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    5 
    6 TitleText('Financial Mathematics')
    7 EditionText('1')
    8 AuthorText('Holt')
    9 
   10 1   >>> Introduction to Interest
   11 1.1 >>> Simple Interest
   12 1.2 >>> Compound Interest
   13 1.3 >>> Effective and Nominal Rates of Interest
   14 1.4 >>> Present and Future Value
   15 
   16 2   >>> Equations of Value
   17 2.1 >>> Time Value of Money
   18 2.2 >>> Unknown Time and Logarithms
   19 2.3 >>> Dollar Weighted Rate of Return
   20 2.4 >>> Time Weighted Rate of Return
   21 
   22 3   >>> Annuities
   23 3.1 >>> Geometric Sums
   24 3.2 >>> Annuities
   25 3.3 >>> Loans
   26 3.4 >>> Sinking Funds
   27 3.5 >>> Varying Payments
   28 3.6 >>> Perpetuities
   29 
   30 4   >>> Bonds
   31 4.1 >>> Yield Rates
   32 4.2 >>> Bonds
   33 4.3 >>> Book Value
   34 4.4 >>> Other Bonds
   35 
   36 5   >>> Probability and Contingent Payments
   37 5.1 >>> Introduction to Probability
   38 5.2 >>> Expected Values
   39 5.3 >>> Contingent Payments
   40 
   41 6   >>> Options
   42 6.1 >>> Introduction to Options
   43 6.2 >>> Hedging Strategies
   44 6.3 >>> Binomial Trees
   45 
   46 TitleText('Mathematical Statistics')
   47 EditionText('6')
   48 AuthorText('Wackerly, Mendenhall, Scheaffer')
   49 
   50 1 >>> What Is Statistics?
   51 1.1 >>> Introduction
   52 1.2 >>> Characterizing a Set of Measurements: Graphical Methods
   53 1.3 >>> Characterizing a Set of Measurements: Numerical Methods
   54 1.4 >>> How Inferences Are Made
   55 1.5 >>> Theory and Reality
   56 1.6 >>> Summary
   57 
   58 2 >>> Probability
   59 2.1 >>> Introduction
   60 2.2 >>> Probability and Inference
   61 2.3 >>> A Review of Set Notation
   62 2.4 >>> A Probabilistic Model for an Experiment: The Discrete Case
   63 2.5 >>> Calculating the Probability of an Event: The Sample-Point Method
   64 2.6 >>> Tools for Counting Sample Points
   65 2.7 >>> Conditional Probability and the Independence of Events
   66 2.8 >>> Two Laws of Probability
   67 2.9 >>> Calculating the Probability of an Event: The Event-Composition Methods
   68 2.10 >>> The Law of Total Probability and Bayes's Rule
   69 2.11 >>> Numerical Events and Random Variables
   70 2.12 >>> Random Sampling
   71 2.13 >>> Summary
   72 
   73 3 >>> Discrete Random Variables and Their Probability Distributions
   74 3.1 >>> Basic Definition
   75 3.2 >>> The Probability Distribution for Discrete Random Variable
   76 3.3 >>> The Expected Value of Random Variable or a Function of Random Variable
   77 3.4 >>> The Binomial Probability Distribution
   78 3.5 >>> The Geometric Probability Distribution
   79 3.6 >>> The Negative Binomial Probability Distribution
   80 3.7 >>> The Hypergeometric Probability Distribution
   81 3.8 >>> Moments and Moment-Generating Functions
   82 3.9 >>> Probability-Generating Functions
   83 3.10 >>> Tchebysheff's Theorem
   84 3.11 >>> Summary
   85 
   86 4 >>> Continuous Random Variables and Their Probability Distributions
   87 4.1 >>> Introduction
   88 4.2 >>> The Probability Distribution for Continuous Random Variable
   89 4.3 >>> The Expected Value for Continuous Random Variable
   90 4.4 >>> The Uniform Probability Distribution
   91 4.5 >>> The Normal Probability Distribution
   92 4.6 >>> The Gamma Probability Distribution
   93 4.7 >>> The Beta Probability Distribution
   94 4.8 >>> Some General Comments
   95 4.9 >>> Other Expected Values
   96 4.10 >>> Tchebysheff's Theorem
   97 4.11 >>> Expectations of Discontinuous Functions and Mixed Probability Distributions
   98 4.12 >>> Summary
   99 
  100 5 >>> Multivariate Probability Distributions
  101 5.1 >>> Introduction
  102 5.2 >>> Bivariate and Multivariate Probability Distributions
  103 5.3 >>> Independent Random Variables
  104 5.4 >>> The Expected Value of a Function of Random Variables
  105 5.5 >>> Special Theorems
  106 5.6 >>> The Covariance of Two Random Variables
  107 5.7 >>> The Expected Value and Variance of Linear Functions of Random Variables
  108 5.8 >>> The Multinomial Probability Distribution
  109 5.9 >>> The Bivariate Normal Distribution
  110 5.10 >>> Conditional Expectations
  111 5.11 >>> Summary
  112 
  113 6 >>> Functions of Random Variables
  114 6.1 >>> Introductions
  115 6.2 >>> Finding the Probability Distribution of a Function of Random Variables
  116 6.3 >>> The Method of Distribution Functions
  117 6.4 >>> The Methods of Transformations
  118 6.5 >>> Multivariable Transformations Using Jacobians
  119 6.6 >>> Order Statistics
  120 6.7 >>> Summary
  121 
  122 7 >>> Sampling Distributions and the Central Limit Theorem
  123 7.1 >>> Introduction
  124 7.2 >>> Sampling Distributions Related to the Normal Distribution
  125 7.3 >>> The Central Limit Theorem
  126 7.4 >>> A Proof of the Central Limit Theorem
  127 7.5 >>> The Normal Approximation to the Binomial Distributions
  128 7.6 >>> Summary
  129 
  130 8 >>> Estimation
  131 8.1 >>> Introduction
  132 8.2 >>> The Bias and Mean Square Error of Point Estimators
  133 8.3 >>> Some Common Unbiased Point Estimators
  134 8.4 >>> Evaluating the Goodness of Point Estimator
  135 8.5 >>> Confidence Intervals
  136 8.6 >>> Large-Sample Confidence Intervals Selecting the Sample Size
  137 8.7 >>> Small-Sample Confidence Intervals for u and u1-u2
  138 8.8 >>> Confidence Intervals for o2
  139 8.9 >>> Summary
  140 
  141 9 >>> Properties of Point Estimators and Methods of Estimation
  142 9.1 >>> Introduction
  143 9.2 >>> Relative Efficiency
  144 9.3 >>> Consistency
  145 9.4 >>> Sufficiency
  146 9.5 >>> The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation
  147 9.6 >>> The Method of Moments
  148 9.7 >>> The Method of Maximum Likelihood
  149 9.8 >>> Some Large-Sample Properties of MLEs
  150 9.9 >>> Summary
  151 
  152 10 >>> Hypothesis Testing
  153 10.1 >>> Introduction
  154 10.2 >>> Elements of a Statistical Test
  155 10.3 >>> Common Large-Sample Tests
  156 10.4 >>> Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test
  157 10.5 >>> Relationships Between Hypothesis Testing Procedures and Confidence Intervals
  158 10.6 >>> Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values
  159 10.7 >>> Some Comments on the Theory of Hypothesis Testing
  160 10.8 >>> Small-Sample Hypothesis Testing for u and u1-u2
  161 10.9 >>> Testing Hypotheses Concerning Variances
  162 10.10 >>> Power of Test and the Neyman-Pearson Lemma
  163 10.11 >>> Likelihood Ration Test
  164 10.12 >>> Summary
  165 
  166 11 >>> Linear Models and Estimation by Least Squares
  167 11.1 >>> Introduction
  168 11.2 >>> Linear Statistical Models
  169 11.3 >>> The Method of Least Squares
  170 11.4 >>> Properties of the Least Squares Estimators for the Simple Linear Regression Model
  171 11.5 >>> Inference Concerning the Parameters BI
  172 11.6 >>> Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression
  173 11.7 >>> Predicting a Particular Value of Y Using Simple Linear Regression
