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TitleText('Financial Mathematics')
EditionText('1')
AuthorText('Holt')

1   >>> Introduction to Interest
1.0 >>> Algebra Prerequisites
1.1 >>> Simple Interest
1.2 >>> Compound Interest
1.3 >>> Effective and Nominal Rates of Interest
1.4 >>> Present and Future Value

2   >>> Equations of Value
2.1 >>> Time Value of Money
2.2 >>> Unknown Time and Logarithms
2.3 >>> Dollar Weighted Rate of Return
2.4 >>> Time Weighted Rate of Return

3   >>> Annuities
3.1 >>> Geometric Sums
3.2 >>> Annuities
3.3 >>> Loans
3.4 >>> Sinking Funds
3.5 >>> Varying Payments
3.6 >>> Perpetuities

4   >>> Bonds
4.1 >>> Yield Rates
4.2 >>> Bonds
4.3 >>> Book Value
4.4 >>> Other Bonds

5   >>> Probability and Contingent Payments
5.1 >>> Introduction to Probability
5.2 >>> Expected Values
5.3 >>> Contingent Payments

6   >>> Options
6.1 >>> Introduction to Options
6.2 >>> Hedging Strategies
6.3 >>> Binomial Trees

TitleText('Mathematical Statistics')
EditionText('6')
AuthorText('Wackerly, Mendenhall, Scheaffer')

1 >>> What Is Statistics?
1.1 >>> Introduction
1.2 >>> Characterizing a Set of Measurements: Graphical Methods
1.3 >>> Characterizing a Set of Measurements: Numerical Methods
1.4 >>> How Inferences Are Made
1.5 >>> Theory and Reality
1.6 >>> Summary

2 >>> Probability
2.1 >>> Introduction
2.2 >>> Probability and Inference
2.3 >>> A Review of Set Notation
2.4 >>> A Probabilistic Model for an Experiment: The Discrete Case
2.5 >>> Calculating the Probability of an Event: The Sample-Point Method
2.6 >>> Tools for Counting Sample Points
2.7 >>> Conditional Probability and the Independence of Events
2.8 >>> Two Laws of Probability
2.9 >>> Calculating the Probability of an Event: The Event-Composition Methods
2.10 >>> The Law of Total Probability and Bayes's Rule
2.11 >>> Numerical Events and Random Variables
2.12 >>> Random Sampling
2.13 >>> Summary

3 >>> Discrete Random Variables and Their Probability Distributions
3.1 >>> Basic Definition
3.2 >>> The Probability Distribution for Discrete Random Variable
3.3 >>> The Expected Value of Random Variable or a Function of Random Variable
3.4 >>> The Binomial Probability Distribution
3.5 >>> The Geometric Probability Distribution
3.6 >>> The Negative Binomial Probability Distribution
3.7 >>> The Hypergeometric Probability Distribution
3.8 >>> Moments and Moment-Generating Functions
3.9 >>> Probability-Generating Functions
3.10 >>> Tchebysheff's Theorem
3.11 >>> Summary

4 >>> Continuous Random Variables and Their Probability Distributions
4.1 >>> Introduction
4.2 >>> The Probability Distribution for Continuous Random Variable
4.3 >>> The Expected Value for Continuous Random Variable
4.4 >>> The Uniform Probability Distribution
4.5 >>> The Normal Probability Distribution
4.6 >>> The Gamma Probability Distribution
4.7 >>> The Beta Probability Distribution
4.8 >>> Some General Comments
4.9 >>> Other Expected Values
4.10 >>> Tchebysheff's Theorem
4.11 >>> Expectations of Discontinuous Functions and Mixed Probability Distributions
4.12 >>> Summary

5 >>> Multivariate Probability Distributions
5.1 >>> Introduction
5.2 >>> Bivariate and Multivariate Probability Distributions
5.3 >>> Independent Random Variables
5.4 >>> The Expected Value of a Function of Random Variables
5.5 >>> Special Theorems
5.6 >>> The Covariance of Two Random Variables
5.7 >>> The Expected Value and Variance of Linear Functions of Random Variables
5.8 >>> The Multinomial Probability Distribution
5.9 >>> The Bivariate Normal Distribution
5.10 >>> Conditional Expectations
5.11 >>> Summary

6 >>> Functions of Random Variables
6.1 >>> Introductions
6.2 >>> Finding the Probability Distribution of a Function of Random Variables
6.3 >>> The Method of Distribution Functions
6.4 >>> The Methods of Transformations
6.5 >>> Multivariable Transformations Using Jacobians
6.6 >>> Order Statistics
6.7 >>> Summary

7 >>> Sampling Distributions and the Central Limit Theorem
7.1 >>> Introduction
7.2 >>> Sampling Distributions Related to the Normal Distribution
7.3 >>> The Central Limit Theorem
7.4 >>> A Proof of the Central Limit Theorem
7.5 >>> The Normal Approximation to the Binomial Distributions
7.6 >>> Summary

8 >>> Estimation
8.1 >>> Introduction
8.2 >>> The Bias and Mean Square Error of Point Estimators
8.3 >>> Some Common Unbiased Point Estimators
8.4 >>> Evaluating the Goodness of Point Estimator
8.5 >>> Confidence Intervals
8.6 >>> Large-Sample Confidence Intervals Selecting the Sample Size
8.7 >>> Small-Sample Confidence Intervals for u and u1-u2
8.8 >>> Confidence Intervals for o2
8.9 >>> Summary

9 >>> Properties of Point Estimators and Methods of Estimation
9.1 >>> Introduction
9.2 >>> Relative Efficiency
9.3 >>> Consistency
9.4 >>> Sufficiency
9.5 >>> The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation
9.6 >>> The Method of Moments
9.7 >>> The Method of Maximum Likelihood
9.8 >>> Some Large-Sample Properties of MLEs
9.9 >>> Summary

