of Y Using Simple Linear Regression | ||
| 175 : | 11.8 >>> Correlation | ||
| 176 : | 11.9 >>> Some Practical Examples | ||
| 177 : | 11.10 >>> Fitting the Linear Model by Using Matrices | ||
| 178 : | 11.11 >>> Properties of the Least Squares Estimators for the Multiple Linear Regression Model | ||
| 179 : | 11.12 >>> Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression | ||
| 180 : | 11.13 >>> Prediction a Particular Value of Y Using Multiple Regression | ||
| 181 : | 11.14 >>> A Test for H0: Bg+1 + Bg+2 = ? = Bk = 0 | ||
| 182 : | 11.15 >>> Summary and Concluding Remarks | ||
| 183 : | jj | 468 | |
| 184 : | 12 >>> Considerations in Designing Experiments | ||
| 185 : | jj | 467 | 12.1 >>> The Elements Affecting the Information in a Sample |
| 186 : | 12.2 >>> Designing Experiment to Increase Accuracy | ||
| 187 : | 12.3 >>> The Matched Pairs Experiment | ||
| 188 : | 12.4 >>> Some Elementary Experimental Designs | ||
| 189 : | 12.5 >>> Summary | ||
| 190 : | jj | 468 | |
| 191 : | jj | 467 | 13 >>> The Analysis of Variance |
| 192 : | 13.1 >>> Introduction | ||
| 193 : | 13.2 >>> The Analysis of Variance Procedure | ||
| 194 : | 13.3 >>> Comparison of More than Two Means: Analysis of Variance for a One-way Layout | ||
| 195 : | 13.4 >>> An Analysis of Variance Table for a One-Way Layout | ||
| 196 : | 13.5 >>> A Statistical Model of the One-Way Layout | ||
| 197 : | 13.6 >>> Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout | ||
| 198 : | 13.7 >>> Estimation in the One-Way Layout | ||
| 199 : | 13.8 >>> A Statistical Model for the Randomized Block Design | ||
| 200 : | 13.9 >>> The Analysis of Variance for a Randomized Block Design | ||
| 201 : | 13.10 >>> Estimation in the Randomized Block Design | ||
| 202 : | 13.11 >>> Selecting the Sample Size | ||
| 203 : | 13.12 >>> Simultaneous Confidence Intervals for More than One Parameter | ||
| 204 : | 13.13 >>> Analysis of Variance Using Linear Models | ||
| 205 : | 13.14 >>> Summary | ||
| 206 : | jj | 468 | |
| 207 : | jj | 467 | 14 >>> Analysis of Categorical Data |
| 208 : | 14.1 >>> A Description of the Experiment | ||
| 209 : | 14.2 >>> The Chi-Square Test | ||
| 210 : | 14.3 >>> A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test | ||
| 211 : | 14.4 >>> Contingency Tables | ||
| 212 : | 14.5 >>> r x c Tables with Fixed Row or Column Totals | ||
| 213 : | 14.6 >>> Other Applications | ||
| 214 : | 14.7 >>> Summary and Concluding Remarks | ||
| 215 : | jj | 468 | |
| 216 : | 15 >>> Nonparametric Statistics | ||
| 217 : | jj | 467 | 15.1 >>> Introduction |
| 218 : | 15.2 >>> A General Two-Sampling Shift Model | ||
| 219 : | 15.3 >>> A Sign Test for a Matched Pairs Experiment | ||
| 220 : | 15.4 >>> The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment | ||
| 221 : | 15.5 >>> The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples | ||
| 222 : | 15.6 >>> The Mann-Whitney U Test: Independent Random Samples | ||
| 223 : | 15.7 >>> The Kruskal-Wallis Test for One-Way Layout | ||
| 224 : | 15.8 >>> The Friedman Test for Randomized Block Designs | ||
| 225 : | 15.9 >>> The Runs Test: A Test for Randomness | ||
| 226 : | 15.10 >>> Rank Correlation Coefficient | ||
| 227 : | 15.11 >>> Some General Comments on Nonparametric Statistical Test | ||
| 228 : | jj | 468 | |
| 229 : | jj | 472 | 16 >>> Appendix 1: Matrices and Other Useful Mathematical Results |
| 230 : | 16.1 >>> Appendix 1.1: Matrices and Matrix Algebra | ||
| 231 : | 16.2 >>> Appendix 1.2: Addition of Matrices | ||
| 232 : | 16.3 >>> Appendix 1.3: Multiplication of a Matrix by a Real Number | ||
| 233 : | 16.4 >>> Appendix 1.4: Matrix Multiplication | ||
| 234 : | 16.5 >>> Appendix 1.5: Identity Elements | ||
| 235 : | 16.6 >>> Appendix 1.6: The Inverse of a Matrix | ||
| 236 : | 16.7 >>> Appendix 1.7: The Transpose of a Matrix | ||
| 237 : | 16.8 >>> Appendix 1.8: A Matrix Expression for a System of Simultaneous Linear Equations | ||
| 238 : | 16.9 >>> Appendix 1.9: Inverting a Matrix | ||
| 239 : | 16.10 >>> Appendix 1.10: Solving a System of Simultaneous Linear Equations | ||
| 240 : | 16.11 >>> Appendix 1.11: Other Useful Mathematical Results | ||
| 241 : | jj | 468 | |
| 242 : | jj | 472 | 17 >>> Appendix 2: Common Probability Distributions, Means, Variances, and Moment Generating Functions |
| 243 : | 17.1 >>> Appendix 2.1: Discrete Distributions | ||
| 244 : | 17.2 >>> Appendix 2.2: Continuous Distributions. | ||
| 245 : | |||
| 246 : | 18 >>> Appendix 3: Tables | ||
| 247 : | 18.1 >>> Appendix 3.1: Binomial Probabilities | ||
| 248 : | 18.2 >>> Appendix 3.2: Table of e-x | ||
| 249 : | 18.3 >>> Appendix 3.3: Poisson Probabilities | ||
| 250 : | 18.4 >>> Appendix 3.4: Normal Curve Areas | ||
| 251 : | 18.5 >>> Appendix 3.5: Percentage Points of the t Distributions | ||
| 252 : | 18.6 >>> Appendix 3.6: Percentage Points of the F Distributions | ||
| 253 : | 18.7 >>> Appendix 3.7: Distribution of Function U | ||
| 254 : | 18.8 >>> Appendix 3.8: Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test | ||
| 255 : | 18.9 >>> Appendix 3.9: Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a) | ||
| 256 : | 18.10 >>> Appendix 3.10: Critical Values of Pearman's Rank Correlation Coefficient | ||
| 257 : | 18.11 >>> Appendix 3.11: Random Numbers | ||
| 258 : | |||
| 259 : | jj | 468 | TitleText('Calculus') |
| 260 : | EditionText('5') | ||
| 261 : | AuthorText('Stewart') | ||
| 262 : | |||
| 263 : | 1 >>> Functions and Models | ||
| 264 : | 1.1 >>> Four Ways to Represent a Function | ||
| 265 : | 1.2 >>> Mathematical Models: A Catalog of Essential Functions | ||
| 266 : | 1.3 >>> New Functions from Old Functions | ||
| 267 : | 1.4 >>> Graphing Calculators and Computers | ||
| 268 : | |||
| 269 : | 2 >>> Limits and Rates of Change | ||
| 270 : | 2.1 >>> The Tangent and Velocity Problems | ||
| 271 : | 2.2 >>> The Limit of a Function | ||
| 272 : | 2.3 >>> Calculating Limits Using the Limit Laws | ||
| 273 : | 2.4 >>> The Precise Definition of a Limit | ||
| 274 : | 2.5 >>> Continuity | ||
| 275 : | 2.6 >>> Tangents, Velocities, and Other Rates of Change | ||
| 276 : | |||
| 277 : | 3 >>> Derivatives | ||
| 278 : | 3.1 >>> Derivatives | ||
| 279 : | 3.2 >>> The Derivative as a Function | ||
| 280 : | 3.3 >>> Differentiation Formulas | ||
| 281 : | 3.4 >>> Rates of Change in the Natural and Social Sciences | ||
| 282 : | 3.5 >>> Derivatives of Trigonometric Functions | ||
| 283 : | 3.6 >>> The Chain Rule | ||
| 284 : | 3.7 >>> Implicit Differentiation | ||
| 285 : | 3.8 >>> Higher Derivatives | ||
| 286 : | 3.9 >>> Related Rates | ||
| 287 : | 3.10 >>> Linear Approximations and Differentials | ||
| 288 : | |||
| 289 : | 4 >>> Applications of Differentiation | ||
| 290 : | 4.1 >>> Maximum and Minimum Values | ||
| 291 : | 4.2 >>> The Mean Value Theorem | ||
| 292 : | 4.3 >>> How Derivatives Affect the Shape of a Graph | ||
| 293 : | 4.4 >>> Limits at Infinity; Horizontal Asymptotes | ||
| 294 : | 4.5 >>> Summary of Curve Sketching | ||
| 295 : | 4.6 >>> Graphing with Calculus and Calculators | ||
| 296 : | 4.7 >>> Optimization Problems | ||
| 297 : | 4.8 >>> Applications to Business and Economics | ||
| 298 : | 4.9 >>> Newton's Method | ||
| 299 : | 4.10 >>> Antiderivatives | ||
| 300 : | |||
| 301 : | 5 >>> Integrals | ||
| 302 : | 5.1 >>> Areas and Distances | ||
| 303 : | 5.2 >>> The Definite Integral | ||
| 304 : | 5.3 >>> The Fundamental Theorem of Calculus | ||
| 305 : | 5.4 >>> Indefinite Integrals and the Net Change Theorem | ||
| 306 : | 5.5 >>> The Substitution Rule | ||
| 307 : | |||
| 308 : | 6 >>> Applications of Integration | ||
| 309 : | 6.1 >>> Areas between Curves | ||
| 310 : | 6.2 >>> Volumes | ||
| 311 : | 6.3 >>> Volumes by Cylindrical Shells | ||
| 312 : | 6.4 >>> Work | ||
| 313 : | 6.5 >>> Average Value of a Function | ||
| 314 : | |||
| 315 : | 7 >>> Inverse Functions | ||
| 316 : | 7.1 >>> Inverse Functions | ||
| 317 : | 7.2 >>> Exponential Functions and Their Derivatives | ||
| 318 : | 7.3 >>> Logarithmic Functions | ||
| 319 : | 7.4 >>> Derivatives of Logarithmic Functions | ||
| 320 : | 7.5 >>> Inverse Trigonometric Functions | ||
| 321 : | 7.6 >>> Hyperbolic Functions | ||
| 322 : | 7.7 >>> Indeterminate Forms and L'Hospital's Rule | ||
| 323 : | |||
| 324 : | 8 >>> Techniques of Integration | ||
| 325 : | 8.1 >>> Integration by Parts | ||
| 326 : | 8.2 >>> Trigonometric Integrals | ||
| 327 : | 8.3 >>> Trigonometric Substitution | ||
| 328 : | 8.4 >>> Integration of Rational Functions by Partial Fractions | ||
| 329 : | 8.5 >>> Strategy for Integration | ||
| 330 : | 8.6 >>> Integration Using Tables and Computer Algebra Systems | ||
| 331 : | 8.7 >>> Approximate Integration | ||
| 332 : | 8.8 >>> Improper Integrals | ||
| 333 : | |||
| 334 : | 9 >>> Further Applications of Integration | ||
| 335 : | 9.1 >>> Arc Length | ||
| 336 : | 9.2 >>> Area of a Surface of Revolution | ||
| 337 : | 9.3 >>> Applications to Physics and Engineering | ||
| 338 : | 9.4 >>> Applications to Economics and Biology | ||
| 339 : | 9.5 >>> Probability | ||
| 340 : | |||
| 341 : | 10 >>> Differential Equations | ||
| 342 : | 10.1 >>> Modeling with Differential Equations | ||
| 343 : | 10.2 >>> Direction Fields and Euler's Method | ||
| 344 : | 10.3 >>> Separable Equations | ||
| 345 : | 10.4 >>> Exponential Growth and Decay | ||
| 346 : | 10.5 >>> The Logistic Equation | ||
| 347 : | 10.6 >>> Linear Equations | ||
| 348 : | 10.7 >>> Predator-Prey Systems | ||
| 349 : | |||
| 350 : | 11 >>> Parametric Equations and Polar Coordinates | ||
| 351 : | 11.1 >>> Curves Defined by Parametric Equations | ||
| 352 : | 11.2 >>> Calculus with Parametric Curves | ||
| 353 : | 11.3 >>> Polar Coordinates | ||
| 354 : | 11.4 >>> Areas and Lengths in Polar Coordinates | ||
| 355 : | 11.5 >>> Conic Sections | ||
| 356 : | 11.6 >>> Conic Sections in Polar Coordinates | ||
| 357 : | |||
| 358 : | 12 >>> Infinite Sequences and Series | ||
| 359 : | 12.1 >>> Sequences | ||
| 360 : | 12.2 >>> Series | ||
| 361 : | 12.3 >>> The Integral Test and Estimates of Sums | ||
| 362 : | 12.4 >>> The Comparison Tests | ||
| 363 : | 12.5 >>> Alternating Series | ||
| 364 : | 12.6 >>> Absolute Convergence and the Ratio and Root Tests | ||
| 365 : | 12.7 >>> Strategy for Testing Series | ||
| 366 : | 12.8 >>> Power Series | ||
| 367 : | 12.9 >>> Representations of Functions as Power Series | ||
| 368 : | 12.10 >>> Taylor and Maclaurin Series | ||
| 369 : | 12.11 >>> The Binomial Series | ||
| 370 : | 12.12 >>> Applications of Taylor Polynomials | ||
| 371 : | |||
| 372 : | 13 >>> Vectors and the Geometry of Space | ||
| 373 : | 13.1 >>> Three-Dimensional Coordinate Systems | ||
| 374 : | 13.2 >>> Vectors | ||
| 375 : | 13.3 >>> The Dot Product | ||
| 376 : | 13.4 >>> The Cross Product | ||
| 377 : | 13.5 >>> Equations of Lines and Planes | ||
| 378 : | 13.6 >>> Cylinders and Quadric Surfaces | ||
| 379 : | 13.7 >>> Cylindrical and Spherical Coordinates | ||
| 380 : | |||
| 381 : | 14 >>> Vector Functions | ||
| 382 : | 14.1 >>> Vector Functions and Space Curves | ||
| 383 : | 14.2 >>> Derivatives and Integrals of Vector Functions | ||
| 384 : | 14.3 >>> Arc Length and Curvature | ||
| 385 : | 14.4 >>> Motion in Space: Velocity and Acceleration | ||
| 386 : | |||
| 387 : | 15 >>> Partial Derivatives | ||
| 388 : | 15.1 >>> Functions of Several Variables | ||
| 389 : | 15.2 >>> Limits and Continuity | ||
| 390 : | 15.3 >>> Partial Derivatives | ||
| 391 : | 15.4 >>> Tangent Planes and Linear Approximations | ||
| 392 : | 15.5 >>> The Chain Rule | ||
| 393 : | 15.6 >>> Directional Derivatives and the Gradient Vector | ||
| 394 : | 15.7 >>> Maximum and Minimum Values | ||
| 395 : | 15.8 >>> Lagrange Multipliers | ||
| 396 : | |||
| 397 : | 16 >>> Multiple Integrals | ||
| 398 : | 16.1 >>> Double Integrals over Rectangles | ||
| 399 : | 16.2 >>> Iterated Integrals | ||
| 400 : | 16.3 >>> Double Integrals over General Regions | ||
| 401 : | 16.4 >>> Double Integrals in Polar Coordinates | ||
| 402 : | 16.5 >>> Applications of Double Integrals | ||
| 403 : | 16.6 >>> Surface Area | ||
| 404 : | 16.7 >>> Triple Integrals | ||
| 405 : | 16.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates | ||
| 406 : | 16.9 >>> Change of Variables in Multiple Integrals | ||
| 407 : | |||
| 408 : | 17 >>> Vector Calculus | ||
| 409 : | 17.1 >>> Vector Fields | ||
| 410 : | 17.2 >>> Line Integrals | ||
| 411 : | 17.3 >>> The Fundamental Theorem for Line Integrals | ||