  174 11.8 >>> Correlation
  175 11.9 >>> Some Practical Examples
  176 11.10 >>> Fitting the Linear Model by Using Matrices
  177 11.11 >>> Properties of the Least Squares Estimators for the Multiple Linear Regression Model
  178 11.12 >>> Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression
  179 11.13 >>> Prediction a Particular Value of Y Using Multiple Regression
  180 11.14 >>> A Test for H0: Bg+1 + Bg+2 = ? = Bk = 0
  181 11.15 >>> Summary and Concluding Remarks
  182 
  183 12 >>> Considerations in Designing Experiments
  184 12.1 >>> The Elements Affecting the Information in a Sample
  185 12.2 >>> Designing Experiment to Increase Accuracy
  186 12.3 >>> The Matched Pairs Experiment
  187 12.4 >>> Some Elementary Experimental Designs
  188 12.5 >>> Summary
  189 
  190 13 >>> The Analysis of Variance
  191 13.1 >>> Introduction
  192 13.2 >>> The Analysis of Variance Procedure
  193 13.3 >>> Comparison of More than Two Means: Analysis of Variance for a One-way Layout
  194 13.4 >>> An Analysis of Variance Table for a One-Way Layout
  195 13.5 >>> A Statistical Model of the One-Way Layout
  196 13.6 >>> Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout
  197 13.7 >>> Estimation in the One-Way Layout
  198 13.8 >>> A Statistical Model for the Randomized Block Design
  199 13.9 >>> The Analysis of Variance for a Randomized Block Design
  200 13.10 >>> Estimation in the Randomized Block Design
  201 13.11 >>> Selecting the Sample Size
  202 13.12 >>> Simultaneous Confidence Intervals for More than One Parameter
  203 13.13 >>> Analysis of Variance Using Linear Models
  204 13.14 >>> Summary
  205 
  206 14 >>> Analysis of Categorical Data
  207 14.1 >>> A Description of the Experiment
  208 14.2 >>> The Chi-Square Test
  209 14.3 >>> A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test
  210 14.4 >>> Contingency Tables
  211 14.5 >>> r x c Tables with Fixed Row or Column Totals
  212 14.6 >>> Other Applications
  213 14.7 >>> Summary and Concluding Remarks
  214 
  215 15 >>> Nonparametric Statistics
  216 15.1 >>> Introduction
  217 15.2 >>> A General Two-Sampling Shift Model
  218 15.3 >>> A Sign Test for a Matched Pairs Experiment
  219 15.4 >>> The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment
  220 15.5 >>> The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples
  221 15.6 >>> The Mann-Whitney U Test: Independent Random Samples
  222 15.7 >>> The Kruskal-Wallis Test for One-Way Layout
  223 15.8 >>> The Friedman Test for Randomized Block Designs
  224 15.9 >>> The Runs Test: A Test for Randomness
  225 15.10 >>> Rank Correlation Coefficient
  226 15.11 >>> Some General Comments on Nonparametric Statistical Test
  227 
  228 16 >>> Appendix 1: Matrices and Other Useful Mathematical Results
  229 16.1 >>> Appendix 1.1: Matrices and Matrix Algebra
  230 16.2 >>> Appendix 1.2: Addition of Matrices
  231 16.3 >>> Appendix 1.3: Multiplication of a Matrix by a Real Number
  232 16.4 >>> Appendix 1.4: Matrix Multiplication
  233 16.5 >>> Appendix 1.5: Identity Elements
  234 16.6 >>> Appendix 1.6: The Inverse of a Matrix
  235 16.7 >>> Appendix 1.7: The Transpose of a Matrix
  236 16.8 >>> Appendix 1.8: A Matrix Expression for a System of Simultaneous Linear Equations
  237 16.9 >>> Appendix 1.9: Inverting a Matrix
  238 16.10 >>> Appendix 1.10: Solving a System of Simultaneous Linear Equations
  239 16.11 >>> Appendix 1.11: Other Useful Mathematical Results
  240 
  241 17 >>> Appendix 2: Common Probability Distributions, Means, Variances, and Moment Generating Functions
  242 17.1 >>> Appendix 2.1: Discrete Distributions
  243 17.2 >>> Appendix 2.2: Continuous Distributions.
  244 
  245 18 >>> Appendix 3: Tables
  246 18.1 >>> Appendix 3.1: Binomial Probabilities
  247 18.2 >>> Appendix 3.2: Table of e-x
  248 18.3 >>> Appendix 3.3: Poisson Probabilities
  249 18.4 >>> Appendix 3.4: Normal Curve Areas
  250 18.5 >>> Appendix 3.5: Percentage Points of the t Distributions
  251 18.6 >>> Appendix 3.6: Percentage Points of the F Distributions
  252 18.7 >>> Appendix 3.7: Distribution of Function U
  253 18.8 >>> Appendix 3.8: Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test
  254 18.9 >>> Appendix 3.9: Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a)
  255 18.10 >>> Appendix 3.10: Critical Values of Pearman's Rank Correlation Coefficient
  256 18.11 >>> Appendix 3.11: Random Numbers
  257 
  258 TitleText('Calculus')
  259 EditionText('5')
  260 AuthorText('Stewart')
  261 
  262 1 >>> Functions and Models
  263 1.1 >>> Four Ways to Represent a Function
  264 1.2 >>> Mathematical Models: A Catalog of Essential Functions
  265 1.3 >>> New Functions from Old Functions
  266 1.4 >>> Graphing Calculators and Computers
  267 
  268 2 >>> Limits and Rates of Change
  269 2.1 >>> The Tangent and Velocity Problems
  270 2.2 >>> The Limit of a Function
  271 2.3 >>> Calculating Limits Using the Limit Laws
  272 2.4 >>> The Precise Definition of a Limit
  273 2.5 >>> Continuity
  274 2.6 >>> Tangents, Velocities, and Other Rates of Change
  275 
  276 3 >>> Derivatives
  277 3.1 >>> Derivatives
  278 3.2 >>> The Derivative as a Function
  279 3.3 >>> Differentiation Formulas
  280 3.4 >>> Rates of Change in the Natural and Social Sciences
  281 3.5 >>> Derivatives of Trigonometric Functions
  282 3.6 >>> The Chain Rule
  283 3.7 >>> Implicit Differentiation
  284 3.8 >>> Higher Derivatives
  285 3.9 >>> Related Rates
  286 3.10 >>> Linear Approximations and Differentials
  287 
  288 4 >>> Applications of Differentiation
  289 4.1 >>> Maximum and Minimum Values
  290 4.2 >>> The Mean Value Theorem
  291 4.3 >>> How Derivatives Affect the Shape of a Graph
  292 4.4 >>> Limits at Infinity; Horizontal Asymptotes
  293 4.5 >>> Summary of Curve Sketching
  294 4.6 >>> Graphing with Calculus and Calculators
  295 4.7 >>> Optimization Problems
  296 4.8 >>> Applications to Business and Economics
  297 4.9 >>> Newton's Method
  298 4.10 >>> Antiderivatives
  299 
  300 5 >>> Integrals
  301 5.1 >>> Areas and Distances
  302 5.2 >>> The Definite Integral
  303 5.3 >>> The Fundamental Theorem of Calculus
  304 5.4 >>> Indefinite Integrals and the Net Change Theorem
  305 5.5 >>> The Substitution Rule
  306 
  307 6 >>> Applications of Integration
  308 6.1 >>> Areas between Curves
  309 6.2 >>> Volumes
  310 6.3 >>> Volumes by Cylindrical Shells
  311 6.4 >>> Work
  312 6.5 >>> Average Value of a Function
  313 
  314 7 >>> Inverse Functions
  315 7.1 >>> Inverse Functions
  316 7.2 >>> Exponential Functions and Their Derivatives
  317 7.3 >>> Logarithmic Functions
  318 7.4 >>> Derivatives of Logarithmic Functions
  319 7.5 >>> Inverse Trigonometric Functions
  320 7.6 >>> Hyperbolic Functions
  321 7.7 >>> Indeterminate Forms and L'Hospital's Rule
  322 
  323 8 >>> Techniques of Integration
  324 8.1 >>> Integration by Parts
  325 8.2 >>> Trigonometric Integrals