10 >>> Hypothesis Testing
10.1 >>> Introduction
10.2 >>> Elements of a Statistical Test
10.3 >>> Common Large-Sample Tests
10.4 >>> Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test
10.5 >>> Relationships Between Hypothesis Testing Procedures and Confidence Intervals
10.6 >>> Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values
10.7 >>> Some Comments on the Theory of Hypothesis Testing
10.8 >>> Small-Sample Hypothesis Testing for u and u1-u2
10.9 >>> Testing Hypotheses Concerning Variances
10.10 >>> Power of Test and the Neyman-Pearson Lemma
10.11 >>> Likelihood Ration Test
10.12 >>> Summary

11 >>> Linear Models and Estimation by Least Squares
11.1 >>> Introduction
11.2 >>> Linear Statistical Models
11.3 >>> The Method of Least Squares
11.4 >>> Properties of the Least Squares Estimators for the Simple Linear Regression Model
11.5 >>> Inference Concerning the Parameters BI
11.6 >>> Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression
11.7 >>> Predicting a Particular Value of Y Using Simple Linear Regression
11.8 >>> Correlation
11.9 >>> Some Practical Examples
11.10 >>> Fitting the Linear Model by Using Matrices
11.11 >>> Properties of the Least Squares Estimators for the Multiple Linear Regression Model
11.12 >>> Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression
11.13 >>> Prediction a Particular Value of Y Using Multiple Regression
11.14 >>> A Test for H0: Bg+1 + Bg+2 = ? = Bk = 0
11.15 >>> Summary and Concluding Remarks

12 >>> Considerations in Designing Experiments
12.1 >>> The Elements Affecting the Information in a Sample
12.2 >>> Designing Experiment to Increase Accuracy
12.3 >>> The Matched Pairs Experiment
12.4 >>> Some Elementary Experimental Designs
12.5 >>> Summary

13 >>> The Analysis of Variance
13.1 >>> Introduction
13.2 >>> The Analysis of Variance Procedure
13.3 >>> Comparison of More than Two Means: Analysis of Variance for a One-way Layout
13.4 >>> An Analysis of Variance Table for a One-Way Layout
13.5 >>> A Statistical Model of the One-Way Layout
13.6 >>> Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout
13.7 >>> Estimation in the One-Way Layout
13.8 >>> A Statistical Model for the Randomized Block Design
13.9 >>> The Analysis of Variance for a Randomized Block Design
13.10 >>> Estimation in the Randomized Block Design
13.11 >>> Selecting the Sample Size
13.12 >>> Simultaneous Confidence Intervals for More than One Parameter
13.13 >>> Analysis of Variance Using Linear Models
13.14 >>> Summary

14 >>> Analysis of Categorical Data
14.1 >>> A Description of the Experiment
14.2 >>> The Chi-Square Test
14.3 >>> A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test
14.4 >>> Contingency Tables
14.5 >>> r x c Tables with Fixed Row or Column Totals
14.6 >>> Other Applications
14.7 >>> Summary and Concluding Remarks

15 >>> Nonparametric Statistics
15.1 >>> Introduction
15.2 >>> A General Two-Sampling Shift Model
15.3 >>> A Sign Test for a Matched Pairs Experiment
15.4 >>> The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment
15.5 >>> The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples
15.6 >>> The Mann-Whitney U Test: Independent Random Samples
15.7 >>> The Kruskal-Wallis Test for One-Way Layout
15.8 >>> The Friedman Test for Randomized Block Designs
15.9 >>> The Runs Test: A Test for Randomness
15.10 >>> Rank Correlation Coefficient
15.11 >>> Some General Comments on Nonparametric Statistical Test

16 >>> Appendix 1: Matrices and Other Useful Mathematical Results
16.1 >>> Appendix 1.1: Matrices and Matrix Algebra
16.2 >>> Appendix 1.2: Addition of Matrices
16.3 >>> Appendix 1.3: Multiplication of a Matrix by a Real Number
16.4 >>> Appendix 1.4: Matrix Multiplication
16.5 >>> Appendix 1.5: Identity Elements
16.6 >>> Appendix 1.6: The Inverse of a Matrix
16.7 >>> Appendix 1.7: The Transpose of a Matrix
16.8 >>> Appendix 1.8: A Matrix Expression for a System of Simultaneous Linear Equations
16.9 >>> Appendix 1.9: Inverting a Matrix
16.10 >>> Appendix 1.10: Solving a System of Simultaneous Linear Equations
16.11 >>> Appendix 1.11: Other Useful Mathematical Results

17 >>> Appendix 2: Common Probability Distributions, Means, Variances, and Moment Generating Functions
17.1 >>> Appendix 2.1: Discrete Distributions
17.2 >>> Appendix 2.2: Continuous Distributions.