| 412 : | 17.4 >>> Green's Theorem | ||
| 413 : | 17.5 >>> Curl and Divergence | ||
| 414 : | 17.6 >>> Parametric Surfaces and Their Areas | ||
| 415 : | 17.7 >>> Surface Integrals | ||
| 416 : | 17.8 >>> Stokes' Theorem | ||
| 417 : | 17.9 >>> The Divergence Theorem | ||
| 418 : | 17.10 >>> Summary | ||
| 419 : | |||
| 420 : | 18 >>> Second-Order Differential Equations | ||
| 421 : | 18.1 >>> Second-Order Linear Equations | ||
| 422 : | 18.2 >>> Nonhomogeneous Linear Equations | ||
| 423 : | 18.3 >>> Applications of Second- Order Differential Equations | ||
| 424 : | 18.4 >>> Series Solutions | ||
| 425 : | |||
| 426 : | jj | 509 | 25 >>> Appendix H: Complex Numbers |
| 427 : | |||
| 428 : | jj | 468 | TitleText('College Algebra') |
| 429 : | EditionText('4') | ||
| 430 : | AuthorText('Stewart, Redlin, Watson') | ||
| 431 : | |||
| 432 : | jj | 472 | 0 >>> Prerequisites |
| 433 : | 0.1 >>> Modeling the Real World | ||
| 434 : | 0.2 >>> Real Numbers | ||
| 435 : | 0.3 >>> Integer Exponents | ||
| 436 : | 0.4 >>> Rational Exponents and Radicals | ||
| 437 : | 0.5 >>> Algebraic Expressions | ||
| 438 : | 0.6 >>> Factoring | ||
| 439 : | 0.7 >>> Rational Expressions | ||
| 440 : | |||
| 441 : | jj | 468 | 1 >>> Equations and Inequalities |
| 442 : | 1.1 >>> Basic Equations | ||
| 443 : | 1.2 >>> Modeling with Equations | ||
| 444 : | 1.3 >>> Quadratic Equations | ||
| 445 : | 1.4 >>> Complex Numbers | ||
| 446 : | 1.5 >>> Other Types of Equations | ||
| 447 : | 1.6 >>> Inequalities | ||
| 448 : | 1.7 >>> Absolute Value Equations and Inequalities | ||
| 449 : | jj | 472 | |
| 450 : | jj | 468 | 2 >>> Coordinates and Graphs |
| 451 : | 2.1 >>> The Coordinate Plane | ||
| 452 : | 2.2 >>> Graphs of Equations in Two Variables | ||
| 453 : | 2.3 >>> Graphing Calculators; Solving Equations and Inequalitie Graphically | ||
| 454 : | 2.4 >>> Lines | ||
| 455 : | 2.5 >>> Modeling: Variation | ||
| 456 : | jj | 472 | |
| 457 : | jj | 468 | 3 >>> Functions |
| 458 : | 3.1 >>> What Is a Function? | ||
| 459 : | 3.2 >>> Graphs of Functions | ||
| 460 : | 3.3 >>> Increasing and Decreasing Functions; Average Rate of Change | ||
| 461 : | 3.4 >>> Transformations of Functions | ||
| 462 : | 3.5 >>> Quadratic Functions; Maxima and Minima | ||
| 463 : | 3.6 >>> Combining Functions | ||
| 464 : | 3.7 >>> One-to-One Functions and Their Inverses | ||
| 465 : | jj | 472 | |
| 466 : | jj | 468 | 4 >>> Polynomial and Rational Functions |
| 467 : | 4.1 >>> Polynomial Functions and Their Graphs | ||
| 468 : | 4.2 >>> Dividing Polynomials | ||
| 469 : | 4.3 >>> Real Zeros of Polynomials | ||
| 470 : | 4.4 >>> Complex Zeros and the Fundamental Theorem of Algebra | ||
| 471 : | 4.5 >>> Rational Functions | ||
| 472 : | 5 >>> Exponential and Logarithmic Functions | ||
| 473 : | 5.1 >>> Exponential Functions | ||
| 474 : | 5.2 >>> Logarithmic Functions | ||
| 475 : | 5.3 >>> Laws of Logarithms | ||
| 476 : | 5.4 >>> Exponential and Logarithmic Equations | ||
| 477 : | 5.5 >>> Modeling with Exponential and Logarithmic Functions | ||
| 478 : | jj | 472 | |
| 479 : | jj | 468 | 6 >>> Systems of Equations and Inequalities |
| 480 : | 6.1 >>> Systems of Equations | ||
| 481 : | 6.2 >>> Systems of Linear Equations in Two Variables | ||
| 482 : | 6.3 >>> Systems of Linear Equations in Several Variables | ||
| 483 : | 6.4 >>> Systems of Inequalities | ||
| 484 : | 6.5 >>> Partial Fractions | ||
| 485 : | jj | 472 | |
| 486 : | jj | 468 | 7 >>> Matrices and Determinants |
| 487 : | 7.1 >>> Matrices and Systems of Linear Equations | ||
| 488 : | 7.2 >>> The Algebra of Matrices | ||
| 489 : | 7.3 >>> Inverses of Matrices and Matrix Equations | ||
| 490 : | 7.4 >>> Determinants and Cramer's Rule | ||
| 491 : | jj | 472 | |
| 492 : | jj | 468 | 8 >>> Conic Sections |
| 493 : | 8.1 >>> Parabolas | ||
| 494 : | 8.2 >>> Ellipses | ||
| 495 : | 8.3 >>> Hyperbolas | ||
| 496 : | 8.4 >>> Shifted Conics | ||
| 497 : | jj | 472 | |
| 498 : | jj | 468 | 9 >>> Sequences and Series |
| 499 : | 9.1 >>> Sequences and Summation Notation | ||
| 500 : | 9.2 >>> Arithmetic Sequences | ||
| 501 : | 9.3 >>> Geometric Sequences | ||
| 502 : | 9.4 >>> Mathematics of Finance | ||
| 503 : | 9.5 >>> Mathematical Induction | ||
| 504 : | 9.6 >>> The Binomial Theorem | ||
| 505 : | jj | 472 | |
| 506 : | jj | 468 | 10 >>> Counting and Probability |
| 507 : | 10.1 >>> Counting Principles | ||
| 508 : | 10.2 >>> Permutations and Combinations | ||
| 509 : | 10.3 >>> Probability | ||
| 510 : | 10.4 >>> Binomial Probability | ||
| 511 : | 10.5 >>> Expected Value | ||
| 512 : | |||
| 513 : | TitleText('Statistics for Management and Economics') | ||
| 514 : | EditionText('7') | ||
| 515 : | AuthorText('Keller') | ||
| 516 : | |||
| 517 : | 1 >>> What is Statistics? | ||
| 518 : | 1.1 >>> Key Statistical Concepts | ||
| 519 : | 1.2 >>> Statistical Applications in Business | ||
| 520 : | 1.3 >>> Statistics and the Computer | ||
| 521 : | 1.4 >>> World Wide Web and Learning Center | ||
| 522 : | 1.A >>> Instructions for the CD-ROM | ||
| 523 : | 1.B >>> Introduction to Microsoft Excel | ||
| 524 : | 1.C >>> Introduction to Minitab | ||
| 525 : | 2 >>> Graphical and Tabular Descriptive Techniques | ||
| 526 : | 2.1 >>> Types of Data and Information | ||
| 527 : | 2.2 >>> Graphical and Tabular Techniques for Nominal Data | ||
| 528 : | 2.3 >>> Graphical Techniques for Interval Data | ||
| 529 : | 2.4 >>> Describing the relationship Between Two Variables | ||
| 530 : | 2.5 >>> Describing Time-Series Data | ||
| 531 : | 3 >>> Art and Science of Graphical Presentations | ||
| 532 : | 3.1 >>> Graphical Excellence | ||
| 533 : | 3.2 >>> Graphical Deception | ||
| 534 : | 3.3 >>> Presenting Statistics: Written Reports and Oral Presentations | ||
| 535 : | 4 >>> Numerical Descriptive Techniques | ||
| 536 : | 4.1 >>> Measures of Central Location | ||
| 537 : | 4.2 >>> Measures of Variability | ||
| 538 : | 4.3 >>> Measures of Relative Standing and Box Plots | ||
| 539 : | 4.4 >>> Measures of Linear Relationship | ||
| 540 : | 4.5 >>> Applications in Professional Sports: Baseball | ||
| 541 : | 4.6 >>> Comparing Graphical and Numerical Techniques | ||
| 542 : | 4.7 >>> General Guidelines for Exploring Data | ||
| 543 : | 5 >>> Data Collection and Sampling | ||
| 544 : | 5.1 >>> Methods of Collecting Data | ||
| 545 : | 5.2 >>> Sampling | ||
| 546 : | 5.3 >>> Sampling Plans | ||
| 547 : | 5.4 >>> Sampling and Nonsampling Errors | ||
| 548 : | 6 >>> Probability | ||
| 549 : | 6.1 >>> Assigning Probability to Events | ||
| 550 : | 6.2 >>> Joint, Marginal, and Conditional Probability | ||
| 551 : | 6.3 >>> Probability Rules and Trees | ||
| 552 : | 6.4 >>> Bayes' Law | ||
| 553 : | 6.5 >>> Identifying the Correct Method | ||
| 554 : | 7 >>> Random Variables and Discrete Probability Distributions | ||
| 555 : | 7.1 >>> Random Variables and Probability Distributions | ||
| 556 : | 7.2 >>> Bivariate Distributions | ||
| 557 : | 7.3 >>> Applications in Finance: Portfolio Diversification and Asset Allocation | ||
| 558 : | 7.4 >>> Binomial Distribution | ||
| 559 : | 7.5 >>> Poisson Distribution | ||
| 560 : | 8 >>> Continuous Probability Distributions | ||
| 561 : | 8.1 >>> Probability Density Functions | ||
| 562 : | 8.2 >>> Normal Distribution | ||
| 563 : | 8.3 >>> Exponential Distribution | ||
| 564 : | 8.4 >>> Other Continuous Distributions | ||
| 565 : | 9 >>> Sampling Distributions | ||
| 566 : | 9.1 >>> Sampling Distribution of the Mean | ||
| 567 : | 9.2 >>> Sampling Distribution of a Proportion | ||
| 568 : | 9.3 >>> Sampling Distribution of the Difference Between Two Means | ||
| 569 : | 9.4 >>> From Here to Inference | ||
| 570 : | 10 >>> Introduction to Estimation | ||
| 571 : | 10.1 >>> Concepts of Estimation | ||
| 572 : | 10.2 >>> Estimating the Population Mean When the Population Standard Deviation is Known | ||
| 573 : | 10.3 >>> Selecting the Sample Size | ||
| 574 : | 11 >>> Introduction to Hypothesis Testing | ||
| 575 : | 11.1 >>> Concepts of Hypothesis Testing | ||
| 576 : | 11.2 >>> Testing the Population Mean When the Population Standard Deviation is Known | ||
| 577 : | 11.3 >>> Calculating the Probability of a Type II Error | ||
| 578 : | 11.4 >>> The Road Ahead | ||
| 579 : | 12 >>> Inference About a Population | ||
| 580 : | 12.1 >>> Inference About a Population Mean When the Standard Deviation is Unknown | ||
| 581 : | 12.2 >>> Inference about a Population Variance | ||
| 582 : | 12.3 >>> inference about a Population Proportion | ||
| 583 : | 12.4 >>> Applications in Marketing: Market Segmentation | ||
| 584 : | 12.5 >>> Applications in Marketing: Auditing | ||
| 585 : | 13 >>> Inference About Comparing Two Populations | ||
| 586 : | 13.1 >>> Inference about the Difference Between Two Means: Independent Samples | ||
| 587 : | 13.2 >>> Observational and Experimental Data | ||
| 588 : | 13.3 >>> Inference about the Difference Between Two Means: Matched Pairs Experiment | ||
| 589 : | 13.4 >>> Inference about the Ratio of Two Variances | ||
| 590 : | 13.5 >>> Inference about the Difference Between Two Population Proportions | ||
| 591 : | 13.A >>> Excel Instructions for Stacked and Unstacked Data | ||
| 592 : | 13.B >>> Minitab Instructions for Stacked and Unstacked Data | ||
| 593 : | 14 >>> Statistical Inference: Review of Chapters 12 and 13 | ||
| 594 : | 14.1 >>> Guide to Identifying the Correct Technique: Chapters 12 and 13 | ||
| 595 : | 15 >>> Analysis of Variance | ||
| 596 : | 15.1 >>> One-Way Analysis of Variance | ||
| 597 : | 15.2 >>> Analysis of Variance Experimental Designs | ||
| 598 : | 15.3 >>> Randomized Blocks (Two-Way) Analysis of Variance | ||
| 599 : | 15.4 >>> Two-Factor Analysis of Variance | ||
| 600 : | 15.5 >>> Appplications in Operations Management: Finding and Reducing Variation | ||
| 601 : | 15.6 >>> Multiple Comparisons | ||
| 602 : | 16 >>> Chi-Squared Tests | ||
| 603 : | 16.1 >>> Chi-Squared Goodness-of-Fit Test | ||
| 604 : | 16.2 >>> Chi-Squared Test of a Contingency Table | ||
| 605 : | 16.3 >>> Summary of Tests on Nominal Data | ||
| 606 : | 16.4 >>> Chi-Squared Tests of Normality | ||
| 607 : | 17 >>> Simple Linear Regression and Correlation | ||
| 608 : | 17.1 >>> Model | ||
| 609 : | 17.2 >>> Estimating the Coefficients | ||
| 610 : | 17.3 >>> Error Variable: Required Conditions | ||
| 611 : | 17.4 >>> Assessing the Model | ||
| 612 : | 17.5 >>> Applications in Finance: Market Model | ||
| 613 : | 17.6 >>> Using the Regression Equation | ||
| 614 : | 17.7 >>> Regression Diagnostics-I | ||
| 615 : | 18 >>> Multiple Regression | ||
| 616 : | 18.1 >>> Model and Required Conditions | ||
| 617 : | 18.2 >>> Estimating the Coefficients and Assessing the Model | ||
| 618 : | 18.3 >>> Regression Diagnostics-II | ||
| 619 : | 18.4 >>> Regression Diagnostics-III (Time Series) | ||
| 620 : | |||
| 621 : | jj | 472 | 19 >>> Appendix A: Excel Troubleshooting and Detailed Instructions |
| 622 : | 20 >>> Appendix B: Minitab Detailed Instructions | ||
| 623 : | 21 >>> Appendix C: Approximating Means and Variances from Grouped Data | ||
| 624 : | 22 >>> Appendix D: Descriptive Techniques Review Exercises | ||
| 625 : | 23 >>> Appendix E: Couting Formulas | ||
| 626 : | 24 >>> Appendix F: Hypergeometric Distribution | ||
| 627 : | 25 >>> Appendix G: Continuous Probability Distributions: Calculus Approach | ||
| 628 : | 26 >>> Appendix H: Using the Laws of Expected Value and Variance to Derive the Parameters of Sampling Distributions | ||
| 629 : | 27 >>> Appendix I: Excel Spreadsheets for Techniques in Chapters 10-13 | ||
| 630 : | 28 >>> Appendix K: Converting Excel's Probabilities to p-Values | ||
| 631 : | 29 >>> Appendix J: Excel and Minitab Instructions for Missing Data and for Recoding Data | ||
| 632 : | 30 >>> Appendix L: Probability of a Type II Error When Testing a Proportion | ||
| 633 : | 31 >>> Appendix M: Approximating p-Values from the Student t Table | ||
| 634 : | 32 >>> Appendix N: Probability of a Type II Error When Testing the Difference Between Two Means | ||
| 635 : | 33 >>> Appendix O: Probability of a Type II Erorr When Testing the Difference Between Two Proportions | ||
| 636 : | 34 >>> Appendix P: Bartlett's Test | ||
| 637 : | 35 >>> Appendix Q: Minitab Instructions for the Chi-Squared Goodness-of-Fit Test and the Test for Normality | ||
| 638 : | 36 >>> Appendix R: The Rule of Five | ||
| 639 : | 37 >>> Appendix S: Deriving the Normal Equations | ||