  326 8.3 >>> Trigonometric Substitution
  327 8.4 >>> Integration of Rational Functions by Partial Fractions
  328 8.5 >>> Strategy for Integration
  329 8.6 >>> Integration Using Tables and Computer Algebra Systems
  330 8.7 >>> Approximate Integration
  331 8.8 >>> Improper Integrals
  332 
  333 9 >>> Further Applications of Integration
  334 9.1 >>> Arc Length
  335 9.2 >>> Area of a Surface of Revolution
  336 9.3 >>> Applications to Physics and Engineering
  337 9.4 >>> Applications to Economics and Biology
  338 9.5 >>> Probability
  339 
  340 10 >>> Differential Equations
  341 10.1 >>> Modeling with Differential Equations
  342 10.2 >>> Direction Fields and Euler's Method
  343 10.3 >>> Separable Equations
  344 10.4 >>> Exponential Growth and Decay
  345 10.5 >>> The Logistic Equation
  346 10.6 >>> Linear Equations
  347 10.7 >>> Predator-Prey Systems
  348 
  349 11 >>> Parametric Equations and Polar Coordinates
  350 11.1 >>> Curves Defined by Parametric Equations
  351 11.2 >>> Calculus with Parametric Curves
  352 11.3 >>> Polar Coordinates
  353 11.4 >>> Areas and Lengths in Polar Coordinates
  354 11.5 >>> Conic Sections
  355 11.6 >>> Conic Sections in Polar Coordinates
  356 
  357 12 >>> Infinite Sequences and Series
  358 12.1 >>> Sequences
  359 12.2 >>> Series
  360 12.3 >>> The Integral Test and Estimates of Sums
  361 12.4 >>> The Comparison Tests
  362 12.5 >>> Alternating Series
  363 12.6 >>> Absolute Convergence and the Ratio and Root Tests
  364 12.7 >>> Strategy for Testing Series
  365 12.8 >>> Power Series
  366 12.9 >>> Representations of Functions as Power Series
  367 12.10 >>> Taylor and Maclaurin Series
  368 12.11 >>> The Binomial Series
  369 12.12 >>> Applications of Taylor Polynomials
  370 
  371 13 >>> Vectors and the Geometry of Space
  372 13.1 >>> Three-Dimensional Coordinate Systems
  373 13.2 >>> Vectors
  374 13.3 >>> The Dot Product
  375 13.4 >>> The Cross Product
  376 13.5 >>> Equations of Lines and Planes
  377 13.6 >>> Cylinders and Quadric Surfaces
  378 13.7 >>> Cylindrical and Spherical Coordinates
  379 
  380 14 >>> Vector Functions
  381 14.1 >>> Vector Functions and Space Curves
  382 14.2 >>> Derivatives and Integrals of Vector Functions
  383 14.3 >>> Arc Length and Curvature
  384 14.4 >>> Motion in Space: Velocity and Acceleration
  385 
  386 15 >>> Partial Derivatives
  387 15.1 >>> Functions of Several Variables
  388 15.2 >>> Limits and Continuity
  389 15.3 >>> Partial Derivatives
  390 15.4 >>> Tangent Planes and Linear Approximations
  391 15.5 >>> The Chain Rule
  392 15.6 >>> Directional Derivatives and the Gradient Vector
  393 15.7 >>> Maximum and Minimum Values
  394 15.8 >>> Lagrange Multipliers
  395 
  396 16 >>> Multiple Integrals
  397 16.1 >>> Double Integrals over Rectangles
  398 16.2 >>> Iterated Integrals
  399 16.3 >>> Double Integrals over General Regions
  400 16.4 >>> Double Integrals in Polar Coordinates
  401 16.5 >>> Applications of Double Integrals
  402 16.6 >>> Surface Area
  403 16.7 >>> Triple Integrals
  404 16.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates
  405 16.9 >>> Change of Variables in Multiple Integrals
  406 
  407 17 >>> Vector Calculus
  408 17.1 >>> Vector Fields
  409 17.2 >>> Line Integrals
  410 17.3 >>> The Fundamental Theorem for Line Integrals
  411 17.4 >>> Green's Theorem
  412 17.5 >>> Curl and Divergence
  413 17.6 >>> Parametric Surfaces and Their Areas
  414 17.7 >>> Surface Integrals
  415 17.8 >>> Stokes' Theorem
  416 17.9 >>> The Divergence Theorem
  417 17.10 >>> Summary
  418 
  419 18 >>> Second-Order Differential Equations
  420 18.1 >>> Second-Order Linear Equations
  421 18.2 >>> Nonhomogeneous Linear Equations
  422 18.3 >>> Applications of Second- Order Differential Equations
  423 18.4 >>> Series Solutions
  424 
  425 TitleText('College Algebra')
  426 EditionText('4')
  427 AuthorText('Stewart, Redlin, Watson')
  428 
  429 0 >>> Prerequisites
  430 0.1 >>> Modeling the Real World
  431 0.2 >>> Real Numbers
  432 0.3 >>> Integer Exponents
  433 0.4 >>> Rational Exponents and Radicals
  434 0.5 >>> Algebraic Expressions
  435 0.6 >>> Factoring
  436 0.7 >>> Rational Expressions
  437 
  438 1 >>> Equations and Inequalities
  439 1.1 >>> Basic Equations
  440 1.2 >>> Modeling with Equations
  441 1.3 >>> Quadratic Equations
  442 1.4 >>> Complex Numbers
  443 1.5 >>> Other Types of Equations
  444 1.6 >>> Inequalities
  445 1.7 >>> Absolute Value Equations and Inequalities
  446 
  447 2 >>> Coordinates and Graphs
  448 2.1 >>> The Coordinate Plane
  449 2.2 >>> Graphs of Equations in Two Variables
  450 2.3 >>> Graphing Calculators; Solving Equations and Inequalitie Graphically
  451 2.4 >>> Lines
  452 2.5 >>> Modeling: Variation
  453 
  454 3 >>> Functions
  455 3.1 >>> What Is a Function?
  456 3.2 >>> Graphs of Functions
  457 3.3 >>> Increasing and Decreasing Functions; Average Rate of Change
  458 3.4 >>> Transformations of Functions
  459 3.5 >>> Quadratic Functions; Maxima and Minima
  460 3.6 >>> Combining Functions
  461 3.7 >>> One-to-One Functions and Their Inverses
  462 
  463 4 >>> Polynomial and Rational Functions
  464 4.1 >>> Polynomial Functions and Their Graphs
  465 4.2 >>> Dividing Polynomials
  466 4.3 >>> Real Zeros of Polynomials
  467 4.4 >>> Complex Zeros and the Fundamental Theorem of Algebra
  468 4.5 >>> Rational Functions
  469 5 >>> Exponential and Logarithmic Functions
  470 5.1 >>> Exponential Functions
  471 5.2 >>> Logarithmic Functions
  472 5.3 >>> Laws of Logarithms
  473 5.4 >>> Exponential and Logarithmic Equations
  474 5.5 >>> Modeling with Exponential and Logarithmic Functions
  475 
  476 6 >>> Systems of Equations and Inequalities
  477 6.1 >>> Systems of Equations
  478 6.2 >>> Systems of Linear Equations in Two Variables
  479 6.3 >>> Systems of Linear Equations in Several Variables
  480 6.4 >>> Systems of Inequalities
  481 6.5 >>> Partial Fractions
  482 
  483 7 >>> Matrices and Determinants
  484 7.1 >>> Matrices and Systems of Linear Equations
  485 7.2 >>> The Algebra of Matrices
  486 7.3 >>> Inverses of Matrices and Matrix Equations
  487 7.4 >>> Determinants and Cramer's Rule
  488 
  489 8 >>> Conic Sections
  490 8.1 >>> Parabolas
  491 8.2 >>> Ellipses
  492 8.3 >>> Hyperbolas
  493 8.4 >>> Shifted Conics
  494 
  495 9 >>> Sequences and Series
  496 9.1 >>> Sequences and Summation Notation
  497 9.2 >>> Arithmetic Sequences
  498 9.3 >>> Geometric Sequences
  499 9.4 >>> Mathematics of Finance
  500 9.5 >>> Mathematical Induction
  501 9.6 >>> The Binomial Theorem
  502 
  503 10 >>> Counting and Probability
  504 10.1 >>> Counting Principles
  505 10.2 >>> Permutations and Combinations
  506 10.3 >>> Probability
  507 10.4 >>> Binomial Probability
  508 10.5 >>> Expected Value
  509 
  510 TitleText('Statistics for Management and Economics')
  511 EditionText('7')
  512 AuthorText('Keller')
  513 
  514 1 >>> What is Statistics?