18 >>> Appendix 3: Tables
18.1 >>> Appendix 3.1: Binomial Probabilities
18.2 >>> Appendix 3.2: Table of e-x
18.3 >>> Appendix 3.3: Poisson Probabilities
18.4 >>> Appendix 3.4: Normal Curve Areas
18.5 >>> Appendix 3.5: Percentage Points of the t Distributions
18.6 >>> Appendix 3.6: Percentage Points of the F Distributions
18.7 >>> Appendix 3.7: Distribution of Function U
18.8 >>> Appendix 3.8: Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test
18.9 >>> Appendix 3.9: Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a)
18.10 >>> Appendix 3.10: Critical Values of Pearman's Rank Correlation Coefficient
18.11 >>> Appendix 3.11: Random Numbers

TitleText('Calculus')
EditionText('5')
AuthorText('Stewart')

1 >>> Functions and Models
1.1 >>> Four Ways to Represent a Function
1.2 >>> Mathematical Models: A Catalog of Essential Functions
1.3 >>> New Functions from Old Functions
1.4 >>> Graphing Calculators and Computers

2 >>> Limits and Rates of Change
2.1 >>> The Tangent and Velocity Problems
2.2 >>> The Limit of a Function
2.3 >>> Calculating Limits Using the Limit Laws
2.4 >>> The Precise Definition of a Limit
2.5 >>> Continuity
2.6 >>> Tangents, Velocities, and Other Rates of Change

3 >>> Derivatives
3.1 >>> Derivatives
3.2 >>> The Derivative as a Function
3.3 >>> Differentiation Formulas
3.4 >>> Rates of Change in the Natural and Social Sciences
3.5 >>> Derivatives of Trigonometric Functions
3.6 >>> The Chain Rule
3.7 >>> Implicit Differentiation
3.8 >>> Higher Derivatives
3.9 >>> Related Rates
3.10 >>> Linear Approximations and Differentials

4 >>> Applications of Differentiation
4.1 >>> Maximum and Minimum Values
4.2 >>> The Mean Value Theorem
4.3 >>> How Derivatives Affect the Shape of a Graph
4.4 >>> Limits at Infinity; Horizontal Asymptotes
4.5 >>> Summary of Curve Sketching
4.6 >>> Graphing with Calculus and Calculators
4.7 >>> Optimization Problems
4.8 >>> Applications to Business and Economics
4.9 >>> Newton's Method
4.10 >>> Antiderivatives

5 >>> Integrals
5.1 >>> Areas and Distances
5.2 >>> The Definite Integral
5.3 >>> The Fundamental Theorem of Calculus
5.4 >>> Indefinite Integrals and the Net Change Theorem
5.5 >>> The Substitution Rule

6 >>> Applications of Integration
6.1 >>> Areas between Curves
6.2 >>> Volumes
6.3 >>> Volumes by Cylindrical Shells
6.4 >>> Work
6.5 >>> Average Value of a Function

7 >>> Inverse Functions
7.1 >>> Inverse Functions
7.2 >>> Exponential Functions and Their Derivatives
7.3 >>> Logarithmic Functions
7.4 >>> Derivatives of Logarithmic Functions
7.5 >>> Inverse Trigonometric Functions
7.6 >>> Hyperbolic Functions
7.7 >>> Indeterminate Forms and L'Hospital's Rule

8 >>> Techniques of Integration
8.1 >>> Integration by Parts
8.2 >>> Trigonometric Integrals
8.3 >>> Trigonometric Substitution
8.4 >>> Integration of Rational Functions by Partial Fractions
8.5 >>> Strategy for Integration
8.6 >>> Integration Using Tables and Computer Algebra Systems
8.7 >>> Approximate Integration
8.8 >>> Improper Integrals

9 >>> Further Applications of Integration
9.1 >>> Arc Length
9.2 >>> Area of a Surface of Revolution
9.3 >>> Applications to Physics and Engineering
9.4 >>> Applications to Economics and Biology
9.5 >>> Probability

10 >>> Differential Equations
10.1 >>> Modeling with Differential Equations
10.2 >>> Direction Fields and Euler's Method
10.3 >>> Separable Equations
10.4 >>> Exponential Growth and Decay
10.5 >>> The Logistic Equation
10.6 >>> Linear Equations
10.7 >>> Predator-Prey Systems

11 >>> Parametric Equations and Polar Coordinates
11.1 >>> Curves Defined by Parametric Equations
11.2 >>> Calculus with Parametric Curves
11.3 >>> Polar Coordinates
11.4 >>> Areas and Lengths in Polar Coordinates
11.5 >>> Conic Sections
11.6 >>> Conic Sections in Polar Coordinates

12 >>> Infinite Sequences and Series
12.1 >>> Sequences
12.2 >>> Series
12.3 >>> The Integral Test and Estimates of Sums
12.4 >>> The Comparison Tests
12.5 >>> Alternating Series
12.6 >>> Absolute Convergence and the Ratio and Root Tests
12.7 >>> Strategy for Testing Series
12.8 >>> Power Series
12.9 >>> Representations of Functions as Power Series
12.10 >>> Taylor and Maclaurin Series
12.11 >>> The Binomial Series
12.12 >>> Applications of Taylor Polynomials

13 >>> Vectors and the Geometry of Space
13.1 >>> Three-Dimensional Coordinate Systems
13.2 >>> Vectors
13.3 >>> The Dot Product
13.4 >>> The Cross Product
13.5 >>> Equations of Lines and Planes
13.6 >>> Cylinders and Quadric Surfaces
13.7 >>> Cylindrical and Spherical Coordinates

14 >>> Vector Functions
14.1 >>> Vector Functions and Space Curves
14.2 >>> Derivatives and Integrals of Vector Functions
14.3 >>> Arc Length and Curvature
14.4 >>> Motion in Space: Velocity and Acceleration

15 >>> Partial Derivatives
15.1 >>> Functions of Several Variables
15.2 >>> Limits and Continuity
15.3 >>> Partial Derivatives
15.4 >>> Tangent Planes and Linear Approximations
15.5 >>> The Chain Rule
15.6 >>> Directional Derivatives and the Gradient Vector
15.7 >>> Maximum and Minimum Values
15.8 >>> Lagrange Multipliers