| 640 : | 38 >>> Appendix T: Szroeter's Test for Heteroscedasticity | ||
| 641 : | 39 >>> Appendix U: Transformations | ||
| 642 : | |||
| 643 : | jj | 468 | TitleText('Elementary Linear Algebra') |
| 644 : | |||
| 645 : | EditionText('5') | ||
| 646 : | |||
| 647 : | AuthorText('Larson, Edwards, Falvo') | ||
| 648 : | |||
| 649 : | |||
| 650 : | 1 >>> Systems of Linear Equations | ||
| 651 : | 1.1 >>> Introduction to Systems of Linear Equations | ||
| 652 : | 1.2 >>> Gaussian Elimination and Gauss-Jordan Elimination | ||
| 653 : | 1.3 >>> Applications of Systems of Linear Equations | ||
| 654 : | |||
| 655 : | 2 >>> Matrices | ||
| 656 : | 2.1 >>> Operations with Matrices | ||
| 657 : | 2.2 >>> Properties of Matrix Operations | ||
| 658 : | 2.3 >>> The Inverse of a Matrix | ||
| 659 : | 2.4 >>> Elementary Matrices | ||
| 660 : | 2.5 >>> Applications of Matrix Operations | ||
| 661 : | |||
| 662 : | 3 >>> Determinants | ||
| 663 : | 3.1 >>> The Determinant of a Matrix | ||
| 664 : | 3.2 >>> Evaluation of a Determinant Using Elementary Operations | ||
| 665 : | 3.3 >>> Properties of Determinants | ||
| 666 : | 3.4 >>> Introduction to Eigenvalues | ||
| 667 : | 3.5 >>> Applications of Determinants | ||
| 668 : | |||
| 669 : | 4 >>> Vector Spaces | ||
| 670 : | |||
| 671 : | 4.1 >>> Vectors in Rn | ||
| 672 : | 4.2 >>> Vector Spaces | ||
| 673 : | 4.3 >>> Subspaces of Vector Spaces | ||
| 674 : | 4.4 >>> Spanning Sets and Linear Independence | ||
| 675 : | 4.5 >>> Basis and Dimension | ||
| 676 : | 4.6 >>> Rank of a Matrix and Systems of Linear Equations | ||
| 677 : | 4.7 >>> Coordinates and Change of Basis | ||
| 678 : | 4.8 >>> Applications of Vector Spaces | ||
| 679 : | |||
| 680 : | 5 >>> Inner Product Spaces | ||
| 681 : | 5.1 >>> Length and Dot Product in Rn | ||
| 682 : | 5.2 >>> Inner Product Spaces | ||
| 683 : | 5.3 >>> Orthonormal Bases: Gram-Schmidt Process | ||
| 684 : | 5.4 >>> Mathematical Models and Least Squares Analysis | ||
| 685 : | 5.5 >>> Applications of Inner Product Spaces | ||
| 686 : | |||
| 687 : | 6 >>> Linear Transformations | ||
| 688 : | 6.1 >>> Introduction to Linear Transformations | ||
| 689 : | 6.2 >>> The Kernel and Range of a Linear Transformation | ||
| 690 : | 6.3 >>> Matrices for Linear Transformations | ||
| 691 : | 6.4 >>> Transition Matrices and Similarity | ||
| 692 : | 6.5 >>> Applications of Linear Transformations | ||
| 693 : | |||
| 694 : | 7 >>> Eigenvalues and Eigenvectors | ||
| 695 : | 7.1 >>> Eigenvalues and Eigenvectors | ||
| 696 : | 7.2 >>> Diagonalization | ||
| 697 : | 7.3 >>> Symmetric Matrices and Orthogonal Diagonalization | ||
| 698 : | 7.4 >>> Applications of Eigenvalues and Eigenvectors | ||
| 699 : | |||
| 700 : | 8 >>> Complex Vector Spaces | ||
| 701 : | 8.1 >>> Complex Numbers | ||
| 702 : | 8.2 >>> Conjugates and Division of Complex Numbers | ||
| 703 : | 8.3 >>> Polar Form and DeMoivre's Theorem | ||
| 704 : | 8.4 >>> Complex Vector Spaces and Inner Products | ||
| 705 : | 8.5 >>> Unitary and Hermitian Matrices | ||
| 706 : | |||
| 707 : | 9 >>> Linear Programming | ||
| 708 : | 9.1 >>> Systems of Linear Inequalities | ||
| 709 : | 9.2 >>> Linear Programming Involving Two Variables | ||
| 710 : | 9.3 >>> The Simplex Method: Maximization | ||
| 711 : | 9.4 >>> The Simplex Method: Minimization | ||
| 712 : | 9.5 >>> The Simplex Method: Mixed Constraints | ||
| 713 : | |||
| 714 : | 10 >>> Numerical Methods | ||
| 715 : | |||
| 716 : | 10.1 >>> Gaussian Elimination with Partial Pivoting | ||
| 717 : | 10.2 >>> Interative Methods for Solving Linear Systems | ||
| 718 : | 10.3 >>> Power Method for Approximating Eigenvalues | ||
| 719 : | 10.4 >>> Applications of Numerical Methods | ||
| 720 : | |||
| 721 : | jj | 472 | 11 >>> Appendix A: Mathematical Induction and Other Forms of Proofs |
| 722 : | jj | 468 | |
| 723 : | jj | 472 | 12 >>> Appendix B: Computer Algebra Systems and Graphing Calculators |
| 724 : | jj | 468 | |
| 725 : | TitleText('Basic Multivariable Calculus') | ||
| 726 : | EditionText('3') | ||
| 727 : | AuthorText('Marsden, Tromba, Weinstein') | ||
| 728 : | |||
| 729 : | 1 >>> Algebra and Geometry of Euclidean Space | ||
| 730 : | 1.1 >>> Vectors in the Plane and Space | ||
| 731 : | 1.2 >>> The Inner Product and Distance | ||
| 732 : | 1.3 >>> 2 x 2 and 3 x 3 Matrices and Determinants | ||
| 733 : | 1.4 >>> The Cross Product and Planes | ||
| 734 : | 1.5 >>> n-Dimensional Euclidean Space | ||
| 735 : | 1.6 >>> Curves in the Plane and in Space | ||
| 736 : | jj | 472 | |
| 737 : | jj | 468 | 2 >>> Differentiation |
| 738 : | 2.1 >>> Graphs and Level Surfaces | ||
| 739 : | 2.2 >>> Partial Derivatives and Continuity | ||
| 740 : | 2.3 >>> Differentiability, the Derivative Matrix, and Tangent Planes | ||
| 741 : | 2.4 >>> The Chain Rule | ||
| 742 : | 2.5 >>> Gradients and Directional Derivatives | ||
| 743 : | 2.6 >>> Implicit Differentiation | ||
| 744 : | jj | 472 | |
| 745 : | jj | 468 | 3 >>> Higher Derivatives and Extrema |
| 746 : | 3.1 >>> Higher Order Partial Derivatives | ||
| 747 : | 3.2 >>> Taylor's Theorem | ||
| 748 : | 3.3 >>> Maxima and Minima | ||
| 749 : | 3.4 >>> Second Derivative Test | ||
| 750 : | 3.5 >>> Constrained Extrema and Lagrange Multipliers | ||
| 751 : | jj | 472 | |
| 752 : | jj | 468 | 4 >>> Vector-Valued Functions |
| 753 : | 4.1 >>> Acceleration | ||
| 754 : | 4.2 >>> Arc Length | ||
| 755 : | 4.3 >>> Vector Fields | ||
| 756 : | 4.4 >>> Divergence and Curl | ||
| 757 : | jj | 472 | |
| 758 : | jj | 468 | 5 >>> Multiple Integrals |
| 759 : | 5.1 >>> Volume and Cavalieri's Principle | ||
| 760 : | 5.2 >>> The Double Integral Over a Rectangle | ||
| 761 : | 5.3 >>> The Double Integral Over Regions | ||
| 762 : | 5.4 >>> Triple Integrals | ||
| 763 : | 5.5 >>> Change of Variables, Cylindrical and Spherical Coordinates | ||
| 764 : | 5.6 >>> Applications of Multiple Integrals | ||
| 765 : | jj | 472 | |
| 766 : | jj | 468 | 6 >>> Integrals Over Curves and Surfaces |
| 767 : | 6.1 >>> Line Integrals | ||
| 768 : | 6.2 >>> Parametrized Surfaces | ||
| 769 : | 6.3 >>> Area of a Surface | ||
| 770 : | 6.4 >>> Surface Integrals | ||
| 771 : | jj | 472 | |
| 772 : | jj | 468 | 7 >>> The Integral Theorems of Vector Analysis |
| 773 : | 7.1 >>> Green's Theorem | ||
| 774 : | 7.2 >>> Stokes' Theorem | ||
| 775 : | 7.3 >>> Gauss' Theorem | ||
| 776 : | 7.4 >>> Path Independence and the Fundamental Theorems of Calculus | ||
| 777 : | |||
| 778 : | TitleText('Precalculus') | ||
| 779 : | EditionText('5') | ||
| 780 : | AuthorText('Stewart, Redlin, Watson') | ||
| 781 : | |||
| 782 : | 1 >>> Fundamentals | ||
| 783 : | 1.1 >>> Real Numbers | ||
| 784 : | 1.2 >>> Exponents and Radicals | ||
| 785 : | 1.3 >>> Algebraic Expressions | ||
| 786 : | 1.4 >>> Rational Expression | ||
| 787 : | 1.5 >>> Equations | ||
| 788 : | 1.6 >>> Modeling with Equations | ||
| 789 : | 1.7 >>> Inequalities | ||
| 790 : | 1.8 >>> Coordinate Geometry | ||
| 791 : | 1.9 >>> Graphing Calculators; Solving Equations and Inequalities Graphically | ||
| 792 : | 1.10 >>> Lines | ||
| 793 : | 1.11 >>> Modeling Variation | ||
| 794 : | jj | 472 | |
| 795 : | jj | 468 | 2 >>> Functions |
| 796 : | 2.1 >>> What is a Function? | ||
| 797 : | 2.2 >>> Graphs of Functions | ||
| 798 : | 2.3 >>> Increasing and Decreasing Functions; Average Rate of Change | ||
| 799 : | 2.4 >>> Transformations of Functions | ||
| 800 : | 2.5 >>> Quadratic Functions; Maxima and Minima | ||
| 801 : | 2.6 >>> Modeling with Functions | ||
| 802 : | 2.7 >>> Combining Functions | ||
| 803 : | 2.8 >>> One-to-One Functions and Their Inverses | ||
| 804 : | jj | 472 | |
| 805 : | jj | 468 | 3 >>> Polynomial and Rational Functions |
| 806 : | 3.1 >>> Polynomial Functions and Their Graphs | ||
| 807 : | 3.2 >>> Dividing Polynomials | ||
| 808 : | 3.3 >>> Real Zeros of Polynomials | ||
| 809 : | 3.4 >>> Complex Numbers | ||
| 810 : | 3.5 >>> Complex Zeros and the Fundamental Theorem of Algebra | ||
| 811 : | 3.6 >>> Rational Functions | ||
| 812 : | jj | 472 | |
| 813 : | jj | 468 | 4 >>> Exponential and Logarithmic Functions |
| 814 : | 4.1 >>> Exponential Functions | ||
| 815 : | 4.2 >>> Logarithmic Functions | ||
| 816 : | 4.3 >>> Laws of Logarithms | ||
| 817 : | 4.4 >>> Exponential and Logarithmic Equations | ||
| 818 : | 4.5 >>> Modeling with Exponential and Logarithmic Functions | ||
| 819 : | jj | 472 | |
| 820 : | jj | 468 | 5 >>> Trigonometric Functions of Real Numbers |
| 821 : | 5.1 >>> The Unit Circle | ||
| 822 : | 5.2 >>> Trigonometric Functions of Real Numbers | ||
| 823 : | 5.3 >>> Trigonometric Graphs | ||
| 824 : | 5.4 >>> More Trigonometric Graphs | ||
| 825 : | 5.5 >>> Modeling Harmonic Motion | ||
| 826 : | jj | 472 | |
| 827 : | jj | 468 | 6 >>> Trigonometric Functions of Angles |
| 828 : | 6.1 >>> Angle Measures | ||
| 829 : | 6.2 >>> Trigonometry of Right Triangles | ||
| 830 : | 6.3 >>> Trigonometric Functions of Angles | ||
| 831 : | 6.4 >>> The Law of Sines | ||
| 832 : | 6.5 >>> The Law of Cosines | ||
| 833 : | jj | 472 | |
| 834 : | jj | 468 | 7 >>> Analytic Trigonometry |
| 835 : | 7.1 >>> Trigonometric Identities | ||
| 836 : | 7.2 >>> Addition and Subtraction Formulas | ||
| 837 : | 7.3 >>> Double-Angle, Half-Angle, and Sum-Product Formulas | ||
| 838 : | 7.4 >>> Inverse Trigonometric Functions | ||
| 839 : | 7.5 >>> Trigonometric Equations | ||
| 840 : | jj | 472 | |
| 841 : | jj | 468 | 8 >>> Polar Coordinates and Vectors |
| 842 : | 8.1 >>> Polar Coordinates | ||
| 843 : | 8.2 >>> Graphs of Polar Equations | ||
| 844 : | 8.3 >>> Polar Form of Complex Numbers; DeMoivre's Theorem | ||
| 845 : | 8.4 >>> Vectors | ||
| 846 : | 8.5 >>> The Dot Product | ||
| 847 : | jj | 472 | |
| 848 : | jj | 468 | 9 >>> Systems of Equations and Inequalities |
| 849 : | 9.1 >>> Systems of Equations | ||
| 850 : | 9.2 >>> Systems of Linear Equations in Two Variables | ||
| 851 : | 9.3 >>> Systems of Linear Equations in Several Variables | ||
| 852 : | 9.4 >>> Systems of Linear Equations: Matrices | ||
| 853 : | 9.5 >>> The Algebra of Matrices | ||
| 854 : | 9.6 >>> Inverses of Matrices and Matrix Equations | ||
| 855 : | 9.7 >>> Determinants and Cramer's Rule | ||
| 856 : | 9.8 >>> Partial Fractions | ||
| 857 : | 9.9 >>> Systems of Inequalities | ||
| 858 : | jj | 472 | |
| 859 : | jj | 468 | 10 >>> Analytic Geometry |
| 860 : | 10.1 >>> Parabolas | ||
| 861 : | 10.2 >>> Ellipses | ||
| 862 : | 10.3 >>> Hyperbolas | ||
| 863 : | 10.4 >>> Shifted Conics | ||
| 864 : | 10.5 >>> Rotation of Axes | ||
| 865 : | 10.6 >>> Polar Equations of Conics | ||
| 866 : | 10.7 >>> Plane Curves and Parametric Equations | ||
| 867 : | jj | 472 | |
| 868 : | jj | 468 | 11 >>> Sequences and Series |
| 869 : | 11.1 >>> Sequences and Summation Notation | ||
| 870 : | 11.2 >>> Arithmetic Sequences | ||
| 871 : | 11.3 >>> Geometric Sequences | ||
| 872 : | 11.4 >>> Mathematics of Finance | ||
| 873 : | 11.5 >>> Mathematical Induction | ||
| 874 : | 11.6 >>> The Binomial Theorem | ||
| 875 : | jj | 472 | |
| 876 : | jj | 468 | 12 >>> Limits: A Preview of Calculus |
| 877 : | 12.1 >>> Finding Limits Numerically and Graphically | ||
| 878 : | 12.2 >>> Finding Limits Algebraically | ||
| 879 : | 12.3 >>> Tangent Lines and Derivatives | ||
| 880 : | 12.4 >>> Limits at Infinity: Limits of Sequences | ||
| 881 : | 12.5 >>> Areas | ||
| 882 : | |||
| 883 : | TitleText('Discrete Mathematics') | ||
| 884 : | EditionText('4') | ||
| 885 : | AuthorText('Rosen') | ||
| 886 : | |||
| 887 : | |||
| 888 : | 1 >>> The Foundations: Logic, Sets, and Functions | ||
| 889 : | 1.1 >>> Logic | ||
| 890 : | 1.2 >>> Propositional Equivalences | ||
| 891 : | 1.3 >>> Predicates and Quantifiers | ||
| 892 : | 1.4 >>> Sets | ||
| 893 : | 1.5 >>> Set Operations | ||
| 894 : | 1.6 >>> Functions | ||
| 895 : | 1.7 >>> Sequences and Summations | ||
| 896 : | 1.8 >>> The Growth Functions | ||
| 897 : | |||
| 898 : | 2 >>> The Fundamentals: Algorithms, the Integers, and Matrices | ||
| 899 : | 2.1 >>> Algorithms | ||
| 900 : | 2.2 >>> Complexity of Algorithms | ||
| 901 : | 2.3 >>> The Integers and Division | ||
| 902 : | 2.4 >>> Integers and Algorithms | ||
| 903 : | 2.5 >>> Applications of Number Theory | ||
| 904 : | 2.6 >>> Matrices | ||
| 905 : | |||
| 906 : | 3 >>> Mathematical Reasoning | ||
| 907 : | |||
| 908 : | 3.1 >>> Methods of Proof | ||
| 909 : | 3.2 >>> Mathematical Induction | ||
| 910 : | 3.3 >>> Recursive Definitions | ||