  515 1.1 >>> Key Statistical Concepts
  516 1.2 >>> Statistical Applications in Business
  517 1.3 >>> Statistics and the Computer
  518 1.4 >>> World Wide Web and Learning Center
  519 1.A >>> Instructions for the CD-ROM
  520 1.B >>> Introduction to Microsoft Excel
  521 1.C >>> Introduction to Minitab
  522 2 >>> Graphical and Tabular Descriptive Techniques
  523 2.1 >>> Types of Data and Information
  524 2.2 >>> Graphical and Tabular Techniques for Nominal Data
  525 2.3 >>> Graphical Techniques for Interval Data
  526 2.4 >>> Describing the relationship Between Two Variables
  527 2.5 >>> Describing Time-Series Data
  528 3 >>> Art and Science of Graphical Presentations
  529 3.1 >>> Graphical Excellence
  530 3.2 >>> Graphical Deception
  531 3.3 >>> Presenting Statistics: Written Reports and Oral Presentations
  532 4 >>> Numerical Descriptive Techniques
  533 4.1 >>> Measures of Central Location
  534 4.2 >>> Measures of Variability
  535 4.3 >>> Measures of Relative Standing and Box Plots
  536 4.4 >>> Measures of Linear Relationship
  537 4.5 >>> Applications in Professional Sports: Baseball
  538 4.6 >>> Comparing Graphical and Numerical Techniques
  539 4.7 >>> General Guidelines for Exploring Data
  540 5 >>> Data Collection and Sampling
  541 5.1 >>> Methods of Collecting Data
  542 5.2 >>> Sampling
  543 5.3 >>> Sampling Plans
  544 5.4 >>> Sampling and Nonsampling Errors
  545 6 >>> Probability
  546 6.1 >>> Assigning Probability to Events
  547 6.2 >>> Joint, Marginal, and Conditional Probability
  548 6.3 >>> Probability Rules and Trees
  549 6.4 >>> Bayes' Law
  550 6.5 >>> Identifying the Correct Method
  551 7 >>> Random Variables and Discrete Probability Distributions
  552 7.1 >>> Random Variables and Probability Distributions
  553 7.2 >>> Bivariate Distributions
  554 7.3 >>> Applications in Finance: Portfolio Diversification and Asset Allocation
  555 7.4 >>> Binomial Distribution
  556 7.5 >>> Poisson Distribution
  557 8 >>> Continuous Probability Distributions
  558 8.1 >>> Probability Density Functions
  559 8.2 >>> Normal Distribution
  560 8.3 >>> Exponential Distribution
  561 8.4 >>> Other Continuous Distributions
  562 9 >>> Sampling Distributions
  563 9.1 >>> Sampling Distribution of the Mean
  564 9.2 >>> Sampling Distribution of a Proportion
  565 9.3 >>> Sampling Distribution of the Difference Between Two Means
  566 9.4 >>> From Here to Inference
  567 10 >>> Introduction to Estimation
  568 10.1 >>> Concepts of Estimation
  569 10.2 >>> Estimating the Population Mean When the Population Standard Deviation is Known
  570 10.3 >>> Selecting the Sample Size
  571 11 >>> Introduction to Hypothesis Testing
  572 11.1 >>> Concepts of Hypothesis Testing
  573 11.2 >>> Testing the Population Mean When the Population Standard Deviation is Known
  574 11.3 >>> Calculating the Probability of a Type II Error
  575 11.4 >>> The Road Ahead
  576 12 >>> Inference About a Population
  577 12.1 >>> Inference About a Population Mean When the Standard Deviation is Unknown
  578 12.2 >>> Inference about a Population Variance
  579 12.3 >>> inference about a Population Proportion
  580 12.4 >>> Applications in Marketing: Market Segmentation
  581 12.5 >>> Applications in Marketing: Auditing
  582 13 >>> Inference About Comparing Two Populations
  583 13.1 >>> Inference about the Difference Between Two Means: Independent Samples
  584 13.2 >>> Observational and Experimental Data
  585 13.3 >>> Inference about the Difference Between Two Means: Matched Pairs Experiment
  586 13.4 >>> Inference about the Ratio of Two Variances
  587 13.5 >>> Inference about the Difference Between Two Population Proportions
  588 13.A >>> Excel Instructions for Stacked and Unstacked Data
  589 13.B >>> Minitab Instructions for Stacked and Unstacked Data
  590 14 >>> Statistical Inference: Review of Chapters 12 and 13
  591 14.1 >>> Guide to Identifying the Correct Technique: Chapters 12 and 13
  592 15 >>> Analysis of Variance
  593 15.1 >>> One-Way Analysis of Variance
  594 15.2 >>> Analysis of Variance Experimental Designs
  595 15.3 >>> Randomized Blocks (Two-Way) Analysis of Variance
  596 15.4 >>> Two-Factor Analysis of Variance
  597 15.5 >>> Appplications in Operations Management: Finding and Reducing Variation
  598 15.6 >>> Multiple Comparisons
  599 16 >>> Chi-Squared Tests
  600 16.1 >>> Chi-Squared Goodness-of-Fit Test
  601 16.2 >>> Chi-Squared Test of a Contingency Table
  602 16.3 >>> Summary of Tests on Nominal Data
  603 16.4 >>> Chi-Squared Tests of Normality
  604 17 >>> Simple Linear Regression and Correlation
  605 17.1 >>> Model
  606 17.2 >>> Estimating the Coefficients
  607 17.3 >>> Error Variable: Required Conditions
  608 17.4 >>> Assessing the Model
  609 17.5 >>> Applications in Finance: Market Model
  610 17.6 >>> Using the Regression Equation
  611 17.7 >>> Regression Diagnostics-I
  612 18 >>> Multiple Regression
  613 18.1 >>> Model and Required Conditions
  614 18.2 >>> Estimating the Coefficients and Assessing the Model
  615 18.3 >>> Regression Diagnostics-II
  616 18.4 >>> Regression Diagnostics-III (Time Series)
  617 
  618 19 >>> Appendix A: Excel Troubleshooting and Detailed Instructions
  619 20 >>> Appendix B: Minitab Detailed Instructions
  620 21 >>> Appendix C: Approximating Means and Variances from Grouped Data
  621 22 >>> Appendix D: Descriptive Techniques Review Exercises
  622 23 >>> Appendix E: Couting Formulas
  623 24 >>> Appendix F: Hypergeometric Distribution
  624 25 >>> Appendix G: Continuous Probability Distributions: Calculus Approach
  625 26 >>> Appendix H: Using the Laws of Expected Value and Variance to Derive the Parameters of Sampling Distributions
  626 27 >>> Appendix I: Excel Spreadsheets for Techniques in Chapters 10-13
  627 28 >>> Appendix K: Converting Excel's Probabilities to p-Values
  628 29 >>> Appendix J: Excel and Minitab Instructions for Missing Data and for Recoding Data
  629 30 >>> Appendix L: Probability of a Type II Error When Testing a Proportion
  630 31 >>> Appendix M: Approximating p-Values from the Student t Table
  631 32 >>> Appendix N: Probability of a Type II Error When Testing the Difference Between Two Means
  632 33 >>> Appendix O: Probability of a Type II Erorr When Testing the Difference Between Two Proportions
  633 34 >>> Appendix P: Bartlett's Test
  634 35 >>> Appendix Q: Minitab Instructions for the Chi-Squared Goodness-of-Fit Test and the Test for Normality
  635 36 >>> Appendix R: The Rule of Five
  636 37 >>> Appendix S: Deriving the Normal Equations
  637 38 >>> Appendix T: Szroeter's Test for Heteroscedasticity
  638 39 >>> Appendix U: Transformations
  639 
  640 TitleText('Elementary Linear Algebra')
  641 
  642 EditionText('5')
  643 
  644 AuthorText('Larson, Edwards, Falvo')
  645 
  646 
  647 1 >>> Systems of Linear Equations
  648 1.1 >>> Introduction to Systems of Linear Equations
  649 1.2 >>> Gaussian Elimination and Gauss-Jordan Elimination