16 >>> Multiple Integrals
16.1 >>> Double Integrals over Rectangles
16.2 >>> Iterated Integrals
16.3 >>> Double Integrals over General Regions
16.4 >>> Double Integrals in Polar Coordinates
16.5 >>> Applications of Double Integrals
16.6 >>> Surface Area
16.7 >>> Triple Integrals
16.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates
16.9 >>> Change of Variables in Multiple Integrals

17 >>> Vector Calculus
17.1 >>> Vector Fields
17.2 >>> Line Integrals
17.3 >>> The Fundamental Theorem for Line Integrals
17.4 >>> Green's Theorem
17.5 >>> Curl and Divergence
17.6 >>> Parametric Surfaces and Their Areas
17.7 >>> Surface Integrals
17.8 >>> Stokes' Theorem
17.9 >>> The Divergence Theorem
17.10 >>> Summary

18 >>> Second-Order Differential Equations
18.1 >>> Second-Order Linear Equations
18.2 >>> Nonhomogeneous Linear Equations
18.3 >>> Applications of Second- Order Differential Equations
18.4 >>> Series Solutions

25 >>> Appendix H: Complex Numbers

TitleText('College Algebra')
EditionText('4')
AuthorText('Stewart, Redlin, Watson')

0 >>> Prerequisites
0.1 >>> Modeling the Real World
0.2 >>> Real Numbers
0.3 >>> Integer Exponents
0.4 >>> Rational Exponents and Radicals
0.5 >>> Algebraic Expressions
0.6 >>> Factoring
0.7 >>> Rational Expressions

1 >>> Equations and Inequalities
1.1 >>> Basic Equations
1.2 >>> Modeling with Equations
1.3 >>> Quadratic Equations
1.4 >>> Complex Numbers
1.5 >>> Other Types of Equations
1.6 >>> Inequalities
1.7 >>> Absolute Value Equations and Inequalities

2 >>> Coordinates and Graphs
2.1 >>> The Coordinate Plane
2.2 >>> Graphs of Equations in Two Variables
2.3 >>> Graphing Calculators; Solving Equations and Inequalitie Graphically
2.4 >>> Lines
2.5 >>> Modeling: Variation

3 >>> Functions
3.1 >>> What Is a Function?
3.2 >>> Graphs of Functions
3.3 >>> Increasing and Decreasing Functions; Average Rate of Change
3.4 >>> Transformations of Functions
3.5 >>> Quadratic Functions; Maxima and Minima
3.6 >>> Combining Functions
3.7 >>> One-to-One Functions and Their Inverses

4 >>> Polynomial and Rational Functions
4.1 >>> Polynomial Functions and Their Graphs
4.2 >>> Dividing Polynomials
4.3 >>> Real Zeros of Polynomials
4.4 >>> Complex Zeros and the Fundamental Theorem of Algebra
4.5 >>> Rational Functions
5 >>> Exponential and Logarithmic Functions
5.1 >>> Exponential Functions
5.2 >>> Logarithmic Functions
5.3 >>> Laws of Logarithms
5.4 >>> Exponential and Logarithmic Equations
5.5 >>> Modeling with Exponential and Logarithmic Functions

6 >>> Systems of Equations and Inequalities
6.1 >>> Systems of Equations
6.2 >>> Systems of Linear Equations in Two Variables
6.3 >>> Systems of Linear Equations in Several Variables
6.4 >>> Systems of Inequalities
6.5 >>> Partial Fractions

7 >>> Matrices and Determinants
7.1 >>> Matrices and Systems of Linear Equations
7.2 >>> The Algebra of Matrices
7.3 >>> Inverses of Matrices and Matrix Equations
7.4 >>> Determinants and Cramer's Rule

8 >>> Conic Sections
8.1 >>> Parabolas
8.2 >>> Ellipses
8.3 >>> Hyperbolas
8.4 >>> Shifted Conics

9 >>> Sequences and Series
9.1 >>> Sequences and Summation Notation
9.2 >>> Arithmetic Sequences
9.3 >>> Geometric Sequences
9.4 >>> Mathematics of Finance
9.5 >>> Mathematical Induction
9.6 >>> The Binomial Theorem

10 >>> Counting and Probability
10.1 >>> Counting Principles
10.2 >>> Permutations and Combinations
10.3 >>> Probability
10.4 >>> Binomial Probability
10.5 >>> Expected Value

TitleText('Statistics for Management and Economics')
EditionText('7')
AuthorText('Keller')