| 911 : | 3.4 >>> Recursive Algorithms | ||
| 912 : | 3.5 >>> Program Correctness | ||
| 913 : | |||
| 914 : | 4 >>> Counting | ||
| 915 : | 4.1 >>> The Basics of Counting | ||
| 916 : | 4.2 >>> The Pigeonhole Principle | ||
| 917 : | 4.3 >>> Permutations and Combinations | ||
| 918 : | 4.4 >>> Discrete Probability | ||
| 919 : | 4.5 >>> Probability Theory | ||
| 920 : | 4.6 >>> Generalized Permutations and Combinations | ||
| 921 : | 4.7 >>> Generating Permutations and Combinations | ||
| 922 : | |||
| 923 : | 5 >>> Advanced Counting Techniques | ||
| 924 : | 5.1 >>> Recurrence Relations | ||
| 925 : | 5.2 >>> Solving Recurrence Relations | ||
| 926 : | 5.3 >>> Divide-and-Conquer Relations | ||
| 927 : | 5.4 >>> Generating Functions | ||
| 928 : | 5.5 >>> Inclusion-Exclusion | ||
| 929 : | 5.6 >>> Applications of Inclusion-Exclusion | ||
| 930 : | |||
| 931 : | 6 >>> Relations | ||
| 932 : | 6.1 >>> Relations and Their Properties | ||
| 933 : | 6.2 >>> n-ary Relations and Their Applications | ||
| 934 : | 6.3 >>> Representing Relations | ||
| 935 : | 6.4 >>> Closures of Relations | ||
| 936 : | 6.5 >>> Equivalence Relations | ||
| 937 : | 6.6 >>> Partial Orderings | ||
| 938 : | |||
| 939 : | 7 >>> Graphs | ||
| 940 : | 7.1 >>> Introduction to Graphs | ||
| 941 : | 7.2 >>> Graph Terminology | ||
| 942 : | 7.3 >>> Representing Graphs and Graph Isomorphism | ||
| 943 : | 7.4 >>> Connectivity | ||
| 944 : | 7.5 >>> Euler and Hamilton Paths | ||
| 945 : | 7.6 >>> Shortest Path Problems | ||
| 946 : | 7.7 >>> Planar Graphs | ||
| 947 : | 7.8 >>> Graph Coloring | ||
| 948 : | |||
| 949 : | 8 >>> Trees | ||
| 950 : | 8.1 >>> Introduction to Trees | ||
| 951 : | 8.2 >>> Applications of Trees | ||
| 952 : | 8.3 >>> Tree Traversal | ||
| 953 : | 8.4 >>> Trees and Sorting | ||
| 954 : | 8.5 >>> Spanning Trees | ||
| 955 : | 8.6 >>> Minimum Spanning Trees | ||
| 956 : | |||
| 957 : | 9 >>> Boolean Algebra | ||
| 958 : | 9.1 >>> Boolean Functions | ||
| 959 : | 9.2 >>> Representing Boolean Functions | ||
| 960 : | 9.3 >>> Logic Gates | ||
| 961 : | 9.4 >>> Minimization of Circuits | ||
| 962 : | |||
| 963 : | 10 >>> Modeling Computation | ||
| 964 : | 10.1 >>> Languages and Grammars | ||
| 965 : | 10.2 >>> Finite-State Machines with Output | ||
| 966 : | 10.3 >>> Finite-State Machines with No Output | ||
| 967 : | 10.4 >>> Language Recognition | ||
| 968 : | 10.5 >>> Turing Machines | ||
| 969 : | |||
| 970 : | jj | 472 | 11 >>> Appendix: Exponential and Logarithmic Functions |
| 971 : | 12 >>> Appendix: Pseudocode | ||
| 972 : | jj | 468 | |
| 973 : | TitleText('Complex Analysis') | ||
| 974 : | EditionText('3') | ||
| 975 : | AuthorText('Saff, Snider') | ||
| 976 : | |||
| 977 : | 1 >>> Complex Numbers | ||
| 978 : | 1.1 >>> The Algebra of Complex Numbers | ||
| 979 : | 1.2 >>> Point Representation of Complex Numbers | ||
| 980 : | 1.3 >>> Vectors and Polar Forms | ||
| 981 : | 1.4 >>> The Complex Exponential | ||
| 982 : | 1.5 >>> Powers and Roots | ||
| 983 : | 1.6 >>> Planar Sets | ||
| 984 : | 1.7 >>> The Riemann Sphere and Stereographic Projection | ||
| 985 : | |||
| 986 : | 2 >>> Analytic Functions | ||
| 987 : | 2.1 >>> Functions of a Complex Variable | ||
| 988 : | 2.2 >>> Limits and Continuity | ||
| 989 : | 2.3 >>> Analyticity | ||
| 990 : | 2.4 >>> The Cauchy-Riemann Equations | ||
| 991 : | 2.5 >>> Harmonic Functions | ||
| 992 : | 2.6 >>> Steady-State Temperature as a Harmonic Function | ||
| 993 : | 2.7 >>> Iterated Maps: Julia and Mandelbrot Sets | ||
| 994 : | |||
| 995 : | 3 >>> Elementary Functions | ||
| 996 : | 3.1 >>> Polynomials and Rational Functions | ||
| 997 : | 3.2 >>> The Exponential, Trigonometric, and Hyperbolic Functions | ||
| 998 : | 3.3 >>> The Logarithmic Function | ||
| 999 : | 3.4 >>> Washers, Wedges, and Walls | ||
| 1000 : | 3.5 >>> Complex Powers and Inverse Trigonometric Functions | ||
| 1001 : | 3.6 >>> Application to Oscillating Systems | ||
| 1002 : | |||
| 1003 : | 4 >>> Complex Integration | ||
| 1004 : | 4.1 >>> Contours | ||
| 1005 : | 4.2 >>> Contour Integrals | ||
| 1006 : | 4.3 >>> Independence of Path | ||
| 1007 : | 4.4 >>> Cauchy's Integral Theorem | ||
| 1008 : | 4.5 >>> Deformation of Contours Approach | ||
| 1009 : | 4.6 >>> Vector Analysis Approach | ||
| 1010 : | 4.7 >>> Cauchy's Integral Formula and Its Consequences | ||
| 1011 : | 4.8 >>> Bounds for Analytic Functions | ||
| 1012 : | 4.9 >>> Applications to Harmonic Functions | ||
| 1013 : | |||
| 1014 : | 5 >>> Series Representations for Analytic Functions | ||
| 1015 : | 5.1 >>> Sequences and Series | ||
| 1016 : | 5.2 >>> Taylor Series | ||
| 1017 : | 5.3 >>> Power Series | ||
| 1018 : | 5.4 >>> Mathematical Theory of Convergence | ||
| 1019 : | 5.5 >>> Laurent Series | ||
| 1020 : | 5.6 >>> Zeros and Singularities | ||
| 1021 : | 5.7 >>> The Point at Infinity | ||
| 1022 : | 5.8 >>> Analytic Continuation | ||
| 1023 : | |||
| 1024 : | 6 >>> Residue Theory | ||
| 1025 : | 6.1 >>> The Residue Theorem | ||
| 1026 : | 6.2 >>> Trigonometric Integrals over [0, 2¹] | ||
| 1027 : | 6.3 >>> Improper Integrals of Certain Functions over (--°, °) | ||
| 1028 : | 6.4 >>> Improper Integrals Involving Trigonometric Functions | ||
| 1029 : | 6.5 >>> Indented Contours | ||
| 1030 : | 6.6 >>> Integrals Involving Multiple-Valued Functions | ||
| 1031 : | 6.7 >>> The Argument Principle and Rouche's Theorem | ||
| 1032 : | |||
| 1033 : | 7 >>> Conformal Mapping | ||
| 1034 : | 7.1 >>> Invariance of Laplace's Equation | ||
| 1035 : | 7.2 >>> Geometric Considerations | ||
| 1036 : | 7.3 >>> Mobius Transformations | ||
| 1037 : | 7.4 >>> Mobius Transformations, Continued | ||
| 1038 : | 7.5 >>> The Schwarz-Christoffel Transformation | ||
| 1039 : | 7.6 >>> Applications in Electrostatics, Heat Flow, and Fluid Mechanics | ||
| 1040 : | 7.7 >>> Further Physical Applications of Conformal Mapping | ||
| 1041 : | |||
| 1042 : | 8 >>> The Transforms of Applied Mathematics | ||
| 1043 : | 8.1 >>> Fourier Series (The Finite Fourier Transform) | ||
| 1044 : | 8.2 >>> The Fourier Transform | ||
| 1045 : | 8.3 >>> The Laplace Transform | ||
| 1046 : | 8.4 >>> The z-Transform | ||
| 1047 : | 8.5 >>> Cauchy Integrals and the Hilbert Transform | ||
| 1048 : | |||
| 1049 : | jj | 472 | 9 >>> Appendix A: Numerical Construction of Conformal Maps |
| 1050 : | 9.1 >>> The Schwarz-Christoffel Parameter Problem | ||
| 1051 : | 9.2 >>> Examples | ||
| 1052 : | 9.3 >>> Numerical Integration | ||
| 1053 : | 9.4 >>> Conformal Mapping of Smooth Domains | ||
| 1054 : | 9.5 >>> Conformal Mapping Software | ||
| 1055 : | jj | 468 | |
| 1056 : | jj | 472 | 10 >>> Appendix B: Table of Conformal Mappings |
| 1057 : | 10.1 >>> Mobius Transformations | ||
| 1058 : | 10.2 >>> Other Transformations | ||
| 1059 : | jj | 468 | |
| 1060 : | jjholt | 475 | TitleText('Calculus: Early Transcendentals') |
| 1061 : | EditionText('5') | ||
| 1062 : | AuthorText('Stewart') | ||
| 1063 : | |||
| 1064 : | 1 >>> Functions and Models | ||
| 1065 : | 1.1 >>> Four Ways to Represent a Function | ||
| 1066 : | 1.2 >>> Mathematical Models: A Catalog of Essential Functions | ||
| 1067 : | 1.3 >>> New Functions from Old Functions | ||
| 1068 : | 1.4 >>> Graphing Calculators and Computers | ||
| 1069 : | 1.5 >>> Exponential Functions | ||
| 1070 : | 1.6 >>> Inverse Functions and Logarithms | ||
| 1071 : | |||
| 1072 : | 2 >>> Limits and Derivatives | ||
| 1073 : | 2.1 >>> The Tangent and Velocity Problems | ||
| 1074 : | 2.2 >>> The Limit of a Function | ||
| 1075 : | 2.3 >>> Calculating Limits Using the Limit Laws | ||
| 1076 : | 2.4 >>> The Precise Definition of a Limit | ||
| 1077 : | 2.5 >>> Continuity | ||
| 1078 : | 2.6 >>> Limits at Infinity; Horizontal Asymptotes | ||
| 1079 : | 2.7 >>> Tangents, Velocities, and Other Rates of Change | ||
| 1080 : | 2.8 >>> Derivatives | ||
| 1081 : | 2.9 >>> The Derivative as a Function | ||
| 1082 : | |||
| 1083 : | 3 >>> Differentiation Rules | ||
| 1084 : | 3.1 >>> Derivatives of Polynomials and Exponential Functions | ||
| 1085 : | 3.2 >>> The Product and Quotient Rules | ||
| 1086 : | 3.3 >>> Rates of Change in the Natural and Social Sciences | ||
| 1087 : | 3.4 >>> Derivatives of Trigonometric Functions | ||
| 1088 : | 3.5 >>> The Chain Rule | ||
| 1089 : | 3.6 >>> Implicit Differentiation | ||
| 1090 : | 3.7 >>> Higher Derivatives | ||
| 1091 : | 3.8 >>> Derivatives of Logarithmic Functions | ||
| 1092 : | 3.9 >>> Hyperbolic Functions | ||
| 1093 : | 3.10 >>> Related Rates | ||
| 1094 : | 3.11 >>> Linear Approximations and Differentials | ||
| 1095 : | |||
| 1096 : | 4 >>> Applications of Differentiation | ||
| 1097 : | 4.1 >>> Maximum and Minimum Values | ||
| 1098 : | 4.2 >>> The Mean Value Theorem | ||
| 1099 : | 4.3 >>> How Derivatives Affect the Shape of a Graph | ||
| 1100 : | 4.4 >>> Indeterminate Forms and L'Hospital's Rule | ||
| 1101 : | 4.5 >>> Summary of Curve Sketching | ||
| 1102 : | 4.6 >>> Graphing with Calculus and Calculators | ||
| 1103 : | 4.7 >>> Optimization Problems | ||
| 1104 : | 4.8 >>> Applications to Business and Economics | ||
| 1105 : | 4.9 >>> Newton's Method | ||
| 1106 : | 4.10 >>> Antiderivatives | ||
| 1107 : | |||
| 1108 : | 5 >>> Integrals | ||
| 1109 : | 5.1 >>> Areas and Distances | ||
| 1110 : | 5.2 >>> The Definite Integral | ||
| 1111 : | 5.3 >>> The Fundamental Theorem of Calculus | ||
| 1112 : | 5.4 >>> Indefinite Integrals and the Net Change Theorem | ||
| 1113 : | 5.5 >>> The Substitution Rule | ||
| 1114 : | 5.6 >>> The Logarithm Defined as an Integral | ||
| 1115 : | |||
| 1116 : | 6 >>> Applications of Integration | ||
| 1117 : | 6.1 >>> Areas between Curves | ||
| 1118 : | 6.2 >>> Volumes | ||
| 1119 : | 6.3 >>> Volumes by Cylindrical Shells | ||
| 1120 : | 6.4 >>> Work | ||
| 1121 : | 6.5 >>> Average Value of a Function | ||
| 1122 : | |||
| 1123 : | 7 >>> Techniques of Integration | ||
| 1124 : | 7.1 >>> Integration by Parts | ||
| 1125 : | 7.2 >>> Trigonometric Integrals | ||
| 1126 : | 7.3 >>> Trigonometric Substitution | ||
| 1127 : | 7.4 >>> Integration of Rational Functions by Partial Fractions | ||
| 1128 : | 7.5 >>> Strategy for Integration | ||
| 1129 : | 7.6 >>> Integration Using Tables and Computer Algebra Systems | ||
| 1130 : | 7.7 >>> Approximate Integration | ||
| 1131 : | 7.8 >>> Improper Integrals | ||
| 1132 : | |||
| 1133 : | 8 >>> Further Applications of Integration | ||
| 1134 : | 8.1 >>> Arc Length | ||
| 1135 : | 8.2 >>> Area of a Surface of Revolution | ||
| 1136 : | 8.3 >>> Applications to Physics and Engineering | ||
| 1137 : | 8.4 >>> Applications to Economics and Biology | ||
| 1138 : | 8.5 >>> Probability | ||
| 1139 : | |||
| 1140 : | 9 >>> Differential Equations | ||
| 1141 : | 9.1 >>> Modeling with Differential Equations | ||
| 1142 : | 9.2 >>> Direction Fields and Euler's Method | ||
| 1143 : | 9.3 >>> Separable Equations | ||
| 1144 : | 9.4 >>> Exponential Growth and Decay | ||
| 1145 : | 9.5 >>> The Logistic Equation | ||
| 1146 : | 9.6 >>> Linear Equations | ||
| 1147 : | 9.7 >>> Predator-Prey Systems | ||
| 1148 : | |||
| 1149 : | 10 >>> Parametric Equations and Polar Coordinates | ||
| 1150 : | 10.1 >>> Curves Defined by Parametric Equations | ||
| 1151 : | 10.2 >>> Calculus with Parametric Curves | ||
| 1152 : | 10.3 >>> Polar Coordinates | ||
| 1153 : | 10.4 >>> Areas and Lengths in Polar Coordinates | ||
| 1154 : | 10.5 >>> Conic Sections | ||
| 1155 : | 10.6 >>> Conic Sections in Polar Coordinates | ||
| 1156 : | |||
| 1157 : | 11 >>> Infinite Sequences and Series | ||
| 1158 : | 11.1 >>> Sequences | ||
| 1159 : | 11.2 >>> Series | ||
| 1160 : | 11.3 >>> The Integral Test and Estimates of Sums | ||
| 1161 : | 11.4 >>> The Comparison Tests | ||
| 1162 : | 11.5 >>> Alternating Series | ||
| 1163 : | 11.6 >>> Absolute Convergence and the Ratio and Root Tests | ||
| 1164 : | 11.7 >>> Strategy for Testing Series | ||
| 1165 : | 11.8 >>> Power Series | ||
| 1166 : | 11.9 >>> Representations of Functions as Power Series | ||
| 1167 : | 11.10 >>> Taylor and Maclaurin Series | ||
| 1168 : | 11.11 >>> The Binomial Series | ||
| 1169 : | 11.12 >>> Applications of Taylor Polynomials | ||
| 1170 : | |||
| 1171 : | 12 >>> Vectors and the Geometry of Space | ||
| 1172 : | 12.1 >>> Three-Dimensional Coordinate Systems | ||
| 1173 : | 12.2 >>> Vectors | ||
| 1174 : | 12.3 >>> The Dot Product | ||
| 1175 : | 12.4 >>> The Cross Product | ||
| 1176 : | 12.5 >>> Equations of Lines and Planes | ||