  650 1.3 >>> Applications of Systems of Linear Equations
  651 
  652 2 >>> Matrices
  653 2.1 >>> Operations with Matrices
  654 2.2 >>> Properties of Matrix Operations
  655 2.3 >>> The Inverse of a Matrix
  656 2.4 >>> Elementary Matrices
  657 2.5 >>> Applications of Matrix Operations
  658 
  659 3 >>> Determinants
  660 3.1 >>> The Determinant of a Matrix
  661 3.2 >>> Evaluation of a Determinant Using Elementary Operations
  662 3.3 >>> Properties of Determinants
  663 3.4 >>> Introduction to Eigenvalues
  664 3.5 >>> Applications of Determinants
  665 
  666 4 >>> Vector Spaces
  667 
  668 4.1 >>> Vectors in Rn
  669 4.2 >>> Vector Spaces
  670 4.3 >>> Subspaces of Vector Spaces
  671 4.4 >>> Spanning Sets and Linear Independence
  672 4.5 >>> Basis and Dimension
  673 4.6 >>> Rank of a Matrix and Systems of Linear Equations
  674 4.7 >>> Coordinates and Change of Basis
  675 4.8 >>> Applications of Vector Spaces
  676 
  677 5 >>> Inner Product Spaces
  678 5.1 >>> Length and Dot Product in Rn
  679 5.2 >>> Inner Product Spaces
  680 5.3 >>> Orthonormal Bases: Gram-Schmidt Process
  681 5.4 >>> Mathematical Models and Least Squares Analysis
  682 5.5 >>> Applications of Inner Product Spaces
  683 
  684 6 >>> Linear Transformations
  685 6.1 >>> Introduction to Linear Transformations
  686 6.2 >>> The Kernel and Range of a Linear Transformation
  687 6.3 >>> Matrices for Linear Transformations
  688 6.4 >>> Transition Matrices and Similarity
  689 6.5 >>> Applications of Linear Transformations
  690 
  691 7 >>> Eigenvalues and Eigenvectors
  692 7.1 >>> Eigenvalues and Eigenvectors
  693 7.2 >>> Diagonalization
  694 7.3 >>> Symmetric Matrices and Orthogonal Diagonalization
  695 7.4 >>> Applications of Eigenvalues and Eigenvectors
  696 
  697 8 >>> Complex Vector Spaces
  698 8.1 >>> Complex Numbers
  699 8.2 >>> Conjugates and Division of Complex Numbers
  700 8.3 >>> Polar Form and DeMoivre's Theorem
  701 8.4 >>> Complex Vector Spaces and Inner Products
  702 8.5 >>> Unitary and Hermitian Matrices
  703 
  704 9 >>> Linear Programming
  705 9.1 >>> Systems of Linear Inequalities
  706 9.2 >>> Linear Programming Involving Two Variables
  707 9.3 >>> The Simplex Method: Maximization
  708 9.4 >>> The Simplex Method: Minimization
  709 9.5 >>> The Simplex Method: Mixed Constraints
  710 
  711 10 >>> Numerical Methods
  712 
  713 10.1 >>> Gaussian Elimination with Partial Pivoting
  714 10.2 >>> Interative Methods for Solving Linear Systems
  715 10.3 >>> Power Method for Approximating Eigenvalues
  716 10.4 >>> Applications of Numerical Methods
  717 
  718 11 >>> Appendix A: Mathematical Induction and Other Forms of Proofs
  719 
  720 12 >>> Appendix B: Computer Algebra Systems and Graphing Calculators
  721 
  722 TitleText('Basic Multivariable Calculus')
  723 EditionText('3')
  724 AuthorText('Marsden, Tromba, Weinstein')
  725 
  726 1 >>> Algebra and Geometry of Euclidean Space
  727 1.1 >>> Vectors in the Plane and Space
  728 1.2 >>> The Inner Product and Distance
  729 1.3 >>> 2 x 2 and 3 x 3 Matrices and Determinants
  730 1.4 >>> The Cross Product and Planes
  731 1.5 >>> n-Dimensional Euclidean Space
  732 1.6 >>> Curves in the Plane and in Space
  733 
  734 2 >>> Differentiation
  735 2.1 >>> Graphs and Level Surfaces
  736 2.2 >>> Partial Derivatives and Continuity
  737 2.3 >>> Differentiability, the Derivative Matrix, and Tangent Planes
  738 2.4 >>> The Chain Rule
  739 2.5 >>> Gradients and Directional Derivatives
  740 2.6 >>> Implicit Differentiation
  741 
  742 3 >>> Higher Derivatives and Extrema
  743 3.1 >>> Higher Order Partial Derivatives
  744 3.2 >>> Taylor's Theorem
  745 3.3 >>> Maxima and Minima
  746 3.4 >>> Second Derivative Test
  747 3.5 >>> Constrained Extrema and Lagrange Multipliers
  748 
  749 4 >>> Vector-Valued Functions
  750 4.1 >>> Acceleration
  751 4.2 >>> Arc Length
  752 4.3 >>> Vector Fields
  753 4.4 >>> Divergence and Curl
  754 
  755 5 >>> Multiple Integrals
  756 5.1 >>> Volume and Cavalieri's Principle
  757 5.2 >>> The Double Integral Over a Rectangle
  758 5.3 >>> The Double Integral Over Regions
  759 5.4 >>> Triple Integrals
  760 5.5 >>> Change of Variables, Cylindrical and Spherical Coordinates
  761 5.6 >>> Applications of Multiple Integrals
  762 
  763 6 >>> Integrals Over Curves and Surfaces
  764 6.1 >>> Line Integrals
  765 6.2 >>> Parametrized Surfaces
  766 6.3 >>> Area of a Surface
  767 6.4 >>> Surface Integrals
  768 
  769 7 >>> The Integral Theorems of Vector Analysis
  770 7.1 >>> Green's Theorem
  771 7.2 >>> Stokes' Theorem
  772 7.3 >>> Gauss' Theorem
  773 7.4 >>> Path Independence and the Fundamental Theorems of Calculus
  774 
  775 TitleText('Precalculus')
  776 EditionText('5')
  777 AuthorText('Stewart, Redlin, Watson')
  778 
  779 1 >>> Fundamentals
  780 1.1 >>> Real Numbers
  781 1.2 >>> Exponents and Radicals
  782 1.3 >>> Algebraic Expressions
  783 1.4 >>> Rational Expression
  784 1.5 >>> Equations
  785 1.6 >>> Modeling with Equations
  786 1.7 >>> Inequalities
  787 1.8 >>> Coordinate Geometry
  788 1.9 >>> Graphing Calculators; Solving Equations and Inequalities Graphically
  789 1.10 >>> Lines
  790 1.11 >>> Modeling Variation
  791 
  792 2 >>> Functions
  793 2.1 >>> What is a Function?
  794 2.2 >>> Graphs of Functions
  795 2.3 >>> Increasing and Decreasing Functions; Average Rate of Change
  796 2.4 >>> Transformations of Functions
  797 2.5 >>> Quadratic Functions; Maxima and Minima
  798 2.6 >>> Modeling with Functions
  799 2.7 >>> Combining Functions
  800 2.8 >>> One-to-One Functions and Their Inverses
  801 
  802 3 >>> Polynomial and Rational Functions
  803 3.1 >>> Polynomial Functions and Their Graphs
  804 3.2 >>> Dividing Polynomials
  805 3.3 >>> Real Zeros of Polynomials
  806 3.4 >>> Complex Numbers
  807 3.5 >>> Complex Zeros and the Fundamental Theorem of Algebra
  808 3.6 >>> Rational Functions
  809 
  810 4 >>> Exponential and Logarithmic Functions
  811 4.1 >>> Exponential Functions
  812 4.2 >>> Logarithmic Functions
  813 4.3 >>> Laws of Logarithms
  814 4.4 >>> Exponential and Logarithmic Equations
  815 4.5 >>> Modeling with Exponential and Logarithmic Functions
  816 
  817 5 >>> Trigonometric Functions of Real Numbers
  818 5.1 >>> The Unit Circle
  819 5.2 >>> Trigonometric Functions of Real Numbers
  820 5.3 >>> Trigonometric Graphs
  821 5.4 >>> More Trigonometric Graphs
  822 5.5 >>> Modeling Harmonic Motion
  823 
  824 6 >>> Trigonometric Functions of Angles
  825 6.1 >>> Angle Measures
  826 6.2 >>> Trigonometry of Right Triangles
  827 6.3 >>> Trigonometric Functions of Angles
  828 6.4 >>> The Law of Sines
  829 6.5 >>> The Law of Cosines
  830 
  831 7 >>> Analytic Trigonometry
  832 7.1 >>> Trigonometric Identities
  833 7.2 >>> Addition and Subtraction Formulas
  834 7.3 >>> Double-Angle, Half-Angle, and Sum-Product Formulas
  835 7.4 >>> Inverse Trigonometric Functions
  836 7.5 >>> Trigonometric Equations
  837 
  838 8 >>> Polar Coordinates and Vectors