1 >>> What is Statistics?
1.1 >>> Key Statistical Concepts
1.2 >>> Statistical Applications in Business
1.3 >>> Statistics and the Computer
1.4 >>> World Wide Web and Learning Center
1.A >>> Instructions for the CD-ROM
1.B >>> Introduction to Microsoft Excel
1.C >>> Introduction to Minitab
2 >>> Graphical and Tabular Descriptive Techniques
2.1 >>> Types of Data and Information
2.2 >>> Graphical and Tabular Techniques for Nominal Data
2.3 >>> Graphical Techniques for Interval Data
2.4 >>> Describing the relationship Between Two Variables
2.5 >>> Describing Time-Series Data
3 >>> Art and Science of Graphical Presentations
3.1 >>> Graphical Excellence
3.2 >>> Graphical Deception
3.3 >>> Presenting Statistics: Written Reports and Oral Presentations
4 >>> Numerical Descriptive Techniques
4.1 >>> Measures of Central Location
4.2 >>> Measures of Variability
4.3 >>> Measures of Relative Standing and Box Plots
4.4 >>> Measures of Linear Relationship
4.5 >>> Applications in Professional Sports: Baseball
4.6 >>> Comparing Graphical and Numerical Techniques
4.7 >>> General Guidelines for Exploring Data
5 >>> Data Collection and Sampling
5.1 >>> Methods of Collecting Data
5.2 >>> Sampling
5.3 >>> Sampling Plans
5.4 >>> Sampling and Nonsampling Errors
6 >>> Probability
6.1 >>> Assigning Probability to Events
6.2 >>> Joint, Marginal, and Conditional Probability
6.3 >>> Probability Rules and Trees
6.4 >>> Bayes' Law
6.5 >>> Identifying the Correct Method
7 >>> Random Variables and Discrete Probability Distributions
7.1 >>> Random Variables and Probability Distributions
7.2 >>> Bivariate Distributions
7.3 >>> Applications in Finance: Portfolio Diversification and Asset Allocation
7.4 >>> Binomial Distribution
7.5 >>> Poisson Distribution
8 >>> Continuous Probability Distributions
8.1 >>> Probability Density Functions
8.2 >>> Normal Distribution
8.3 >>> Exponential Distribution
8.4 >>> Other Continuous Distributions
9 >>> Sampling Distributions
9.1 >>> Sampling Distribution of the Mean
9.2 >>> Sampling Distribution of a Proportion
9.3 >>> Sampling Distribution of the Difference Between Two Means
9.4 >>> From Here to Inference
10 >>> Introduction to Estimation
10.1 >>> Concepts of Estimation
10.2 >>> Estimating the Population Mean When the Population Standard Deviation is Known
10.3 >>> Selecting the Sample Size
11 >>> Introduction to Hypothesis Testing
11.1 >>> Concepts of Hypothesis Testing
11.2 >>> Testing the Population Mean When the Population Standard Deviation is Known
11.3 >>> Calculating the Probability of a Type II Error
11.4 >>> The Road Ahead
12 >>> Inference About a Population
12.1 >>> Inference About a Population Mean When the Standard Deviation is Unknown
12.2 >>> Inference about a Population Variance
12.3 >>> inference about a Population Proportion
12.4 >>> Applications in Marketing: Market Segmentation
12.5 >>> Applications in Marketing: Auditing
13 >>> Inference About Comparing Two Populations
13.1 >>> Inference about the Difference Between Two Means: Independent Samples
13.2 >>> Observational and Experimental Data
13.3 >>> Inference about the Difference Between Two Means: Matched Pairs Experiment
13.4 >>> Inference about the Ratio of Two Variances
13.5 >>> Inference about the Difference Between Two Population Proportions
13.A >>> Excel Instructions for Stacked and Unstacked Data
13.B >>> Minitab Instructions for Stacked and Unstacked Data
14 >>> Statistical Inference: Review of Chapters 12 and 13
14.1 >>> Guide to Identifying the Correct Technique: Chapters 12 and 13
15 >>> Analysis of Variance
15.1 >>> One-Way Analysis of Variance
15.2 >>> Analysis of Variance Experimental Designs
15.3 >>> Randomized Blocks (Two-Way) Analysis of Variance
15.4 >>> Two-Factor Analysis of Variance
15.5 >>> Appplications in Operations Management: Finding and Reducing Variation
15.6 >>> Multiple Comparisons
16 >>> Chi-Squared Tests
16.1 >>> Chi-Squared Goodness-of-Fit Test
16.2 >>> Chi-Squared Test of a Contingency Table
16.3 >>> Summary of Tests on Nominal Data
16.4 >>> Chi-Squared Tests of Normality
17 >>> Simple Linear Regression and Correlation
17.1 >>> Model
17.2 >>> Estimating the Coefficients
17.3 >>> Error Variable: Required Conditions
17.4 >>> Assessing the Model
17.5 >>> Applications in Finance: Market Model
17.6 >>> Using the Regression Equation
17.7 >>> Regression Diagnostics-I
18 >>> Multiple Regression
18.1 >>> Model and Required Conditions
18.2 >>> Estimating the Coefficients and Assessing the Model
18.3 >>> Regression Diagnostics-II
18.4 >>> Regression Diagnostics-III (Time Series)

19 >>> Appendix A: Excel Troubleshooting and Detailed Instructions
20 >>> Appendix B: Minitab Detailed Instructions
21 >>> Appendix C: Approximating Means and Variances from Grouped Data
22 >>> Appendix D: Descriptive Techniques Review Exercises
23 >>> Appendix E: Couting Formulas
24 >>> Appendix F: Hypergeometric Distribution
25 >>> Appendix G: Continuous Probability Distributions: Calculus Approach
26 >>> Appendix H: Using the Laws of Expected Value and Variance to Derive the Parameters of Sampling Distributions
27 >>> Appendix I: Excel Spreadsheets for Techniques in Chapters 10-13
28 >>> Appendix K: Converting Excel's Probabilities to p-Values
29 >>> Appendix J: Excel and Minitab Instructions for Missing Data and for Recoding Data
30 >>> Appendix L: Probability of a Type II Error When Testing a Proportion
31 >>> Appendix M: Approximating p-Values from the Student t Table
32 >>> Appendix N: Probability of a Type II Error When Testing the Difference Between Two Means
33 >>> Appendix O: Probability of a Type II Erorr When Testing the Difference Between Two Proportions
34 >>> Appendix P: Bartlett's Test
35 >>> Appendix Q: Minitab Instructions for the Chi-Squared Goodness-of-Fit Test and the Test for Normality
36 >>> Appendix R: The Rule of Five
37 >>> Appendix S: Deriving the Normal Equations
38 >>> Appendix T: Szroeter's Test for Heteroscedasticity
39 >>> Appendix U: Transformations

TitleText('Elementary Linear Algebra')

EditionText('5')

AuthorText('Larson, Edwards, Falvo')