| 1177 : | 12.6 >>> Cylinders and Quadric Surfaces | ||
| 1178 : | 12.7 >>> Cylindrical and Spherical Coordinates | ||
| 1179 : | |||
| 1180 : | 13 >>> Vector Functions | ||
| 1181 : | 13.1 >>> Vector Functions and Space Curves | ||
| 1182 : | 13.2 >>> Derivatives and Integrals of Vector Functions | ||
| 1183 : | 13.3 >>> Arc Length and Curvature | ||
| 1184 : | 13.4 >>> Motion in Space: Velocity and Acceleration | ||
| 1185 : | |||
| 1186 : | 14 >>> Partial Derivatives | ||
| 1187 : | 14.1 >>> Functions of Several Variables | ||
| 1188 : | 14.2 >>> Limits and Continuity | ||
| 1189 : | 14.3 >>> Partial Derivatives | ||
| 1190 : | 14.4 >>> Tangent Planes and Linear Approximations | ||
| 1191 : | 14.5 >>> The Chain Rule | ||
| 1192 : | 14.6 >>> Directional Derivatives and the Gradient Vector | ||
| 1193 : | 14.7 >>> Maximum and Minimum Values | ||
| 1194 : | 14.8 >>> Lagrange Multipliers | ||
| 1195 : | |||
| 1196 : | 15 >>> Multiple Integrals | ||
| 1197 : | 15.1 >>> Double Integrals over Rectangles | ||
| 1198 : | 15.2 >>> Iterated Integrals | ||
| 1199 : | 15.3 >>> Double Integrals over General Regions | ||
| 1200 : | 15.4 >>> Double Integrals in Polar Coordinates | ||
| 1201 : | 15.5 >>> Applications of Double Integrals | ||
| 1202 : | 15.6 >>> Surface Area | ||
| 1203 : | 15.7 >>> Triple Integrals | ||
| 1204 : | 15.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates | ||
| 1205 : | 15.9 >>> Change of Variables in Multiple Integrals | ||
| 1206 : | |||
| 1207 : | 16 >>> Vector Calculus | ||
| 1208 : | 16.1 >>> Vector Fields | ||
| 1209 : | 16.2 >>> Line Integrals | ||
| 1210 : | 16.3 >>> The Fundamental Theorem for Line Integrals | ||
| 1211 : | 16.4 >>> Green's Theorem | ||
| 1212 : | 16.5 >>> Curl and Divergence | ||
| 1213 : | 16.6 >>> Parametric Surfaces and their Areas | ||
| 1214 : | 16.7 >>> Surface Integrals | ||
| 1215 : | 16.8 >>> Stokes' Theorem | ||
| 1216 : | 16.9 >>> The Divergence Theorem | ||
| 1217 : | 16.10 >>> Summary | ||
| 1218 : | |||
| 1219 : | 17 >>> Second-Order Differential Equations | ||
| 1220 : | 17.1 >>> Second-Order Linear Equations | ||
| 1221 : | 17.2 >>> Nonhomogeneous Linear Equations | ||
| 1222 : | 17.3 >>> Applications of Second-Order Differential Equations | ||
| 1223 : | 17.4 >>> Series Solutions | ||
| 1224 : | |||
| 1225 : | jj | 506 | 18 >>> Appendix A: Numbers, Inequalities, and Absolute Values |
| 1226 : | 19 >>> Appendix B: Coordinate Geometry and Lines | ||
| 1227 : | 20 >>> Appendix C: Graphs of Second-Degree Equations | ||
| 1228 : | 21 >>> Appendix D: Trigonometry | ||
| 1229 : | 22 >>> Appendix E: Sigma Notation | ||
| 1230 : | 23 >>> Appendix F: Proofs of Theorems | ||
| 1231 : | 24 >>> Appendix G: Complex Numbers | ||
| 1232 : | 25 >>> Appendix H: Answers to Odd-Numbered Exercises | ||
| 1233 : | jjholt | 475 | |
| 1234 : | |||
| 1235 : | TitleText('Calculus: Early Transcendentals') | ||
| 1236 : | EditionText('6') | ||
| 1237 : | AuthorText('Stewart') | ||
| 1238 : | |||
| 1239 : | 1 >>> Functions and Models | ||
| 1240 : | 1.1 >>> Four Ways to Represent a Function | ||
| 1241 : | 1.2 >>> Mathematical Models: A Catalog of Essential Functions | ||
| 1242 : | 1.3 >>> New Functions from Old Functions | ||
| 1243 : | 1.4 >>> Graphing Calculators and Computers | ||
| 1244 : | 1.5 >>> Exponential Functions | ||
| 1245 : | 1.6 >>> Inverse Functions and Logarithms | ||
| 1246 : | |||
| 1247 : | 2 >>> Limits and Derivatives | ||
| 1248 : | 2.1 >>> The Tangent and Velocity Problems | ||
| 1249 : | 2.2 >>> The Limit of a Function | ||
| 1250 : | 2.3 >>> Calculating Limits Using the Limit Laws | ||
| 1251 : | 2.4 >>> The Precise Definition of a Limit | ||
| 1252 : | 2.5 >>> Continuity | ||
| 1253 : | 2.6 >>> Limits at Infinity; Horizontal Asymptotes | ||
| 1254 : | 2.7 >>> Derivatives and Rates of Change | ||
| 1255 : | 2.8 >>> The Derivative as a Function | ||
| 1256 : | |||
| 1257 : | 3 >>> Differentiation Rules | ||
| 1258 : | 3.1 >>> Derivatives of Polynomials and Exponential Functions | ||
| 1259 : | 3.2 >>> The Product and Quotient Rules | ||
| 1260 : | 3.3 >>> Derivatives of Trigonometric Functions | ||
| 1261 : | 3.4 >>> The Chain Rule | ||
| 1262 : | 3.5 >>> Implicit Differentiation | ||
| 1263 : | 3.6 >>> Derivatives of Logarithmic Functions | ||
| 1264 : | 3.7 >>> Rates of Change in the Natural and Social Sciences | ||
| 1265 : | 3.8 >>> Exponential Growth and Decay | ||
| 1266 : | 3.9 >>> Related Rates | ||
| 1267 : | 3.10 >>> Linear Approximations and Differentials | ||
| 1268 : | 3.11 >>> Hyperbolic Functions | ||
| 1269 : | |||
| 1270 : | 4 >>> Applications of Differentiation | ||
| 1271 : | 4.1 >>> Maximum and Minimum Values | ||
| 1272 : | 4.2 >>> The Mean Value Theorem | ||
| 1273 : | 4.3 >>> How Derivatives Affect the Shape of a Graph | ||
| 1274 : | 4.4 >>> Indeterminate Forms and L'Hospital's Rule | ||
| 1275 : | 4.5 >>> Summary of Curve Sketching | ||
| 1276 : | 4.6 >>> Graphing with Calculus and Calculators | ||
| 1277 : | 4.7 >>> Optimization Problems | ||
| 1278 : | 4.8 >>> Newton's Method | ||
| 1279 : | 4.9 >>> Antiderivatives | ||
| 1280 : | |||
| 1281 : | 5 >>> Integrals | ||
| 1282 : | 5.1 >>> Areas and Distances | ||
| 1283 : | 5.2 >>> The Definite Integral | ||
| 1284 : | 5.3 >>> The Fundamental Theorem of Calculus | ||
| 1285 : | 5.4 >>> Indefinite Integrals and the Net Change Theorem | ||
| 1286 : | 5.5 >>> The Substitution Rule | ||
| 1287 : | |||
| 1288 : | 6 >>> Applications of Integration | ||
| 1289 : | 6.1 >>> Areas between Curves | ||
| 1290 : | 6.2 >>> Volumes | ||
| 1291 : | 6.3 >>> Volumes by Cylindrical Shells | ||
| 1292 : | 6.4 >>> Work | ||
| 1293 : | 6.5 >>> Average Value of a Function | ||
| 1294 : | |||
| 1295 : | 7 >>> Techniques of Integration | ||
| 1296 : | 7.1 >>> Integration by Parts | ||
| 1297 : | 7.2 >>> Trigonometric Integrals | ||
| 1298 : | 7.3 >>> Trigonometric Substitution | ||
| 1299 : | 7.4 >>> Integration of Rational Functions by Partial Fractions | ||
| 1300 : | 7.5 >>> Strategy for Integration | ||
| 1301 : | 7.6 >>> Integration Using Tables and Computer Algebra Systems | ||
| 1302 : | 7.7 >>> Approximate Integration | ||
| 1303 : | 7.8 >>> Improper Integrals | ||
| 1304 : | |||
| 1305 : | 8 >>> Further Applications of Integration | ||
| 1306 : | 8.1 >>> Arc Length | ||
| 1307 : | 8.2 >>> Area of a Surface of Revolution | ||
| 1308 : | 8.3 >>> Applications to Physics and Engineering | ||
| 1309 : | 8.4 >>> Applications to Economics and Biology | ||
| 1310 : | 8.5 >>> Probability | ||
| 1311 : | |||
| 1312 : | 9 >>> Differential Equations | ||
| 1313 : | 9.1 >>> Modeling with Differential Equations | ||
| 1314 : | 9.2 >>> Direction Fields and Euler's Method | ||
| 1315 : | 9.3 >>> Separable Equations | ||
| 1316 : | 9.4 >>> Models for Population Growth | ||
| 1317 : | 9.5 >>> Linear Equations | ||
| 1318 : | 9.6 >>> Predator-Prey Systems | ||
| 1319 : | |||
| 1320 : | 10 >>> Parametric Equations and Polar Coordinates | ||
| 1321 : | 10.1 >>> Curves Defined by Parametric Equations | ||
| 1322 : | 10.2 >>> Calculus with Parametric Curves | ||
| 1323 : | 10.3 >>> Polar Coordinates | ||
| 1324 : | 10.4 >>> Areas and Lengths in Polar Coordinates | ||
| 1325 : | 10.5 >>> Conic Sections | ||
| 1326 : | 10.6 >>> Conic Sections in Polar Coordinates | ||
| 1327 : | |||
| 1328 : | 11 >>> Infinite Sequences and Series | ||
| 1329 : | 11.1 >>> Sequences | ||
| 1330 : | 11.2 >>> Series | ||
| 1331 : | 11.3 >>> The Integral Test and Estimates of Sum | ||
| 1332 : | 11.4 >>> The Comparison Tests | ||
| 1333 : | 11.5 >>> Alternating Series | ||
| 1334 : | 11.6 >>> Absolute Convergence and the Ratio and Root Tests | ||
| 1335 : | 11.7 >>> Strategy for Testing Series | ||
| 1336 : | 11.8 >>> Power Series | ||
| 1337 : | 11.9 >>> Representations of Functions as Power Series | ||
| 1338 : | 11.10 >>> Taylor and Maclaurin Series | ||
| 1339 : | 11.11 >>> Applications of Taylor Polynomials | ||
| 1340 : | |||
| 1341 : | 12 >>> Vectors and the Geometry of Space | ||
| 1342 : | 12.1 >>> Three-Dimensional Coordinate Systems | ||
| 1343 : | 12.2 >>> Vectors | ||
| 1344 : | 12.3 >>> The Dot Product | ||
| 1345 : | 12.4 >>> The Cross Product | ||
| 1346 : | 12.5 >>> Equations of Lines and Planes | ||
| 1347 : | 12.6 >>> Cylinders and Quadric Surfaces | ||
| 1348 : | |||
| 1349 : | 13 >>> Vector Functions | ||
| 1350 : | 13.1 >>> Vector Functions and Space Curves | ||
| 1351 : | 13.2 >>> Derivatives and Integrals of Vector Functions | ||
| 1352 : | 13.3 >>> Arc Length and Curvature | ||
| 1353 : | 13.4 >>> Motion in Space: Velocity and Acceleration | ||
| 1354 : | |||
| 1355 : | 14 >>> Partial Derivatives | ||
| 1356 : | 14.1 >>> Functions of Several Variables | ||
| 1357 : | 14.2 >>> Limits and Continuity | ||
| 1358 : | 14.3 >>> Partial Derivatives | ||
| 1359 : | 14.4 >>> Tangent Planes and Linear Approximations | ||
| 1360 : | 14.5 >>> The Chain Rule | ||
| 1361 : | 14.6 >>> Directional Derivatives and the Gradient Vector | ||
| 1362 : | 14.7 >>> Maximum and Minimum Values | ||
| 1363 : | 14.8 >>> Lagrange Multipliers | ||
| 1364 : | |||
| 1365 : | 15 >>> Multiple Integrals | ||
| 1366 : | 15.1 >>> Double Integrals over Rectangles | ||
| 1367 : | 15.2 >>> Iterated Integrals | ||
| 1368 : | 15.3 >>> Double Integrals over General Regions | ||
| 1369 : | 15.4 >>> Double Integrals in Polar Coordinates | ||
| 1370 : | 15.5 >>> Applications of Double Integrals | ||
| 1371 : | 15.6 >>> Triple Integrals | ||
| 1372 : | 15.7 >>> Triple Integrals in Cylindrical Coordinates | ||
| 1373 : | 15.8 >>> Triple Integrals in Spherical Coordinates | ||
| 1374 : | 15.9 >>> Change of Variables in Multiple Integrals | ||
| 1375 : | |||
| 1376 : | 16 >>> Vector Calculus | ||
| 1377 : | 16.1 >>> Vector Fields | ||
| 1378 : | 16.2 >>> Line Integrals | ||
| 1379 : | 16.3 >>> The Fundamental Theorem for Line Integrals | ||
| 1380 : | 16.4 >>> Green's Theorem | ||
| 1381 : | 16.5 >>> Curl and Divergence | ||
| 1382 : | 16.6 >>> Parametric Surfaces and their Areas | ||
| 1383 : | 16.7 >>> Surface Integrals | ||
| 1384 : | 16.8 >>> Stokes' Theorem | ||
| 1385 : | 16.9 >>> The Divergence Theorem | ||
| 1386 : | 16.10 >>> Summary | ||
| 1387 : | |||
| 1388 : | 17 >>> Second-Order Differential Equations | ||
| 1389 : | 17.1 >>> Second-Order Linear Equations | ||
| 1390 : | 17.2 >>> Nonhomogeneous Linear Equations | ||
| 1391 : | 17.3 >>> Applications of Second-Order Differential Equations | ||
| 1392 : | 17.4 >>> Series Solutions | ||
| 1393 : | |||
| 1394 : | jj | 506 | 18 >>> Appendix A: Numbers, Inequalities, and Absolute Values |
| 1395 : | 19 >>> Appendix B: Coordinate Geometry and Lines | ||
| 1396 : | 20 >>> Appendix C: Graphs of Second-Degree Equations | ||
| 1397 : | 21 >>> Appendix D: Trigonometry | ||
| 1398 : | 22 >>> Appendix E: Sigma Notation | ||
| 1399 : | 23 >>> Appendix F: Proofs of Theorems | ||
| 1400 : | 24 >>> Appendix G: The Logarithm Defined as an Integral | ||
| 1401 : | 25 >>> Appendix H: Complex Numbers | ||
| 1402 : | 26 >>> Appendix I: Answers to Odd-Numbered Exercises | ||
| 1403 : | jj | 505 | |
| 1404 : | TitleText('College Algebra') | ||
| 1405 : | EditionText('3') | ||
| 1406 : | AuthorText('Stewart, Redlin, Watson') | ||
| 1407 : | |||
| 1408 : | 1 >>> Basic Algebra | ||
| 1409 : | 1.1 >>> What is Algebra? | ||
| 1410 : | 1.2 >>> Real Numbers | ||
| 1411 : | 1.3 >>> Exponentials and Radicals | ||
| 1412 : | 1.4 >>> Algebraic Equations | ||
| 1413 : | 1.5 >>> Fractional Expressions | ||
| 1414 : | 1.6 >>> Basic Equations | ||
| 1415 : | 2 >>> Coordinates and Graphs | ||
| 1416 : | 2.1 >>> The Coordinate Plane | ||
| 1417 : | 2.2 >>> Graphs of Equations | ||
| 1418 : | 2.3 >>> Graphing Calculators and Computers | ||
| 1419 : | 2.4 >>> Lines | ||
| 1420 : | 3 >>> Equations and Inequalities | ||
| 1421 : | 3.1 >>> Algebraic and Graphical Solutions of Equations | ||
| 1422 : | 3.2 >>> Modeling with Equations | ||
| 1423 : | 3.3 >>> Quadratic Equations | ||
| 1424 : | 3.4 >>> Complex Numbers | ||
| 1425 : | 3.5 >>> Other Equations | ||
| 1426 : | 3.6 >>> Linear Inequalities | ||
| 1427 : | 3.7 >>> Nonlinear Inequalities | ||
| 1428 : | 3.8 >>> Absolute Value | ||
| 1429 : | 4 >>> Functions | ||
| 1430 : | 4.1 >>> What is a Function? | ||
| 1431 : | 4.2 >>> Graphs of Functions | ||
| 1432 : | 4.3 >>> Applied Functions: Variation | ||
| 1433 : | 4.4 >>> Average Rate of Change: Increasing and Decreasing Functions | ||
| 1434 : | 4.5 >>> Transformations of Functions | ||