  839 8.1 >>> Polar Coordinates
  840 8.2 >>> Graphs of Polar Equations
  841 8.3 >>> Polar Form of Complex Numbers; DeMoivre's Theorem
  842 8.4 >>> Vectors
  843 8.5 >>> The Dot Product
  844 
  845 9 >>> Systems of Equations and Inequalities
  846 9.1 >>> Systems of Equations
  847 9.2 >>> Systems of Linear Equations in Two Variables
  848 9.3 >>> Systems of Linear Equations in Several Variables
  849 9.4 >>> Systems of Linear Equations: Matrices
  850 9.5 >>> The Algebra of Matrices
  851 9.6 >>> Inverses of Matrices and Matrix Equations
  852 9.7 >>> Determinants and Cramer's Rule
  853 9.8 >>> Partial Fractions
  854 9.9 >>> Systems of Inequalities
  855 
  856 10 >>> Analytic Geometry
  857 10.1 >>> Parabolas
  858 10.2 >>> Ellipses
  859 10.3 >>> Hyperbolas
  860 10.4 >>> Shifted Conics
  861 10.5 >>> Rotation of Axes
  862 10.6 >>> Polar Equations of Conics
  863 10.7 >>> Plane Curves and Parametric Equations
  864 
  865 11 >>> Sequences and Series
  866 11.1 >>> Sequences and Summation Notation
  867 11.2 >>> Arithmetic Sequences
  868 11.3 >>> Geometric Sequences
  869 11.4 >>> Mathematics of Finance
  870 11.5 >>> Mathematical Induction
  871 11.6 >>> The Binomial Theorem
  872 
  873 12 >>> Limits: A Preview of Calculus
  874 12.1 >>> Finding Limits Numerically and Graphically
  875 12.2 >>> Finding Limits Algebraically
  876 12.3 >>> Tangent Lines and Derivatives
  877 12.4 >>> Limits at Infinity: Limits of Sequences
  878 12.5 >>> Areas
  879 
  880 TitleText('Discrete Mathematics')
  881 EditionText('4')
  882 AuthorText('Rosen')
  883 
  884 
  885 1 >>> The Foundations: Logic, Sets, and Functions
  886 1.1 >>> Logic
  887 1.2 >>> Propositional Equivalences
  888 1.3 >>> Predicates and Quantifiers
  889 1.4 >>> Sets
  890 1.5 >>> Set Operations
  891 1.6 >>> Functions
  892 1.7 >>> Sequences and Summations
  893 1.8 >>> The Growth Functions
  894 
  895 2 >>> The Fundamentals: Algorithms, the Integers, and Matrices
  896 2.1 >>> Algorithms
  897 2.2 >>> Complexity of Algorithms
  898 2.3 >>> The Integers and Division
  899 2.4 >>> Integers and Algorithms
  900 2.5 >>> Applications of Number Theory
  901 2.6 >>> Matrices
  902 
  903 3 >>> Mathematical Reasoning
  904 
  905 3.1 >>> Methods of Proof
  906 3.2 >>> Mathematical Induction
  907 3.3 >>> Recursive Definitions
  908 3.4 >>> Recursive Algorithms
  909 3.5 >>> Program Correctness
  910 
  911 4 >>> Counting
  912 4.1 >>> The Basics of Counting
  913 4.2 >>> The Pigeonhole Principle
  914 4.3 >>> Permutations and Combinations
  915 4.4 >>> Discrete Probability
  916 4.5 >>> Probability Theory
  917 4.6 >>> Generalized Permutations and Combinations
  918 4.7 >>> Generating Permutations and Combinations
  919 
  920 5 >>> Advanced Counting Techniques
  921 5.1 >>> Recurrence Relations
  922 5.2 >>> Solving Recurrence Relations
  923 5.3 >>> Divide-and-Conquer Relations
  924 5.4 >>> Generating Functions
  925 5.5 >>> Inclusion-Exclusion
  926 5.6 >>> Applications of Inclusion-Exclusion
  927 
  928 6 >>> Relations
  929 6.1 >>> Relations and Their Properties
  930 6.2 >>> n-ary Relations and Their Applications
  931 6.3 >>> Representing Relations
  932 6.4 >>> Closures of Relations
  933 6.5 >>> Equivalence Relations
  934 6.6 >>> Partial Orderings
  935 
  936 7 >>> Graphs
  937 7.1 >>> Introduction to Graphs
  938 7.2 >>> Graph Terminology
  939 7.3 >>> Representing Graphs and Graph Isomorphism
  940 7.4 >>> Connectivity
  941 7.5 >>> Euler and Hamilton Paths
  942 7.6 >>> Shortest Path Problems
  943 7.7 >>> Planar Graphs
  944 7.8 >>> Graph Coloring
  945 
  946 8 >>> Trees
  947 8.1 >>> Introduction to Trees
  948 8.2 >>> Applications of Trees
  949 8.3 >>> Tree Traversal
  950 8.4 >>> Trees and Sorting
  951 8.5 >>> Spanning Trees
  952 8.6 >>> Minimum Spanning Trees
  953 
  954 9 >>> Boolean Algebra
  955 9.1 >>> Boolean Functions
  956 9.2 >>> Representing Boolean Functions
  957 9.3 >>> Logic Gates
  958 9.4 >>> Minimization of Circuits
  959 
  960 10 >>> Modeling Computation
  961 10.1 >>> Languages and Grammars
  962 10.2 >>> Finite-State Machines with Output
  963 10.3 >>> Finite-State Machines with No Output
  964 10.4 >>> Language Recognition
  965 10.5 >>> Turing Machines
  966 
  967 11 >>> Appendix: Exponential and Logarithmic Functions
  968 12 >>> Appendix: Pseudocode
  969 
  970 TitleText('Complex Analysis')
  971 EditionText('3')
  972 AuthorText('Saff, Snider')
  973 
  974 1 >>> Complex Numbers
  975 1.1 >>> The Algebra of Complex Numbers
  976 1.2 >>> Point Representation of Complex Numbers
  977 1.3 >>> Vectors and Polar Forms
  978 1.4 >>> The Complex Exponential
  979 1.5 >>> Powers and Roots
  980 1.6 >>> Planar Sets
  981 1.7 >>> The Riemann Sphere and Stereographic Projection
  982 
  983 2 >>> Analytic Functions
  984 2.1 >>> Functions of a Complex Variable
  985 2.2 >>> Limits and Continuity
  986 2.3 >>> Analyticity
  987 2.4 >>> The Cauchy-Riemann Equations
  988 2.5 >>> Harmonic Functions
  989 2.6 >>> Steady-State Temperature as a Harmonic Function
  990 2.7 >>> Iterated Maps: Julia and Mandelbrot Sets
  991 
  992 3 >>> Elementary Functions
  993 3.1 >>> Polynomials and Rational Functions
  994 3.2 >>> The Exponential, Trigonometric, and Hyperbolic Functions
  995 3.3 >>> The Logarithmic Function
  996 3.4 >>> Washers, Wedges, and Walls
  997 3.5 >>> Complex Powers and Inverse Trigonometric Functions
  998 3.6 >>> Application to Oscillating Systems
  999 
 1000 4 >>> Complex Integration
 1001 4.1 >>> Contours
 1002 4.2 >>> Contour Integrals
 1003 4.3 >>> Independence of Path
 1004 4.4 >>> Cauchy's Integral Theorem
 1005 4.5 >>> Deformation of Contours Approach
 1006 4.6 >>> Vector Analysis Approach
 1007 4.7 >>> Cauchy's Integral Formula and Its Consequences
 1008 4.8 >>> Bounds for Analytic Functions
 1009 4.9 >>> Applications to Harmonic Functions
 1010 
 1011 5 >>> Series Representations for Analytic Functions
 1012 5.1 >>> Sequences and Series
 1013 5.2 >>> Taylor Series
 1014 5.3 >>> Power Series
 1015 5.4 >>> Mathematical Theory of Convergence
 1016 5.5 >>> Laurent Series
 1017 5.6 >>> Zeros and Singularities
 1018 5.7 >>> The Point at Infinity
 1019 5.8 >>> Analytic Continuation
 1020 
 1021 6 >>> Residue Theory
 1022 6.1 >>> The Residue Theorem
 1023 6.2 >>> Trigonometric Integrals over [0, 2¹]
 1024 6.3 >>> Improper Integrals of Certain Functions over (--°, °)
 1025 6.4 >>> Improper Integrals Involving Trigonometric Functions
 1026 6.5 >>> Indented Contours
 1027 6.6 >>> Integrals Involving Multiple-Valued Functions
 1028 6.7 >>> The Argument Principle and Rouche's Theorem
 1029 
 1030 7 >>> Conformal Mapping
 1031 7.1 >>> Invariance of Laplace's Equation
 1032 7.2 >>> Geometric Considerations
 1033 7.3 >>> Mobius Transformations
 1034 7.4 >>> Mobius Transformations, Continued
 1035 7.5 >>> The Schwarz-Christoffel Transformation
 1036 7.6 >>> Applications in Electrostatics, Heat Flow, and Fluid Mechanics
 1037 7.7 >>> Further Physical Applications of Conformal Mapping