1 >>> Systems of Linear Equations
1.1 >>> Introduction to Systems of Linear Equations
1.2 >>> Gaussian Elimination and Gauss-Jordan Elimination
1.3 >>> Applications of Systems of Linear Equations

2 >>> Matrices
2.1 >>> Operations with Matrices
2.2 >>> Properties of Matrix Operations
2.3 >>> The Inverse of a Matrix
2.4 >>> Elementary Matrices
2.5 >>> Applications of Matrix Operations

3 >>> Determinants
3.1 >>> The Determinant of a Matrix
3.2 >>> Evaluation of a Determinant Using Elementary Operations
3.3 >>> Properties of Determinants
3.4 >>> Introduction to Eigenvalues
3.5 >>> Applications of Determinants

4 >>> Vector Spaces

4.1 >>> Vectors in Rn
4.2 >>> Vector Spaces
4.3 >>> Subspaces of Vector Spaces
4.4 >>> Spanning Sets and Linear Independence
4.5 >>> Basis and Dimension
4.6 >>> Rank of a Matrix and Systems of Linear Equations
4.7 >>> Coordinates and Change of Basis
4.8 >>> Applications of Vector Spaces

5 >>> Inner Product Spaces
5.1 >>> Length and Dot Product in Rn
5.2 >>> Inner Product Spaces
5.3 >>> Orthonormal Bases: Gram-Schmidt Process
5.4 >>> Mathematical Models and Least Squares Analysis
5.5 >>> Applications of Inner Product Spaces

6 >>> Linear Transformations
6.1 >>> Introduction to Linear Transformations
6.2 >>> The Kernel and Range of a Linear Transformation
6.3 >>> Matrices for Linear Transformations
6.4 >>> Transition Matrices and Similarity
6.5 >>> Applications of Linear Transformations

7 >>> Eigenvalues and Eigenvectors
7.1 >>> Eigenvalues and Eigenvectors
7.2 >>> Diagonalization
7.3 >>> Symmetric Matrices and Orthogonal Diagonalization
7.4 >>> Applications of Eigenvalues and Eigenvectors

8 >>> Complex Vector Spaces
8.1 >>> Complex Numbers
8.2 >>> Conjugates and Division of Complex Numbers
8.3 >>> Polar Form and DeMoivre's Theorem
8.4 >>> Complex Vector Spaces and Inner Products
8.5 >>> Unitary and Hermitian Matrices

9 >>> Linear Programming
9.1 >>> Systems of Linear Inequalities
9.2 >>> Linear Programming Involving Two Variables
9.3 >>> The Simplex Method: Maximization
9.4 >>> The Simplex Method: Minimization
9.5 >>> The Simplex Method: Mixed Constraints

10 >>> Numerical Methods

10.1 >>> Gaussian Elimination with Partial Pivoting
10.2 >>> Interative Methods for Solving Linear Systems
10.3 >>> Power Method for Approximating Eigenvalues
10.4 >>> Applications of Numerical Methods

11 >>> Appendix A: Mathematical Induction and Other Forms of Proofs

12 >>> Appendix B: Computer Algebra Systems and Graphing Calculators

TitleText('Basic Multivariable Calculus')
EditionText('3')
AuthorText('Marsden, Tromba, Weinstein')

1 >>> Algebra and Geometry of Euclidean Space
1.1 >>> Vectors in the Plane and Space
1.2 >>> The Inner Product and Distance
1.3 >>> 2 x 2 and 3 x 3 Matrices and Determinants
1.4 >>> The Cross Product and Planes
1.5 >>> n-Dimensional Euclidean Space
1.6 >>> Curves in the Plane and in Space

2 >>> Differentiation
2.1 >>> Graphs and Level Surfaces
2.2 >>> Partial Derivatives and Continuity
2.3 >>> Differentiability, the Derivative Matrix, and Tangent Planes
2.4 >>> The Chain Rule
2.5 >>> Gradients and Directional Derivatives
2.6 >>> Implicit Differentiation

3 >>> Higher Derivatives and Extrema
3.1 >>> Higher Order Partial Derivatives
3.2 >>> Taylor's Theorem
3.3 >>> Maxima and Minima
3.4 >>> Second Derivative Test
3.5 >>> Constrained Extrema and Lagrange Multipliers

4 >>> Vector-Valued Functions
4.1 >>> Acceleration
4.2 >>> Arc Length
4.3 >>> Vector Fields
4.4 >>> Divergence and Curl

5 >>> Multiple Integrals
5.1 >>> Volume and Cavalieri's Principle
5.2 >>> The Double Integral Over a Rectangle
5.3 >>> The Double Integral Over Regions
5.4 >>> Triple Integrals
5.5 >>> Change of Variables, Cylindrical and Spherical Coordinates
5.6 >>> Applications of Multiple Integrals

6 >>> Integrals Over Curves and Surfaces
6.1 >>> Line Integrals
6.2 >>> Parametrized Surfaces
6.3 >>> Area of a Surface
6.4 >>> Surface Integrals

7 >>> The Integral Theorems of Vector Analysis
7.1 >>> Green's Theorem
7.2 >>> Stokes' Theorem
7.3 >>> Gauss' Theorem
7.4 >>> Path Independence and the Fundamental Theorems of Calculus

TitleText('Precalculus')
EditionText('5')
AuthorText('Stewart, Redlin, Watson')

1 >>> Fundamentals
1.1 >>> Real Numbers
1.2 >>> Exponents and Radicals
1.3 >>> Algebraic Expressions
1.4 >>> Rational Expression
1.5 >>> Equations
1.6 >>> Modeling with Equations
1.7 >>> Inequalities
1.8 >>> Coordinate Geometry
1.9 >>> Graphing Calculators; Solving Equations and Inequalities Graphically
1.10 >>> Lines
1.11 >>> Modeling Variation