| 1435 : | 4.6 >>> Extreme Values of Functions | ||
| 1436 : | 4.7 >>> Combining Functions | ||
| 1437 : | 4.8 >>> One-to-One Functions and Their Inverses | ||
| 1438 : | 5 >>> Polynomial and Rational Functions | ||
| 1439 : | 5.1 >>> Polynomial Functions and Their Graphs | ||
| 1440 : | 5.2 >>> Dividing Polynomials | ||
| 1441 : | 5.3 >>> Real Zeros of Polynomials | ||
| 1442 : | 5.4 >>> The Fundamental Theorem of Algebra | ||
| 1443 : | 5.5 >>> Rational Functions | ||
| 1444 : | 6 >>> Exponential and Logarithmic Functions | ||
| 1445 : | 6.1 >>> Exponential Functions | ||
| 1446 : | 6.2 >>> The Natural Exponential Function | ||
| 1447 : | 6.3 >>> Logistic Functions | ||
| 1448 : | 6.4 >>> Laws of Logarithms | ||
| 1449 : | 6.5 >>> Exponential and Logarithmic Equations | ||
| 1450 : | 6.6 >>> Applications of Exponential and Logarithmic Functions | ||
| 1451 : | 7 >>> Systems of Equations and Inequalities | ||
| 1452 : | 7.1 >>> Systems of Equations | ||
| 1453 : | 7.2 >>> Pairs of Lines | ||
| 1454 : | 7.3 >>> Systems of Linear Equations | ||
| 1455 : | 7.4 >>> The Algebra of Matrices | ||
| 1456 : | 7.5 >>> Inverses of Matrices and Matrix Equations | ||
| 1457 : | 7.6 >>> Determinants and Cramer's Rule | ||
| 1458 : | 7.7 >>> Systems of Inequalities | ||
| 1459 : | 7.8 >>> Partial Fractions | ||
| 1460 : | 8 >>> Conic Sections | ||
| 1461 : | 8.1 >>> Parabolas | ||
| 1462 : | 8.2 >>> Ellipses | ||
| 1463 : | 8.3 >>> Hyperbolas | ||
| 1464 : | 8.4 >>> Shifted Conics | ||
| 1465 : | 9 >>> Sequences and Series | ||
| 1466 : | 9.1 >>> Sequences and Summation Notation | ||
| 1467 : | 9.2 >>> Arithmetic Sequences | ||
| 1468 : | 9.3 >>> Geometric Sequences | ||
| 1469 : | 9.4 >>> Annuities and Installment Buying | ||
| 1470 : | 9.5 >>> Mathematical Induction | ||
| 1471 : | 9.6 >>> The Binomial Theorem | ||
| 1472 : | 10 >>> Counting and Probability | ||
| 1473 : | 10.1 >>> Counting Principles | ||
| 1474 : | 10.2 >>> Permutations and Combinations | ||
| 1475 : | 10.3 >>> Probability | ||
| 1476 : | 10.4 >>> Expected Value | ||
| 1477 : | |||
| 1478 : | TitleText('Precalculus') | ||
| 1479 : | EditionText('3') | ||
| 1480 : | AuthorText('Stewart, Redlin, Watson') | ||
| 1481 : | |||
| 1482 : | 1 >>> Fundamentals | ||
| 1483 : | 1.1 >>> Real Numbers | ||
| 1484 : | 1.2 >>> Exponents and Radicals | ||
| 1485 : | 1.3 >>> Algebraic Expressions | ||
| 1486 : | 1.4 >>> Fractional Expressions | ||
| 1487 : | 1.5 >>> Equations | ||
| 1488 : | 1.6 >>> Problem Solving with Equations | ||
| 1489 : | 1.7 >>> Inequalities | ||
| 1490 : | 1.8 >>> Coordinate Geometry | ||
| 1491 : | 1.9 >>> Graphing Calculators and Computers | ||
| 1492 : | 1.10 >>> Lines | ||
| 1493 : | jj | 510 | |
| 1494 : | jj | 505 | 2 >>> Functions |
| 1495 : | 2.1 >>> What is a Function? | ||
| 1496 : | jj | 510 | 2.2 >>> Graphs of Functions |
| 1497 : | jj | 505 | 2.3 >>> Applied Functions |
| 1498 : | 2.4 >>> Transformations of Functions | ||
| 1499 : | 2.5 >>> Extreme Values of Functions | ||
| 1500 : | 2.6 >>> Combining Functions | ||
| 1501 : | 2.7 >>> One-to-One Functions and Their Inverses | ||
| 1502 : | jj | 510 | |
| 1503 : | jj | 505 | 3 >>> Polynomials and Rational Functions |
| 1504 : | 3.1 >>> Polynomial Functions and Their Graphs | ||
| 1505 : | 3.2 >>> Real Zeros of Polynomials | ||
| 1506 : | 3.3 >>> Complex Numbers | ||
| 1507 : | 3.4 >>> Complex Roots and The Fundamental Theorem of Algebra | ||
| 1508 : | 3.5 >>> Rational Functions | ||
| 1509 : | 4 >>> Exponential and Logarithmic Functions | ||
| 1510 : | 4.1 >>> Exponential Functions | ||
| 1511 : | 4.2 >>> The Natural Exponential Function | ||
| 1512 : | 4.3 >>> Logarithmic Functions | ||
| 1513 : | 4.4 >>> Laws of Logarithms | ||
| 1514 : | 4.5 >>> Exponential and Logarithmic Equations | ||
| 1515 : | 4.6 >>> Applications of Exponential and Logarithmic Equations | ||
| 1516 : | 5 >>> Trigonometric Functions | ||
| 1517 : | 5.1 >>> The Unit Circle | ||
| 1518 : | 5.2 >>> Trigonometric Functions of Real Numbers | ||
| 1519 : | 5.3 >>> Trigonometric Graphs | ||
| 1520 : | 5.4 >>> More Trigonometric Graphs | ||
| 1521 : | 6 >>> Trigonometric Functions of Angles | ||
| 1522 : | 6.1 >>> Angle Measure | ||
| 1523 : | 6.2 >>> Trigonometry of Right Triangles | ||
| 1524 : | 6.3 >>> Trigonometric Functions of Angles | ||
| 1525 : | 6.4 >>> The Law of Sines | ||
| 1526 : | 6.5 >>> The Law of Cosines | ||
| 1527 : | 7 >>> Analytic Trigonometry | ||
| 1528 : | 7.1 >>> Trigonometric Identities | ||
| 1529 : | 7.2 >>> Addition and Subtraction Formulas | ||
| 1530 : | 7.3 >>> Double-Angle, Half-Angle, and Product-Sum Formulas | ||
| 1531 : | 7.4 >>> Inverse Trigonometric Functions | ||
| 1532 : | 7.5 >>> Trigonometric Equations | ||
| 1533 : | 7.6 >>> Trigonometric Form of Complex Numbers; DeMoivre's Theorem | ||
| 1534 : | 7.7 >>> Vectors | ||
| 1535 : | 8 >>> Systems of Equations and Inequalities | ||
| 1536 : | 8.1 >>> Systems of Equations | ||
| 1537 : | 8.2 >>> Pairs of Lines | ||
| 1538 : | 8.3 >>> Systems of Linear Equations | ||
| 1539 : | 8.4 >>> The Algebra of Matrices | ||
| 1540 : | 8.5 >>> Inverses of Matrices and Matrix Equations | ||
| 1541 : | 8.6 >>> Determinants and Cramer's Rule | ||
| 1542 : | 8.7 >>> Systems of Inequalities | ||
| 1543 : | 8.8 >>> Partial Fractions | ||
| 1544 : | 9 >>> Topics in Analytic Geometry | ||
| 1545 : | 9.1 >>> Parabolas | ||
| 1546 : | 9.2 >>> Ellipses | ||
| 1547 : | 9.3 >>> Hyperbolas | ||
| 1548 : | 9.4 >>> Shifted Conics | ||
| 1549 : | 9.5 >>> Rotation of Axes | ||
| 1550 : | 9.6 >>> Polar Coordinates | ||
| 1551 : | 9.7 >>> Polar Equations of Conics | ||
| 1552 : | 9.8 >>> Parametric Equations | ||
| 1553 : | 10 >>> Sequences and Series | ||
| 1554 : | 10.1 >>> Sequences and Summation Notation | ||
| 1555 : | 10.2 >>> Arithmetic Sequences | ||
| 1556 : | 10.3 >>> Geometric Sequences | ||
| 1557 : | 10.4 >>> Annuities and Installment Buying | ||
| 1558 : | 10.5 >>> Mathematical Induction | ||
| 1559 : | 10.6 >>> The Binomial Theorem | ||
| 1560 : | 11 >>> Counting and Probability | ||
| 1561 : | 11.1 >>> Counting Principles | ||
| 1562 : | 11.2 >>> Permutations and Combinations | ||
| 1563 : | 11.3 >>> Probability | ||
| 1564 : | 11.4 >>> Expected Value | ||
| 1565 : | |||
| 1566 : | jjholt | 551 | |
| 1567 : | glarose | 1292 | TitleText('Functions Modeling Change') |
| 1568 : | EditionText('3') | ||
| 1569 : | AuthorText('Connally') | ||
| 1570 : | |||
| 1571 : | 1 >>> Linear Functions and Change | ||
| 1572 : | 1.1 >>> Functions and Function Notation | ||
| 1573 : | 1.2 >>> Rate of Change | ||
| 1574 : | 1.3 >>> Linear Functions | ||
| 1575 : | 1.4 >>> Formulas for Linear Functions | ||
| 1576 : | 1.5 >>> Geometric Properties of Linear Functions | ||
| 1577 : | 1.6 >>> Fitting Linear Functions to Data | ||
| 1578 : | 2 >>> Functions | ||
| 1579 : | 2.1 >>> Input and Output | ||
| 1580 : | 2.2 >>> Domain and Range | ||
| 1581 : | 2.3 >>> Piecewise Defined Functions | ||
| 1582 : | 2.4 >>> Composite and Inverse Functions | ||
| 1583 : | 2.5 >>> Concavity | ||
| 1584 : | 2.6 >>> Quadratic Functions | ||
| 1585 : | 3 >>> Exponential Functions | ||
| 1586 : | 3.1 >>> Introduction to the Family of Exponential Functions | ||
| 1587 : | 3.2 >>> Comparing Exponential and Linear Functions | ||
| 1588 : | 3.3 >>> Graphs of Exponential Functions | ||
| 1589 : | 3.4 >>> Continuous Growth and the Number e | ||
| 1590 : | 3.5 >>> Compound Interest | ||
| 1591 : | 4 >>> Logarithmic Functions | ||
| 1592 : | 4.1 >>> Logarithms and their Properties | ||
| 1593 : | 4.2 >>> Logarithms and Exponential Models | ||
| 1594 : | 4.3 >>> The Logarithmic Function | ||
| 1595 : | 4.4 >>> Logarithmic Scales | ||
| 1596 : | 5 >>> Transformations of Functions and their Graphs | ||
| 1597 : | 5.1 >>> Vertical and Horizontal Shifts | ||
| 1598 : | 5.2 >>> Reflections and Symmetry | ||
| 1599 : | 5.3 >>> Vertical Stretches and Compressions | ||
| 1600 : | 5.4 >>> Horizontal Stretches and Compressions | ||
| 1601 : | 5.5 >>> The Family of Quadratic Functions | ||
| 1602 : | 6 >>> Trigonometric Functions | ||
| 1603 : | 6.1 >>> Introduction to Periodic Functions | ||
| 1604 : | 6.2 >>> The Sine and Cosine Functions | ||
| 1605 : | 6.3 >>> Radians | ||
| 1606 : | 6.4 >>> Graphs of the Sine and Cosine | ||
| 1607 : | 6.5 >>> Sinusoidal Functions | ||
| 1608 : | 6.6 >>> Other Trigonometric Functions | ||
| 1609 : | 6.7 >>> Inverse Trigonometric Functions | ||
| 1610 : | 7 >>> Trigonometry | ||
| 1611 : | 7.1 >>> General Triangles: Laws of Sines and Cosines | ||
| 1612 : | 7.2 >>> Trigonometric Identities | ||
| 1613 : | 7.3 >>> Sum and Difference Formulas for Sine and Cosine | ||
| 1614 : | 7.4 >>> Trigonometric Models | ||
| 1615 : | 7.5 >>> Polar Coordinates | ||
| 1616 : | 7.6 >>> Complex Numbers and Polar Coordinates | ||
| 1617 : | 8 >>> Compositions, Inverses and Combinations of Functions | ||
| 1618 : | 8.1 >>> Composition of Functions | ||
| 1619 : | 8.2 >>> Inverse Functions | ||
| 1620 : | 8.3 >>> Combinations of Functions | ||
| 1621 : | 9 >>> Polynomial and Rational Functions | ||
| 1622 : | 9.1 >>> Power Functions | ||
| 1623 : | 9.2 >>> Polynomial Functions | ||
| 1624 : | 9.3 >>> The Short-Run Behavior of Polynomials | ||
| 1625 : | 9.4 >>> Rational Functions | ||
| 1626 : | 9.5 >>> The Short-Run Behavior of Rational Functions | ||
| 1627 : | 9.6 >>> Comparing Power, Exponential and Log Functions | ||
| 1628 : | 9.7 >>> Fitting Exponentials and Polynomials to Data | ||
| 1629 : | 10 >>> Vector and Matrices | ||
| 1630 : | 10.1 >>> Vectors | ||
| 1631 : | 10.2 >>> The Components of a Vector | ||
| 1632 : | 10.3 >>> Application of Vectors | ||
| 1633 : | 10.4 >>> The Dot Product | ||
| 1634 : | 10.5 >>> Matrices | ||
| 1635 : | 11 >>> Sequences and Series | ||
| 1636 : | 11.1 >>> Sequences | ||
| 1637 : | 11.2 >>> Defining Functions Using Sums: Arithmetic Series | ||
| 1638 : | 11.3 >>> Finite Geometric Series | ||
| 1639 : | 11.4 Infinite Geometric Series | ||
| 1640 : | 12 >>> Parametric Equations and Conic Sections | ||
| 1641 : | 12.1 >>> Parametric Equations | ||
| 1642 : | 12.2 >>> Implicitly Defined Curves and Circles | ||
| 1643 : | 12.3 >>> Ellipses | ||
| 1644 : | 12.4 >>> Hyperbolas | ||
| 1645 : | 12.5 >>> Geometric Properties of Conic Sections | ||
| 1646 : | 12.6 >>> Hyperbolic Functions | ||
| 1647 : | |||
| 1648 : | glarose | 2645 | TitleText('Functions Modeling Change') |
| 1649 : | EditionText('4') | ||
| 1650 : | AuthorText('Connally') | ||
| 1651 : | glarose | 1292 | |
| 1652 : | glarose | 2645 | 1 >>> Linear Functions and Change |
| 1653 : | 1.1 >>> Functions and Function Notation | ||
| 1654 : | 1.2 >>> Rate of Change | ||
| 1655 : | 1.3 >>> Linear Functions | ||
| 1656 : | 1.4 >>> Formulas for Linear Functions | ||
| 1657 : | 1.5 >>> Geometric Properties of Linear Functions | ||
| 1658 : | 1.6 >>> Fitting Linear Functions to Data | ||
| 1659 : | 2 >>> Functions | ||
| 1660 : | 2.1 >>> Input and Output | ||
| 1661 : | 2.2 >>> Domain and Range | ||
| 1662 : | 2.3 >>> Piecewise Defined Functions | ||
| 1663 : | 2.4 >>> Composite and Inverse Functions | ||
| 1664 : | 2.5 >>> Concavity | ||
| 1665 : | 3 >>> Quadratic Functions | ||
| 1666 : | 3.1 >>> Introduction to the Family of Quadratic Functions | ||
| 1667 : | 3.2 >>> The Vertex of a Parabola | ||
| 1668 : | 4 >>> Exponential Functions | ||
| 1669 : | 4.1 >>> Introduction to the Family of Exponential Functions | ||
| 1670 : | 4.2 >>> Comparing Exponential and Linear Functions | ||
| 1671 : | 4.3 >>> Graphs of Exponential Functions | ||
| 1672 : | 4.4 >>> Applications to Compound Interest | ||
| 1673 : | 4.5 >>> The Number e | ||
| 1674 : | 5 >>> Logarithmic Functions | ||
| 1675 : | 5.1 >>> Logarithms and their Properties | ||
| 1676 : | 5.2 >>> Logarithms and Exponential Models | ||
| 1677 : | 5.3 >>> The Logarithmic Function | ||
| 1678 : | 5.4 >>> Logarithmic Scales | ||
| 1679 : | 6 >>> Transformations of Functions and Their Graphs | ||
| 1680 : | 6.1 >>> Vertical and Horizontal Shifts | ||
| 1681 : | 6.2 >>> Reflections and Symmetry | ||
| 1682 : | 6.3 >>> Vertical Stretches and Compressions | ||
| 1683 : | 6.4 >>> Horizontal Stretches and Compressions | ||
| 1684 : | 6.5 >>> Combining Transformations | ||
| 1685 : | 7 >>> Trigonometric in Circles and Triangles | ||
| 1686 : | 7.1 >>> Introduction to Periodic Functions | ||
| 1687 : | 7.2 >>> The Sine and Cosine Functions | ||