 1038 
 1039 8 >>> The Transforms of Applied Mathematics
 1040 8.1 >>> Fourier Series (The Finite Fourier Transform)
 1041 8.2 >>> The Fourier Transform
 1042 8.3 >>> The Laplace Transform
 1043 8.4 >>> The z-Transform
 1044 8.5 >>> Cauchy Integrals and the Hilbert Transform
 1045 
 1046 9 >>> Appendix A: Numerical Construction of Conformal Maps
 1047 9.1 >>> The Schwarz-Christoffel Parameter Problem
 1048 9.2 >>> Examples
 1049 9.3 >>> Numerical Integration
 1050 9.4 >>> Conformal Mapping of Smooth Domains
 1051 9.5 >>> Conformal Mapping Software
 1052 
 1053 10 >>> Appendix B: Table of Conformal Mappings
 1054 10.1 >>> Mobius Transformations
 1055 10.2 >>> Other Transformations
 1056 
 1057 TitleText('Calculus: Early Transcendentals')
 1058 EditionText('5')
 1059 AuthorText('Stewart')
 1060 
 1061 1 >>> Functions and Models
 1062 1.1 >>> Four Ways to Represent a Function
 1063 1.2 >>> Mathematical Models: A Catalog of Essential Functions
 1064 1.3 >>> New Functions from Old Functions
 1065 1.4 >>> Graphing Calculators and Computers
 1066 1.5 >>> Exponential Functions
 1067 1.6 >>> Inverse Functions and Logarithms
 1068 
 1069 2 >>> Limits and Derivatives
 1070 2.1 >>> The Tangent and Velocity Problems
 1071 2.2 >>> The Limit of a Function
 1072 2.3 >>> Calculating Limits Using the Limit Laws
 1073 2.4 >>> The Precise Definition of a Limit
 1074 2.5 >>> Continuity
 1075 2.6 >>> Limits at Infinity; Horizontal Asymptotes
 1076 2.7 >>> Tangents, Velocities, and Other Rates of Change
 1077 2.8 >>> Derivatives
 1078 2.9 >>> The Derivative as a Function
 1079 
 1080 3 >>> Differentiation Rules
 1081 3.1 >>> Derivatives of Polynomials and Exponential Functions
 1082 3.2 >>> The Product and Quotient Rules
 1083 3.3 >>> Rates of Change in the Natural and Social Sciences
 1084 3.4 >>> Derivatives of Trigonometric Functions
 1085 3.5 >>> The Chain Rule
 1086 3.6 >>> Implicit Differentiation
 1087 3.7 >>> Higher Derivatives
 1088 3.8 >>> Derivatives of Logarithmic Functions
 1089 3.9 >>> Hyperbolic Functions
 1090 3.10 >>> Related Rates
 1091 3.11 >>> Linear Approximations and Differentials
 1092 
 1093 4 >>> Applications of Differentiation
 1094 4.1 >>> Maximum and Minimum Values
 1095 4.2 >>> The Mean Value Theorem
 1096 4.3 >>> How Derivatives Affect the Shape of a Graph
 1097 4.4 >>> Indeterminate Forms and L'Hospital's Rule
 1098 4.5 >>> Summary of Curve Sketching
 1099 4.6 >>> Graphing with Calculus and Calculators
 1100 4.7 >>> Optimization Problems
 1101 4.8 >>> Applications to Business and Economics
 1102 4.9 >>> Newton's Method
 1103 4.10 >>> Antiderivatives
 1104 
 1105 5 >>> Integrals
 1106 5.1 >>> Areas and Distances
 1107 5.2 >>> The Definite Integral
 1108 5.3 >>> The Fundamental Theorem of Calculus
 1109 5.4 >>> Indefinite Integrals and the Net Change Theorem
 1110 5.5 >>> The Substitution Rule
 1111 5.6 >>> The Logarithm Defined as an Integral
 1112 
 1113 6 >>> Applications of Integration
 1114 6.1 >>> Areas between Curves
 1115 6.2 >>> Volumes
 1116 6.3 >>> Volumes by Cylindrical Shells
 1117 6.4 >>> Work
 1118 6.5 >>> Average Value of a Function
 1119 
 1120 7 >>> Techniques of Integration
 1121 7.1 >>> Integration by Parts
 1122 7.2 >>> Trigonometric Integrals
 1123 7.3 >>> Trigonometric Substitution
 1124 7.4 >>> Integration of Rational Functions by Partial Fractions
 1125 7.5 >>> Strategy for Integration
 1126 7.6 >>> Integration Using Tables and Computer Algebra Systems
 1127 7.7 >>> Approximate Integration
 1128 7.8 >>> Improper Integrals
 1129 
 1130 8 >>> Further Applications of Integration
 1131 8.1 >>> Arc Length
 1132 8.2 >>> Area of a Surface of Revolution
 1133 8.3 >>> Applications to Physics and Engineering
 1134 8.4 >>> Applications to Economics and Biology
 1135 8.5 >>> Probability
 1136 
 1137 9 >>> Differential Equations
 1138 9.1 >>> Modeling with Differential Equations
 1139 9.2 >>> Direction Fields and Euler's Method
 1140 9.3 >>> Separable Equations
 1141 9.4 >>> Exponential Growth and Decay
 1142 9.5 >>> The Logistic Equation
 1143 9.6 >>> Linear Equations
 1144 9.7 >>> Predator-Prey Systems
 1145 
 1146 10 >>> Parametric Equations and Polar Coordinates
 1147 10.1 >>> Curves Defined by Parametric Equations
 1148 10.2 >>> Calculus with Parametric Curves
 1149 10.3 >>> Polar Coordinates
 1150 10.4 >>> Areas and Lengths in Polar Coordinates
 1151 10.5 >>> Conic Sections
 1152 10.6 >>> Conic Sections in Polar Coordinates
 1153 
 1154 11 >>> Infinite Sequences and Series
 1155 11.1 >>> Sequences
 1156 11.2 >>> Series
 1157 11.3 >>> The Integral Test and Estimates of Sums
 1158 11.4 >>> The Comparison Tests
 1159 11.5 >>> Alternating Series
 1160 11.6 >>> Absolute Convergence and the Ratio and Root Tests
 1161 11.7 >>> Strategy for Testing Series
 1162 11.8 >>> Power Series
 1163 11.9 >>> Representations of Functions as Power Series
 1164 11.10 >>> Taylor and Maclaurin Series
 1165 11.11 >>> The Binomial Series
 1166 11.12 >>> Applications of Taylor Polynomials
 1167 
 1168 12 >>> Vectors and the Geometry of Space
 1169 12.1 >>> Three-Dimensional Coordinate Systems
 1170 12.2 >>> Vectors
 1171 12.3 >>> The Dot Product
 1172 12.4 >>> The Cross Product
 1173 12.5 >>> Equations of Lines and Planes
 1174 12.6 >>> Cylinders and Quadric Surfaces
 1175 12.7 >>> Cylindrical and Spherical Coordinates
 1176 
 1177 13 >>> Vector Functions
 1178 13.1 >>> Vector Functions and Space Curves
 1179 13.2 >>> Derivatives and Integrals of Vector Functions
 1180 13.3 >>> Arc Length and Curvature
 1181 13.4 >>> Motion in Space: Velocity and Acceleration
 1182 
 1183 14 >>> Partial Derivatives
 1184 14.1 >>> Functions of Several Variables
 1185 14.2 >>> Limits and Continuity
 1186 14.3 >>> Partial Derivatives
 1187 14.4 >>> Tangent Planes and Linear Approximations
 1188 14.5 >>> The Chain Rule
 1189 14.6 >>> Directional Derivatives and the Gradient Vector
 1190 14.7 >>> Maximum and Minimum Values
 1191 14.8 >>> Lagrange Multipliers
 1192 
 1193 15 >>> Multiple Integrals
 1194 15.1 >>> Double Integrals over Rectangles
 1195 15.2 >>> Iterated Integrals
 1196 15.3 >>> Double Integrals over General Regions
 1197 15.4 >>> Double Integrals in Polar Coordinates
 1198 15.5 >>> Applications of Double Integrals
 1199 15.6 >>> Surface Area
 1200 15.7 >>> Triple Integrals
 1201 15.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates
 1202 15.9 >>> Change of Variables in Multiple Integrals
 1203 
 1204 16 >>> Vector Calculus
 1205 16.1 >>> Vector Fields
 1206 16.2 >>> Line Integrals
 1207 16.3 >>> The Fundamental Theorem for Line Integrals
 1208 16.4 >>> Green's Theorem
 1209 16.5 >>> Curl and Divergence
 1210 16.6 >>> Parametric Surfaces and their Areas
 1211 16.7 >>> Surface Integrals
 1212 16.8 >>> Stokes' Theorem
 1213 16.9 >>> The Divergence Theorem
 1214 16.10 >>> Summary
 1215 
 1216 17 >>> Second-Order Differential Equations
 1217 17.1 >>> Second-Order Linear Equations
 1218 17.2 >>> Nonhomogeneous Linear Equations