2 >>> Functions
2.1 >>> What is a Function?
2.2 >>> Graphs of Functions
2.3 >>> Increasing and Decreasing Functions; Average Rate of Change
2.4 >>> Transformations of Functions
2.5 >>> Quadratic Functions; Maxima and Minima
2.6 >>> Modeling with Functions
2.7 >>> Combining Functions
2.8 >>> One-to-One Functions and Their Inverses

3 >>> Polynomial and Rational Functions
3.1 >>> Polynomial Functions and Their Graphs
3.2 >>> Dividing Polynomials
3.3 >>> Real Zeros of Polynomials
3.4 >>> Complex Numbers
3.5 >>> Complex Zeros and the Fundamental Theorem of Algebra
3.6 >>> Rational Functions

4 >>> Exponential and Logarithmic Functions
4.1 >>> Exponential Functions
4.2 >>> Logarithmic Functions
4.3 >>> Laws of Logarithms
4.4 >>> Exponential and Logarithmic Equations
4.5 >>> Modeling with Exponential and Logarithmic Functions

5 >>> Trigonometric Functions of Real Numbers
5.1 >>> The Unit Circle
5.2 >>> Trigonometric Functions of Real Numbers
5.3 >>> Trigonometric Graphs
5.4 >>> More Trigonometric Graphs
5.5 >>> Modeling Harmonic Motion

6 >>> Trigonometric Functions of Angles
6.1 >>> Angle Measures
6.2 >>> Trigonometry of Right Triangles
6.3 >>> Trigonometric Functions of Angles
6.4 >>> The Law of Sines
6.5 >>> The Law of Cosines

7 >>> Analytic Trigonometry
7.1 >>> Trigonometric Identities
7.2 >>> Addition and Subtraction Formulas
7.3 >>> Double-Angle, Half-Angle, and Sum-Product Formulas
7.4 >>> Inverse Trigonometric Functions
7.5 >>> Trigonometric Equations

8 >>> Polar Coordinates and Vectors
8.1 >>> Polar Coordinates
8.2 >>> Graphs of Polar Equations
8.3 >>> Polar Form of Complex Numbers; DeMoivre's Theorem
8.4 >>> Vectors
8.5 >>> The Dot Product

9 >>> Systems of Equations and Inequalities
9.1 >>> Systems of Equations
9.2 >>> Systems of Linear Equations in Two Variables
9.3 >>> Systems of Linear Equations in Several Variables
9.4 >>> Systems of Linear Equations: Matrices
9.5 >>> The Algebra of Matrices
9.6 >>> Inverses of Matrices and Matrix Equations
9.7 >>> Determinants and Cramer's Rule
9.8 >>> Partial Fractions
9.9 >>> Systems of Inequalities

10 >>> Analytic Geometry
10.1 >>> Parabolas
10.2 >>> Ellipses
10.3 >>> Hyperbolas
10.4 >>> Shifted Conics
10.5 >>> Rotation of Axes
10.6 >>> Polar Equations of Conics
10.7 >>> Plane Curves and Parametric Equations

11 >>> Sequences and Series
11.1 >>> Sequences and Summation Notation
11.2 >>> Arithmetic Sequences
11.3 >>> Geometric Sequences
11.4 >>> Mathematics of Finance
11.5 >>> Mathematical Induction
11.6 >>> The Binomial Theorem

12 >>> Limits: A Preview of Calculus
12.1 >>> Finding Limits Numerically and Graphically
12.2 >>> Finding Limits Algebraically
12.3 >>> Tangent Lines and Derivatives
12.4 >>> Limits at Infinity: Limits of Sequences
12.5 >>> Areas

TitleText('Discrete Mathematics')
EditionText('4')
AuthorText('Rosen')


1 >>> The Foundations: Logic, Sets, and Functions
1.1 >>> Logic
1.2 >>> Propositional Equivalences
1.3 >>> Predicates and Quantifiers
1.4 >>> Sets
1.5 >>> Set Operations
1.6 >>> Functions
1.7 >>> Sequences and Summations
1.8 >>> The Growth Functions

2 >>> The Fundamentals: Algorithms, the Integers, and Matrices
2.1 >>> Algorithms
2.2 >>> Complexity of Algorithms
2.3 >>> The Integers and Division
2.4 >>> Integers and Algorithms
2.5 >>> Applications of Number Theory
2.6 >>> Matrices

3 >>> Mathematical Reasoning

3.1 >>> Methods of Proof
3.2 >>> Mathematical Induction
3.3 >>> Recursive Definitions
3.4 >>> Recursive Algorithms
3.5 >>> Program Correctness

4 >>> Counting
4.1 >>> The Basics of Counting
4.2 >>> The Pigeonhole Principle
4.3 >>> Permutations and Combinations
4.4 >>> Discrete Probability
4.5 >>> Probability Theory
4.6 >>> Generalized Permutations and Combinations
4.7 >>> Generating Permutations and Combinations

5 >>> Advanced Counting Techniques
5.1 >>> Recurrence Relations
5.2 >>> Solving Recurrence Relations
5.3 >>> Divide-and-Conquer Relations
5.4 >>> Generating Functions
5.5 >>> Inclusion-Exclusion
5.6 >>> Applications of Inclusion-Exclusion

6 >>> Relations
6.1 >>> Relations and Their Properties
6.2 >>> n-ary Relations and Their Applications
6.3 >>> Representing Relations
6.4 >>> Closures of Relations
6.5 >>> Equivalence Relations
6.6 >>> Partial Orderings