| 1688 : | 7.3 >>> Graphs of Sine and Cosine | ||
| 1689 : | 7.4 >>> The Tangent Function | ||
| 1690 : | 7.5 >>> Right Triangles: Inverse Trigonometric Functions | ||
| 1691 : | 7.6 >>> Non-Right Triangles | ||
| 1692 : | 8 >>> The Trigonometric Functions | ||
| 1693 : | 8.1 >>> Radians and Arc Length | ||
| 1694 : | 8.2 >>> Sinusoidal Functions and Their Graphs | ||
| 1695 : | 8.3 >>> Trigonometric Functions: Relationships and Graphs | ||
| 1696 : | 8.4 >>> Trigonometric Equations and Inverse Functions | ||
| 1697 : | 8.5 >>> Polar Coordinates | ||
| 1698 : | 8.6 >>> Complex Numbers and Polar Coordinates | ||
| 1699 : | 9 >>> Trigonometric Identities and Their Applications | ||
| 1700 : | 9.1 >>> Identities, Expressions and Equations | ||
| 1701 : | 9.2 >>> Sum and Difference Formulas for Sine and Cosine | ||
| 1702 : | 9.3 >>> Trigonometric Models | ||
| 1703 : | 10 >>> Compositions, Inverses and Combinations of Functions | ||
| 1704 : | 10.1 >>> Composition of Functions | ||
| 1705 : | 10.2 >>> Invertibility and Properties of Inverse Functions | ||
| 1706 : | 10.3 >>> Combinations of Functions | ||
| 1707 : | 11 >>> Polynomial and Rational Functions | ||
| 1708 : | 11.1 >>> Power Functions | ||
| 1709 : | 11.2 >>> Polynomial Functions | ||
| 1710 : | 11.3 >>> The Short-Run Behavior of Polynomials | ||
| 1711 : | 11.4 >>> Rational Functions | ||
| 1712 : | 11.5 >>> The Short-Run Behavior of Rational Functions | ||
| 1713 : | 11.6 >>> Comparing Power, Exponential and Log Functions | ||
| 1714 : | 11.7 >>> Fitting Exponentials and Polynomials to Data | ||
| 1715 : | 12 >>> Vector and Matrices | ||
| 1716 : | 12.1 >>> Vectors | ||
| 1717 : | 12.2 >>> The Components of a Vector | ||
| 1718 : | 12.3 >>> Application of Vectors | ||
| 1719 : | 12.4 >>> The Dot Product | ||
| 1720 : | 12.5 >>> Matrices | ||
| 1721 : | 13 >>> Sequences and Series | ||
| 1722 : | 13.1 >>> Sequences | ||
| 1723 : | 13.2 >>> Defining Functions Using Sums: Arithmetic Series | ||
| 1724 : | 13.3 >>> Finite Geometric Series | ||
| 1725 : | 13.4 Infinite Geometric Series | ||
| 1726 : | 14 >>> Parametric Equations and Conic Sections | ||
| 1727 : | 14.1 >>> Parametric Equations | ||
| 1728 : | 14.2 >>> Implicitly Defined Curves and Circles | ||
| 1729 : | 14.3 >>> Ellipses | ||
| 1730 : | 14.4 >>> Hyperbolas | ||
| 1731 : | 14.5 >>> Geometric Properties of Conic Sections | ||
| 1732 : | 14.6 >>> Hyperbolic Functions | ||
| 1733 : | |||
| 1734 : | jjholt | 551 | TitleText('Calculus') |
| 1735 : | EditionText('4') | ||
| 1736 : | AuthorText('Hughes-Hallett') | ||
| 1737 : | |||
| 1738 : | 1 >>> A Library of Functions | ||
| 1739 : | 1.1 >>> Functions and Change | ||
| 1740 : | 1.2 >>> Exponential Functions | ||
| 1741 : | 1.3 >>> New Functions from Old | ||
| 1742 : | 1.4 >>> Logarithmic Functions | ||
| 1743 : | 1.5 >>> Trigonometric Functions | ||
| 1744 : | 1.6 >>> Powers, Polynomials, and Rational Functions | ||
| 1745 : | 1.7 >>> Introduction to Continuity | ||
| 1746 : | 1.8 >>> Limits | ||
| 1747 : | 2 >>> Key Concept: The Derivative | ||
| 1748 : | 2.1 >>> How do we measure speed? | ||
| 1749 : | 2.2 >>> The Derivative at a Point | ||
| 1750 : | 2.3 >>> The Derivative Function | ||
| 1751 : | 2.4 >>> Interpretations of the Derivative | ||
| 1752 : | 2.5 >>> The Second Derivative | ||
| 1753 : | 2.6 >>> Differentiability | ||
| 1754 : | 3 >>> Shortcuts to Differentiation | ||
| 1755 : | 3.1 >>> Powers and Polynomials | ||
| 1756 : | 3.2 >>> The Exponential Function | ||
| 1757 : | 3.3 >>> The Product and Quotient Rules | ||
| 1758 : | 3.4 >>> The Chain Rule | ||
| 1759 : | 3.5 >>> The Trigonometric Functions | ||
| 1760 : | 3.6 >>> The Chain Rule and Inverse Functions | ||
| 1761 : | 3.7 >>> Implicit Functions | ||
| 1762 : | 3.8 >>> Hyperbolic Functions | ||
| 1763 : | 3.9 >>> Linear Approximation and the Derivative | ||
| 1764 : | 3.10 >>> Theorems About Differentiable Functions | ||
| 1765 : | 4 >>> Using the Derivative | ||
| 1766 : | 4.1 >>> Using First and Second Derivatives | ||
| 1767 : | 4.2 >>> Families of Curves | ||
| 1768 : | 4.3 >>> Optimization | ||
| 1769 : | 4.4 >>> Applications to Marginality | ||
| 1770 : | 4.5 >>> Optimization and Modeling | ||
| 1771 : | 4.6 >>> Rates and Related Rates | ||
| 1772 : | 4.7 >>> L'Hopital's Rule, Growth, and Dominance | ||
| 1773 : | 4.8 >>> Parametric Equations | ||
| 1774 : | 5 >>> Key Concept: The Definite Integral | ||
| 1775 : | 5.1 >>> How do we measure distance traveled? | ||
| 1776 : | 5.2 >>> The Definite Integral | ||
| 1777 : | 5.3 >>> The Fundamental Theorem and Interpretations | ||
| 1778 : | 5.4 >>> Theorems About Definite Integrals | ||
| 1779 : | 6 >>> Constructing Antiderivatives | ||
| 1780 : | 6.1 >>> Antiderivatives Graphically and Numerically | ||
| 1781 : | 6.2 >>> Constructing Antiderivatives Analytically | ||
| 1782 : | 6.3 >>> Differential Equations | ||
| 1783 : | 6.4 >>> Second Fundamental Theorem of Calculus | ||
| 1784 : | 6.5 >>> The Equations of Motion | ||
| 1785 : | 7 >>> Integration | ||
| 1786 : | 7.1 >>> Integration by Substitution | ||
| 1787 : | 7.2 >>> Integration by Parts | ||
| 1788 : | 7.3 >>> Tables of Integrals | ||
| 1789 : | 7.4 >>> Algebraic Identities and Trigonometric Substitutions | ||
| 1790 : | 7.5 >>> Approximating Definite Integrals | ||
| 1791 : | 7.6 >>> Approximation Errors an Simpson's Rule | ||
| 1792 : | 7.7 >>> Improper Integrals | ||
| 1793 : | 7.8 >>> Comparison of Improper Integrals | ||
| 1794 : | 8 >>> Using the Definite Integral | ||
| 1795 : | 8.1 >>> Areas and Volumes | ||
| 1796 : | 8.2 >>> Applications to Geometry | ||
| 1797 : | 8.3 >>> Area and Arc Length in Polar Coordinates | ||
| 1798 : | 8.4 >>> Density and Center of Mass | ||
| 1799 : | 8.5 >>> Applications to Physics | ||
| 1800 : | 8.6 >>> Applications to Economics | ||
| 1801 : | 8.7 >>> Distribution Functions | ||
| 1802 : | 8.8 >>> Probability, Mean, and Median | ||
| 1803 : | 9 >>> Sequences and Series | ||
| 1804 : | 9.1 >>> Sequences | ||
| 1805 : | 9.2 >>> Geometric Series | ||
| 1806 : | 9.3 >>> Convergence of Series | ||
| 1807 : | 9.4 >>> Tests for Convergence | ||
| 1808 : | 9.5 >>> Power Series and Interval of Convergence | ||
| 1809 : | 10 >>> Approximating Functions Using Series | ||
| 1810 : | 10.1 >>> Taylor Polynomials | ||
| 1811 : | 10.2 >>> Taylor Series | ||
| 1812 : | 10.3 >>> Finding and Using Taylor Series | ||
| 1813 : | 10.4 >>> The Error in Taylor Polynomial Approximations | ||
| 1814 : | 10.5 >>> Fourier Series | ||
| 1815 : | 11 >>> Differential Equations | ||
| 1816 : | 11.1 >>> What is a differential equation? | ||
| 1817 : | 11.2 >>> Slope Fields | ||
| 1818 : | 11.3 >>> Euler's Method | ||
| 1819 : | 11.4 >>> Separation of Variables | ||
| 1820 : | 11.5 >>> Growth and Decay | ||
| 1821 : | 11.6 >>> Applications and Modeling | ||
| 1822 : | 11.7 >>> Models of Population Growth | ||
| 1823 : | 11.8 >>> Systems of Differential Equations | ||
| 1824 : | 11.9 >>> Analyzing the Phase Plane | ||
| 1825 : | 11.10 >>> Second-Order Differential Equations: Oscillations | ||
| 1826 : | 11.11 >>> Linear Second-Order Differential Equations | ||
| 1827 : | 12 >>> Functions of Several Variables | ||
| 1828 : | 12.1 >>> Functions of Two Variables | ||
| 1829 : | 12.2 >>> Graphs of Functions of Two Variables | ||
| 1830 : | 12.3 >>> Control Diagrams | ||
| 1831 : | 12.4 >>> Linear Functions | ||
| 1832 : | 12.5 >>> Functions of Three Variables | ||
| 1833 : | 12.6 >>> Limits and Continuity | ||
| 1834 : | 13 >>> A Fundamental Tool: Vectors | ||
| 1835 : | 13.1 >>> Displacement Vectors | ||
| 1836 : | 13.2 >>> Vectors in General | ||
| 1837 : | 13.3 >>> The Dot Product | ||
| 1838 : | 13.4 >>> The Cross Product | ||
| 1839 : | 14 >>> Differentiating Functions of Several Variables | ||
| 1840 : | 14.1 >>> The Partial Derivative | ||
| 1841 : | 14.2 >>> Computing Partial Derivatives Algebraically | ||
| 1842 : | 14.3 >>> Local Linearity and the Differential | ||
| 1843 : | 14.4 >>> Gradients and Directional Derivatives in the Plane | ||
| 1844 : | 14.5 >>> Gradients and Directional Derivatives in Space | ||
| 1845 : | 14.6 >>> The Chain Rule | ||
| 1846 : | 14.7 >>> Second-Order Partial Derivatives | ||
| 1847 : | 14.8 >>> Differentiability | ||
| 1848 : | 15 >>> Optimization: Local and Global Extrema | ||
| 1849 : | 15.1 >>> Local Extrema | ||
| 1850 : | 15.2 >>> Optimization | ||
| 1851 : | 15.3 >>> Constrained Optimization: Lagrange Multipliers | ||
| 1852 : | 16 >>> Integrating Functions of Several Variables | ||
| 1853 : | 16.1 >>> The Definite Integral of a Function of Two Variables | ||
| 1854 : | 16.2 >>> Iterated Integrals | ||
| 1855 : | 16.3 >>> Triple Integrals | ||
| 1856 : | 16.4 >>> Double Integrals in Polar Coordinates | ||
| 1857 : | 16.5 >>> Integrals in Cylindrical and Spherical Coordinates | ||
| 1858 : | 16.6 >>> Applications of Integration to Probability | ||
| 1859 : | 16.7 >>> Change of Variables in Multiple Integral | ||
| 1860 : | 17 >>> Parameterization and Vector Fields | ||
| 1861 : | 17.1 >>> Parameterized Curves | ||
| 1862 : | 17.2 >>> Motion, Velocity, and Acceleration | ||
| 1863 : | 17.3 >>> Vector Fields | ||
| 1864 : | 17.4 >>> The Flow of a Vector Field | ||
| 1865 : | 17.5 >>> Parameterized Surfaces | ||
| 1866 : | 18 >>> Line Integrals | ||
| 1867 : | 18.1 >>> The Idea of a Line Integral | ||
| 1868 : | 18.2 >>> Computing Line Integrals Over Parameterized Curves | ||
| 1869 : | 18.3 >>> Gradient Fields and Path-Independent Fields | ||
| 1870 : | 18.4 >>> Path-Independent Vector Fields and Green's Theorem | ||
| 1871 : | 19 >>> Flux Integrals | ||
| 1872 : | 19.1 >>> The Idea of a Flux Integral | ||
| 1873 : | 19.2 >>> Flux Integrals for Graphs, Cylinders, and Spheres | ||
| 1874 : | 19.3 >>> Flux Integrals over Parameterized Surfaces | ||
| 1875 : | 20 >>> Calculus of Vector Fields | ||
| 1876 : | 20.1 >>> The Divergence of a Vector Field | ||
| 1877 : | 20.2 >>> The Divergence Theorem | ||
| 1878 : | 20.3 >>> The Curl of a Vector Field | ||
| 1879 : | 20.4 >>> Stokes' Theorem | ||
| 1880 : | 20.5 >>> The Three Fundamental Theorems | ||
| 1881 : | sh002i | 556 | |
| 1882 : | glarose | 1203 | TitleText('Calculus') |
| 1883 : | EditionText('5') | ||
| 1884 : | AuthorText('Hughes-Hallett') | ||
| 1885 : | |||
| 1886 : | 1 >>> A Library of Functions | ||
| 1887 : | 1.1 >>> Functions and Change | ||
| 1888 : | 1.2 >>> Exponential Functions | ||
| 1889 : | 1.3 >>> New Functions From Old | ||
| 1890 : | 1.4 >>> Logarithmic Functions | ||
| 1891 : | 1.5 >>> Trigonometric Functions | ||
| 1892 : | 1.6 >>> Powers, Polynomials and Rational Functions | ||
| 1893 : | 1.7 >>> Introduction to Continuity | ||
| 1894 : | 1.8 >>> Limits | ||
| 1895 : | 2 >>> Key Concept: The Derivative | ||
| 1896 : | 2.1 >>> How Do We Measure Speed | ||
| 1897 : | 2.2 >>> The Derivative at a Point | ||
| 1898 : | 2.3 >>> The Derivative Function | ||
| 1899 : | 2.4 >>> Interpretations of the Derivative | ||
| 1900 : | 2.5 >>> The Second Derivative | ||
| 1901 : | 2.6 >>> Differentiability | ||
| 1902 : | 3 >>> Short-Cuts to Differentiation | ||
| 1903 : | 3.1 >>> Powers and Polynomials | ||
| 1904 : | 3.2 >>> The Exponential Function | ||
| 1905 : | 3.3 >>> The Product and Quotient Rules | ||
| 1906 : | 3.4 >>> The Chain Rule | ||
| 1907 : | 3.5 >>> The Trigonometric Functions | ||
| 1908 : | 3.6 >>> The Chain Rule and Inverse Functions | ||
| 1909 : | 3.7 >>> Implicit Functions | ||
| 1910 : | 3.8 >>> Hyperbolic Functions | ||
| 1911 : | 3.9 >>> Linear Approximation and the Derivative | ||
| 1912 : | 3.10 >>> Theorems About Differentiable Functions | ||
| 1913 : | 4 >>> Using the Derivative | ||
| 1914 : | 4.1 >>> Using First and Second Derivatives | ||
| 1915 : | 4.2 >>> Optimization | ||
| 1916 : | 4.3 >>> Families of Functions | ||
| 1917 : | 4.4 >>> Optimization, Geometry and Modeling | ||
| 1918 : | 4.5 >>> Applications to Marginality | ||
| 1919 : | 4.6 >>> Rates and Related Rates | ||
| 1920 : | 4.7 >>> L'Hopital's Rule, Growth and Dominance | ||
| 1921 : | 4.8 >>> Parametric Equations | ||
| 1922 : | 5 >>> Key Concept: The Definite Integral | ||
| 1923 : | 5.1 >>> How Do We Measure Distance Traveled | ||
| 1924 : | 5.2 >>> The Definite Integral | ||
| 1925 : | 5.3 >>> The Fundamental Theorem and Interpretations | ||
| 1926 : | 5.4 >>> Theorems about Definite Integrals | ||
| 1927 : | 6 >>> Constructing Antiderivatives | ||
| 1928 : | 6.1 >>> Antiderivatives Graphically and Numerically | ||