 1219 17.3 >>> Applications of Second-Order Differential Equations
 1220 17.4 >>> Series Solutions
 1221 
 1222 Appendix A >>> Numbers, Inequalities, and Absolute Values
 1223 Appendix B >>> Coordinate Geometry and Lines
 1224 Appendix C >>> Graphs of Second-Degree Equations
 1225 Appendix D >>> Trigonometry
 1226 Appendix E >>> Sigma Notation
 1227 Appendix F >>> Proofs of Theorems
 1228 Appendix G >>> Complex Numbers
 1229 Appendix H >>> Answers to Odd-Numbered Exercises
 1230 
 1231 
 1232 TitleText('Calculus: Early Transcendentals')
 1233 EditionText('6')
 1234 AuthorText('Stewart')
 1235 
 1236 1 >>> Functions and Models
 1237 1.1 >>> Four Ways to Represent a Function
 1238 1.2 >>> Mathematical Models: A Catalog of Essential Functions
 1239 1.3 >>> New Functions from Old Functions
 1240 1.4 >>> Graphing Calculators and Computers
 1241 1.5 >>> Exponential Functions
 1242 1.6 >>> Inverse Functions and Logarithms
 1243 
 1244 2 >>> Limits and Derivatives
 1245 2.1 >>> The Tangent and Velocity Problems
 1246 2.2 >>> The Limit of a Function
 1247 2.3 >>> Calculating Limits Using the Limit Laws
 1248 2.4 >>> The Precise Definition of a Limit
 1249 2.5 >>> Continuity
 1250 2.6 >>> Limits at Infinity; Horizontal Asymptotes
 1251 2.7 >>> Derivatives and Rates of Change
 1252 2.8 >>> The Derivative as a Function
 1253 
 1254 3 >>> Differentiation Rules
 1255 3.1 >>> Derivatives of Polynomials and Exponential Functions
 1256 3.2 >>> The Product and Quotient Rules
 1257 3.3 >>> Derivatives of Trigonometric Functions
 1258 3.4 >>> The Chain Rule
 1259 3.5 >>> Implicit Differentiation
 1260 3.6 >>> Derivatives of Logarithmic Functions
 1261 3.7 >>> Rates of Change in the Natural and Social Sciences
 1262 3.8 >>> Exponential Growth and Decay
 1263 3.9 >>> Related Rates
 1264 3.10 >>> Linear Approximations and Differentials
 1265 3.11 >>> Hyperbolic Functions
 1266 
 1267 4 >>> Applications of Differentiation
 1268 4.1 >>> Maximum and Minimum Values
 1269 4.2 >>> The Mean Value Theorem
 1270 4.3 >>> How Derivatives Affect the Shape of a Graph
 1271 4.4 >>> Indeterminate Forms and L'Hospital's Rule
 1272 4.5 >>> Summary of Curve Sketching
 1273 4.6 >>> Graphing with Calculus and Calculators
 1274 4.7 >>> Optimization Problems
 1275 4.8 >>> Newton's Method
 1276 4.9 >>> Antiderivatives
 1277 
 1278 5 >>> Integrals
 1279 5.1 >>> Areas and Distances
 1280 5.2 >>> The Definite Integral
 1281 5.3 >>> The Fundamental Theorem of Calculus
 1282 5.4 >>> Indefinite Integrals and the Net Change Theorem
 1283 5.5 >>> The Substitution Rule
 1284 
 1285 6 >>> Applications of Integration
 1286 6.1 >>> Areas between Curves
 1287 6.2 >>> Volumes
 1288 6.3 >>> Volumes by Cylindrical Shells
 1289 6.4 >>> Work
 1290 6.5 >>> Average Value of a Function
 1291 
 1292 7 >>> Techniques of Integration
 1293 7.1 >>> Integration by Parts
 1294 7.2 >>> Trigonometric Integrals
 1295 7.3 >>> Trigonometric Substitution
 1296 7.4 >>> Integration of Rational Functions by Partial Fractions
 1297 7.5 >>> Strategy for Integration
 1298 7.6 >>> Integration Using Tables and Computer Algebra Systems
 1299 7.7 >>> Approximate Integration
 1300 7.8 >>> Improper Integrals
 1301 
 1302 8 >>> Further Applications of Integration
 1303 8.1 >>> Arc Length
 1304 8.2 >>> Area of a Surface of Revolution
 1305 8.3 >>> Applications to Physics and Engineering
 1306 8.4 >>> Applications to Economics and Biology
 1307 8.5 >>> Probability
 1308 
 1309 9 >>> Differential Equations
 1310 9.1 >>> Modeling with Differential Equations
 1311 9.2 >>> Direction Fields and Euler's Method
 1312 9.3 >>> Separable Equations
 1313 9.4 >>> Models for Population Growth
 1314 9.5 >>> Linear Equations
 1315 9.6 >>> Predator-Prey Systems
 1316 
 1317 10 >>> Parametric Equations and Polar Coordinates
 1318 10.1 >>> Curves Defined by Parametric Equations
 1319 10.2 >>> Calculus with Parametric Curves
 1320 10.3 >>> Polar Coordinates
 1321 10.4 >>> Areas and Lengths in Polar Coordinates
 1322 10.5 >>> Conic Sections
 1323 10.6 >>> Conic Sections in Polar Coordinates
 1324 
 1325 11 >>> Infinite Sequences and Series
 1326 11.1 >>> Sequences
 1327 11.2 >>> Series
 1328 11.3 >>> The Integral Test and Estimates of Sum
 1329 11.4 >>> The Comparison Tests
 1330 11.5 >>> Alternating Series
 1331 11.6 >>> Absolute Convergence and the Ratio and Root Tests
 1332 11.7 >>> Strategy for Testing Series
 1333 11.8 >>> Power Series
 1334 11.9 >>> Representations of Functions as Power Series
 1335 11.10 >>> Taylor and Maclaurin Series
 1336 11.11 >>> Applications of Taylor Polynomials
 1337 
 1338 12 >>> Vectors and the Geometry of Space
 1339 12.1 >>> Three-Dimensional Coordinate Systems
 1340 12.2 >>> Vectors
 1341 12.3 >>> The Dot Product
 1342 12.4 >>> The Cross Product
 1343 12.5 >>> Equations of Lines and Planes
 1344 12.6 >>> Cylinders and Quadric Surfaces
 1345 
 1346 13 >>> Vector Functions
 1347 13.1 >>> Vector Functions and Space Curves
 1348 13.2 >>> Derivatives and Integrals of Vector Functions
 1349 13.3 >>> Arc Length and Curvature
 1350 13.4 >>> Motion in Space: Velocity and Acceleration
 1351 
 1352 14 >>> Partial Derivatives
 1353 14.1 >>> Functions of Several Variables
 1354 14.2 >>> Limits and Continuity
 1355 14.3 >>> Partial Derivatives
 1356 14.4 >>> Tangent Planes and Linear Approximations
 1357 14.5 >>> The Chain Rule
 1358 14.6 >>> Directional Derivatives and the Gradient Vector
 1359 14.7 >>> Maximum and Minimum Values
 1360 14.8 >>> Lagrange Multipliers
 1361 
 1362 15 >>> Multiple Integrals
 1363 15.1 >>> Double Integrals over Rectangles
 1364 15.2 >>> Iterated Integrals
 1365 15.3 >>> Double Integrals over General Regions
 1366 15.4 >>> Double Integrals in Polar Coordinates
 1367 15.5 >>> Applications of Double Integrals
 1368 15.6 >>> Triple Integrals
 1369 15.7 >>> Triple Integrals in Cylindrical Coordinates
 1370 15.8 >>> Triple Integrals in Spherical Coordinates
 1371 15.9 >>> Change of Variables in Multiple Integrals
 1372 
 1373 16 >>> Vector Calculus
 1374 16.1 >>> Vector Fields
 1375 16.2 >>> Line Integrals
 1376 16.3 >>> The Fundamental Theorem for Line Integrals
 1377 16.4 >>> Green's Theorem
 1378 16.5 >>> Curl and Divergence
 1379 16.6 >>> Parametric Surfaces and their Areas
 1380 16.7 >>> Surface Integrals
 1381 16.8 >>> Stokes' Theorem
 1382 16.9 >>> The Divergence Theorem
 1383 16.10 >>> Summary
 1384 
 1385 17 >>> Second-Order Differential Equations
 1386 17.1 >>> Second-Order Linear Equations
 1387 17.2 >>> Nonhomogeneous Linear Equations
 1388 17.3 >>> Applications of Second-Order Differential Equations
 1389 17.4 >>> Series Solutions
 1390 
 1391 Appendix A >>>  Numbers, Inequalities, and Absolute Values
 1392 Appendix B >>> Coordinate Geometry and Lines
 1393 Appendix C >>> Graphs of Second-Degree Equations
 1394 Appendix D >>> Trigonometry
 1395 Appendix E >>> Sigma Notation
 1396 Appendix F >>> Proofs of Theorems
 1397 Appendix G >>> The Logarithm Defined as an Integral
 1398 Appendix H >>> Complex Numbers
 1399 Appendix I >>> Answers to Odd-Numbered Exercises