| 1929 : | 6.2 >>> Constructing Antiderivatives Analytically | ||
| 1930 : | 6.3 >>> Differential Equations | ||
| 1931 : | 6.4 >>> The Second Fundamental Theorem of Calculus | ||
| 1932 : | 6.5 >>> The Equations of Motion | ||
| 1933 : | 7 >>> Integration | ||
| 1934 : | 7.1 >>> Integration by Substitution | ||
| 1935 : | 7.2 >>> Integration by Parts | ||
| 1936 : | 7.3 >>> Tables of Integrals | ||
| 1937 : | 7.4 >>> Algebraic Identities and Trigonometric Substitutions | ||
| 1938 : | 7.5 >>> Approximating Definite Integrals | ||
| 1939 : | 7.6 >>> Approximation Errors and Simpson's Rule | ||
| 1940 : | 7.7 >>> Improper Integrals | ||
| 1941 : | 7.8 >>> Comparison of Improper Integrals | ||
| 1942 : | 8 >>> Using the Definite Integral | ||
| 1943 : | 8.1 >>> Areas and Volumes | ||
| 1944 : | 8.2 >>> Applications to Geometry | ||
| 1945 : | 8.3 >>> Area and Arc Length in Polar Coordinates | ||
| 1946 : | 8.4 >>> Density and Center of Mass | ||
| 1947 : | 8.5 >>> Applications to Physics | ||
| 1948 : | 8.6 >>> Applications to Economics | ||
| 1949 : | 8.7 >>> Distribution Functions | ||
| 1950 : | 8.8 >>> Probability, Mean and Median | ||
| 1951 : | 9 >>> Sequences and Series | ||
| 1952 : | 9.1 >>> Sequences | ||
| 1953 : | 9.2 >>> Geometric Series | ||
| 1954 : | 9.3 >>> Convergence of Series | ||
| 1955 : | 9.4 >>> Tests for Convergence | ||
| 1956 : | 9.5 >>> Power Series and Interval of Convergence | ||
| 1957 : | 10 >>> Approximating Functions Using Series | ||
| 1958 : | 10.1 >>> Taylor Polynomials | ||
| 1959 : | 10.2 >>> Taylor Series | ||
| 1960 : | 10.3 >>> Finding and Using Taylor Series | ||
| 1961 : | 10.4 >>> The Error in Taylor Polynomial Approximations | ||
| 1962 : | 10.5 >>> Fourier Series | ||
| 1963 : | 11 >>> Differential Equations | ||
| 1964 : | 11.1 >>> What is a Differential Equation | ||
| 1965 : | 11.2 >>> Slope Fields | ||
| 1966 : | 11.3 >>> Euler's Method | ||
| 1967 : | 11.4 >>> Separation of Variables | ||
| 1968 : | 11.5 >>> Growth and Decay | ||
| 1969 : | 11.6 >>> Applications and Modeling | ||
| 1970 : | 11.7 >>> The Logistic Model | ||
| 1971 : | 11.8 >>> Systems of Differential Equations | ||
| 1972 : | 11.9 >>> Analyzing the Phase Plane | ||
| 1973 : | 11.10 >>> Second-Order Differential Equations: Oscillations | ||
| 1974 : | 11.11 >>> Linear Second-Order Differential Equations | ||
| 1975 : | 12 >>> Functions of Several Variables | ||
| 1976 : | 12.1 >>> Functions of Two Variables | ||
| 1977 : | 12.2 >>> Graphs of Functions of Two Variables | ||
| 1978 : | 12.3 >>> Control Diagrams | ||
| 1979 : | 12.4 >>> Linear Functions | ||
| 1980 : | 12.5 >>> Functions of Three Variables | ||
| 1981 : | 12.6 >>> Limits and Continuity | ||
| 1982 : | 13 >>> A Fundamental Tool: Vectors | ||
| 1983 : | 13.1 >>> Displacement Vectors | ||
| 1984 : | 13.2 >>> Vectors in General | ||
| 1985 : | 13.3 >>> The Dot Product | ||
| 1986 : | 13.4 >>> The Cross Product | ||
| 1987 : | 14 >>> Differentiating Functions of Several Variables | ||
| 1988 : | 14.1 >>> The Partial Derivative | ||
| 1989 : | 14.2 >>> Computing Partial Derivatives Algebraically | ||
| 1990 : | 14.3 >>> Local Linearity and the Differential | ||
| 1991 : | 14.4 >>> Gradients and Directional Derivatives in the Plane | ||
| 1992 : | 14.5 >>> Gradients and Directional Derivatives in Space | ||
| 1993 : | 14.6 >>> The Chain Rule | ||
| 1994 : | 14.7 >>> Second-Order Partial Derivatives | ||
| 1995 : | 14.8 >>> Differentiability | ||
| 1996 : | 15 >>> Optimization: Local and Global Extrema | ||
| 1997 : | 15.1 >>> Local Extrema | ||
| 1998 : | 15.2 >>> Optimization | ||
| 1999 : | 15.3 >>> Constrained Optimization: Lagrange Multipliers | ||
| 2000 : | 16 >>> Integrating Functions of Several Variables | ||
| 2001 : | 16.1 >>> The Definite Integral of a Function of Two Variables | ||
| 2002 : | 16.2 >>> Iterated Integrals | ||
| 2003 : | 16.3 >>> Triple Integrals | ||
| 2004 : | 16.4 >>> Double Integrals in Polar Coordinates | ||
| 2005 : | 16.5 >>> Integrals in Cylindrical and Spherical Coordinates | ||
| 2006 : | 16.6 >>> Applications of Integration to Probability | ||
| 2007 : | 16.7 >>> Change of Variables in Multiple Integral | ||
| 2008 : | 17 >>> Parameterization and Vector Fields | ||
| 2009 : | 17.1 >>> Parameterized Curves | ||
| 2010 : | 17.2 >>> Motion, Velocity, and Acceleration | ||
| 2011 : | 17.3 >>> Vector Fields | ||
| 2012 : | 17.4 >>> The Flow of a Vector Field | ||
| 2013 : | 17.5 >>> Parameterized Surfaces | ||
| 2014 : | 18 >>> Line Integrals | ||
| 2015 : | 18.1 >>> The Idea of a Line Integral | ||
| 2016 : | 18.2 >>> Computing Line Integrals Over Parameterized Curves | ||
| 2017 : | 18.3 >>> Gradient Fields and Path-Independent Fields | ||
| 2018 : | 18.4 >>> Path-Independent Vector Fields and Green's Theorem | ||
| 2019 : | 19 >>> Flux Integrals | ||
| 2020 : | 19.1 >>> The Idea of a Flux Integral | ||
| 2021 : | 19.2 >>> Flux Integrals for Graphs, Cylinders, and Spheres | ||
| 2022 : | 19.3 >>> Flux Integrals over Parameterized Surfaces | ||
| 2023 : | 20 >>> Calculus of Vector Fields | ||
| 2024 : | 20.1 >>> The Divergence of a Vector Field | ||
| 2025 : | 20.2 >>> The Divergence Theorem | ||
| 2026 : | 20.3 >>> The Curl of a Vector Field | ||
| 2027 : | 20.4 >>> Stokes' Theorem | ||
| 2028 : | 20.5 >>> The Three Fundamental Theorems | ||
| 2029 : | |||
| 2030 : | sh002i | 556 | TitleText('Calculus: Early Transcendentals') |
| 2031 : | EditionText('1') | ||
| 2032 : | AuthorText('Rogawski') | ||
| 2033 : | |||
| 2034 : | 1 >>> Precalculus Review | ||
| 2035 : | sh002i | 587 | 1.1 >>> Real Numbers, Functions, and Graphs |
| 2036 : | sh002i | 556 | 1.2 >>> Linear and Quadratic Functions |
| 2037 : | 1.3 >>> The Basic Classes of Functions | ||
| 2038 : | 1.4 >>> Trigonometric Functions | ||
| 2039 : | 1.5 >>> Inverse Functions | ||
| 2040 : | 1.6 >>> Exponential and Logarithmic Functions | ||
| 2041 : | 1.7 >>> Technology: Calculators and Computers | ||
| 2042 : | 2 >>> Limits | ||
| 2043 : | 2.1 >>> Limits, Rates of Change, and Tangent Lines | ||
| 2044 : | 2.2 >>> Limits: A Numerical and Graphical Approach | ||
| 2045 : | 2.3 >>> Basic Limit Laws | ||
| 2046 : | 2.4 >>> Limits and Continuity | ||
| 2047 : | 2.5 >>> Evaluating Limits Algebraically | ||
| 2048 : | 2.6 >>> Trigonometric Limits | ||
| 2049 : | 2.7 >>> Intermediate Value Theorem | ||
| 2050 : | 2.8 >>> The Formal Definition of a Limit | ||
| 2051 : | 3 >>> Differentiation | ||
| 2052 : | 3.1 >>> Definition of the Derivative | ||
| 2053 : | 3.2 >>> The Derivative as a Function | ||
| 2054 : | 3.3 >>> Product and Quotient Rules | ||
| 2055 : | 3.4 >>> Rates of Change | ||
| 2056 : | 3.5 >>> Higher Derivatives | ||
| 2057 : | sh002i | 587 | 3.6 >>> Trigonometric Functions |
| 2058 : | sh002i | 556 | 3.7 >>> The Chain Rule |
| 2059 : | 3.8 >>> Implicit Differentiation | ||
| 2060 : | 3.9 >>> Derivatives of Inverse Functions | ||
| 2061 : | sh002i | 587 | 3.10 >>> Derivatives of General Exponential and Logarithmic Functions |
| 2062 : | sh002i | 556 | 3.11 >>> Related Rates |
| 2063 : | 4 >>> Applications of the Derivative | ||
| 2064 : | 4.1 >>> Linear Approximation and Applications | ||
| 2065 : | 4.2 >>> Extreme Values | ||
| 2066 : | 4.3 >>> The Mean Value Theorem and Monotonicity | ||
| 2067 : | 4.4 >>> The Shape of a Graph | ||
| 2068 : | 4.5 >>> Graph Sketching and Asymptotes | ||
| 2069 : | 4.6 >>> Applied Optimization | ||
| 2070 : | 4.7 >>> L'Hopital's Rule | ||
| 2071 : | 4.8 >>> Newton's Method | ||
| 2072 : | 4.9 >>> Antiderivatives | ||
| 2073 : | 5 >>> The Integral | ||
| 2074 : | 5.1 >>> Approximating and Computing Area | ||
| 2075 : | 5.2 >>> The Definite Integral | ||
| 2076 : | 5.3 >>> The Fundamental Theorem of Calculus, Part I | ||
| 2077 : | 5.4 >>> The Fundamental Theorem of Calculus, Part II | ||
| 2078 : | 5.5 >>> Net or Total Change as the Integral of a Rate | ||
| 2079 : | 5.6 >>> Substitution Method | ||
| 2080 : | sh002i | 587 | 5.7 >>> Further Transcendental Functions |
| 2081 : | sh002i | 556 | 5.8 >>> Exponential Growth and Decay |
| 2082 : | 6 >>> Applications of the Integral | ||
| 2083 : | 6.1 >>> Area Between Two Curves | ||
| 2084 : | 6.2 >>> Setting Up Integrals: Volumes, Density, Average Value | ||
| 2085 : | 6.3 >>> Volumes of Revolution | ||
| 2086 : | 6.4 >>> The Method of Cylindrical Shells | ||
| 2087 : | 6.5 >>> Work and Energy | ||
| 2088 : | 7 >>> Techniques of Integration | ||
| 2089 : | 7.1 >>> Numerical Integration | ||
| 2090 : | 7.2 >>> Integration by Parts | ||
| 2091 : | 7.3 >>> Trigonometric Integrals | ||
| 2092 : | 7.4 >>> Trigonometric Substitution | ||
| 2093 : | 7.5 >>> Integrals of Hyperbolic and Inverse Hyperbolic Functions | ||
| 2094 : | 7.6 >>> The Method of Partial Fractions | ||
| 2095 : | 7.7 >>> Improper Integrals | ||
| 2096 : | 8 >>> Further Applications of the Integral and Taylor Polynomials | ||
| 2097 : | 8.1 >>> Arc Length and Surface Area | ||
| 2098 : | 8.2 >>> Fluid Pressure and Force | ||
| 2099 : | 8.3 >>> Center of Mass | ||
| 2100 : | 8.4 >>> Taylor Polynomials | ||
| 2101 : | 9 >>> Introduction to Differential Equations | ||
| 2102 : | sh002i | 587 | 9.1 >>> Solving Differential Equations |
| 2103 : | 9.2 >>> Models Involving y'=k(y-b) | ||
| 2104 : | sh002i | 558 | 9.3 >>> Graphical and Numerical Methods |
| 2105 : | sh002i | 556 | 9.4 >>> The Logistic Equation |
| 2106 : | sh002i | 558 | 9.5 >>> First-Order Linear Equations |
| 2107 : | sh002i | 556 | 10 >>> Infinite Series |
| 2108 : | 10.1 >>> Sequences | ||
| 2109 : | 10.2 >>> Summing an Infinite Series | ||
| 2110 : | 10.3 >>> Convergence of Series with Positive Terms | ||
| 2111 : | 10.4 >>> Absolute and Conditional Convergence | ||
| 2112 : | 10.5 >>> The Ratio and Root Tests | ||
| 2113 : | 10.6 >>> Power Series | ||
| 2114 : | 10.7 >>> Taylor Series | ||
| 2115 : | 11 >>> Parametric Equations, Polar Coordinates, and Conic Sections | ||
| 2116 : | 11.1 >>> Parametric Equations | ||
| 2117 : | 11.2 >>> Arc Length and Speed | ||
| 2118 : | 11.3 >>> Polar Coordinates | ||
| 2119 : | 11.4 >>> Area and Arc Length in Polar Coordinates | ||
| 2120 : | 11.5 >>> Conic Sections | ||
| 2121 : | 12 >>> Vector Geometry | ||
| 2122 : | 12.1 >>> Vectors in the Plane | ||
| 2123 : | 12.2 >>> Vectors in Three Dimensions | ||
| 2124 : | 12.3 >>> Dot Product and the Angle Between Two Vectors | ||
| 2125 : | 12.4 >>> The Cross Product | ||
| 2126 : | 12.5 >>> Planes in Three-Space | ||
| 2127 : | sh002i | 587 | 12.6 >>> A Survey of Quadric Surfaces |
| 2128 : | sh002i | 556 | 12.7 >>> Cylindrical and Spherical Coordinates |
| 2129 : | 13 >>> Calculus of Vector-Valued Functions | ||
| 2130 : | 13.1 >>> Vector-Valued Functions | ||
| 2131 : | 13.2 >>> Calculus of Vector-Valued Functions | ||
| 2132 : | 13.3 >>> Arc Length and Speed | ||
| 2133 : | 13.4 >>> Curvature | ||
| 2134 : | 13.5 >>> Motion in Three-Space | ||
| 2135 : | 13.6 >>> Planetary Motion According to Kepler and Newton | ||
| 2136 : | 14 >>> Differentiation in Several Variables | ||
| 2137 : | 14.1 >>> Functions in Two or More Variables | ||
| 2138 : | 14.2 >>> Limits and Continuity in Several Variables | ||
| 2139 : | 14.3 >>> Partial Derivatives | ||
| 2140 : | sh002i | 587 | 14.4 >>> Differentiability, Linear Approximation, and Tangent Planes |
| 2141 : | sh002i | 556 | 14.5 >>> The Gradient and Directional Derivatives |
| 2142 : | 14.6 >>> The Chain Rule | ||
| 2143 : | 14.7 >>> Optimization in Several Variables | ||
| 2144 : | 14.8 >>> Lagrange Multipliers: Optimizing with a Constraint | ||
| 2145 : | 15 >>> Multiple Integration | ||
| 2146 : | 15.1 >>> Integrals in Several Variables | ||
| 2147 : | 15.2 >>> Double Integrals over More General Regions | ||
| 2148 : | 15.3 >>> Triple Integrals | ||
| 2149 : | 15.4 >>> Integration in Polar, Cylindrical, and Spherical Coordinates | ||
| 2150 : | 15.5 >>> Change of Variables | ||
| 2151 : | 16 >>> Line and Surface Integrals | ||
| 2152 : | 16.1 >>> Vector Fields | ||
| 2153 : | 16.2 >>> Line Integrals | ||
| 2154 : | 16.3 >>> Conservative Vector Fields | ||
| 2155 : | 16.4 >>> Parametrized Surfaces and Surface Integrals | ||
| 2156 : | 16.5 >>> Integrals of Vector Fields | ||
| 2157 : | 17 >>> Fundamental Theorems of Vector Analysis | ||
| 2158 : | 17.1 >>> Green's Theorem | ||
| 2159 : | 17.2 >>> Stokes' Theorem | ||
| 2160 : | 17.3 >>> Divergence Theorem |
| aubreyja at gmail dot com | ViewVC Help |
| Powered by ViewVC 1.0.9 |