7 >>> Graphs
7.1 >>> Introduction to Graphs
7.2 >>> Graph Terminology
7.3 >>> Representing Graphs and Graph Isomorphism
7.4 >>> Connectivity
7.5 >>> Euler and Hamilton Paths
7.6 >>> Shortest Path Problems
7.7 >>> Planar Graphs
7.8 >>> Graph Coloring

8 >>> Trees
8.1 >>> Introduction to Trees
8.2 >>> Applications of Trees
8.3 >>> Tree Traversal
8.4 >>> Trees and Sorting
8.5 >>> Spanning Trees
8.6 >>> Minimum Spanning Trees

9 >>> Boolean Algebra
9.1 >>> Boolean Functions
9.2 >>> Representing Boolean Functions
9.3 >>> Logic Gates
9.4 >>> Minimization of Circuits

10 >>> Modeling Computation
10.1 >>> Languages and Grammars
10.2 >>> Finite-State Machines with Output
10.3 >>> Finite-State Machines with No Output
10.4 >>> Language Recognition
10.5 >>> Turing Machines

11 >>> Appendix: Exponential and Logarithmic Functions
12 >>> Appendix: Pseudocode

TitleText('Complex Analysis')
EditionText('3')
AuthorText('Saff, Snider')

1 >>> Complex Numbers
1.1 >>> The Algebra of Complex Numbers
1.2 >>> Point Representation of Complex Numbers
1.3 >>> Vectors and Polar Forms
1.4 >>> The Complex Exponential
1.5 >>> Powers and Roots
1.6 >>> Planar Sets
1.7 >>> The Riemann Sphere and Stereographic Projection

2 >>> Analytic Functions
2.1 >>> Functions of a Complex Variable
2.2 >>> Limits and Continuity
2.3 >>> Analyticity
2.4 >>> The Cauchy-Riemann Equations
2.5 >>> Harmonic Functions
2.6 >>> Steady-State Temperature as a Harmonic Function
2.7 >>> Iterated Maps: Julia and Mandelbrot Sets

3 >>> Elementary Functions
3.1 >>> Polynomials and Rational Functions
3.2 >>> The Exponential, Trigonometric, and Hyperbolic Functions
3.3 >>> The Logarithmic Function
3.4 >>> Washers, Wedges, and Walls
3.5 >>> Complex Powers and Inverse Trigonometric Functions
3.6 >>> Application to Oscillating Systems

4 >>> Complex Integration
4.1 >>> Contours
4.2 >>> Contour Integrals
4.3 >>> Independence of Path
4.4 >>> Cauchy's Integral Theorem
4.5 >>> Deformation of Contours Approach
4.6 >>> Vector Analysis Approach
4.7 >>> Cauchy's Integral Formula and Its Consequences
4.8 >>> Bounds for Analytic Functions
4.9 >>> Applications to Harmonic Functions

5 >>> Series Representations for Analytic Functions
5.1 >>> Sequences and Series
5.2 >>> Taylor Series
5.3 >>> Power Series
5.4 >>> Mathematical Theory of Convergence
5.5 >>> Laurent Series
5.6 >>> Zeros and Singularities
5.7 >>> The Point at Infinity
5.8 >>> Analytic Continuation

6 >>> Residue Theory
6.1 >>> The Residue Theorem
6.2 >>> Trigonometric Integrals over [0, 2¹]
6.3 >>> Improper Integrals of Certain Functions over (--°, °)
6.4 >>> Improper Integrals Involving Trigonometric Functions
6.5 >>> Indented Contours
6.6 >>> Integrals Involving Multiple-Valued Functions
6.7 >>> The Argument Principle and Rouche's Theorem

7 >>> Conformal Mapping
7.1 >>> Invariance of Laplace's Equation
7.2 >>> Geometric Considerations
7.3 >>> Mobius Transformations
7.4 >>> Mobius Transformations, Continued
7.5 >>> The Schwarz-Christoffel Transformation
7.6 >>> Applications in Electrostatics, Heat Flow, and Fluid Mechanics
7.7 >>> Further Physical Applications of Conformal Mapping

8 >>> The Transforms of Applied Mathematics
8.1 >>> Fourier Series (The Finite Fourier Transform)
8.2 >>> The Fourier Transform
8.3 >>> The Laplace Transform
8.4 >>> The z-Transform
8.5 >>> Cauchy Integrals and the Hilbert Transform

9 >>> Appendix A: Numerical Construction of Conformal Maps
9.1 >>> The Schwarz-Christoffel Parameter Problem
9.2 >>> Examples
9.3 >>> Numerical Integration
9.4 >>> Conformal Mapping of Smooth Domains
9.5 >>> Conformal Mapping Software

10 >>> Appendix B: Table of Conformal Mappings
10.1 >>> Mobius Transformations
10.2 >>> Other Transformations

TitleText('Calculus: Early Transcendentals')
EditionText('5')
AuthorText('Stewart')

1 >>> Functions and Models
1.1 >>> Four Ways to Represent a Function
1.2 >>> Mathematical Models: A Catalog of Essential Functions
1.3 >>> New Functions from Old Functions
1.4 >>> Graphing Calculators and Computers
1.5 >>> Exponential Functions
1.6 >>> Inverse Functions and Logarithms

2 >>> Limits and Derivatives
2.1 >>> The Tangent and Velocity Problems
2.2 >>> The Limit of a Function
2.3 >>> Calculating Limits Using the Limit Laws
2.4 >>> The Precise Definition of a Limit
2.5 >>> Continuity
2.6 >>> Limits at Infinity; Horizontal Asymptotes
2.7 >>> Tangents, Velocities, and Other Rates of Change
2.8 >>> Derivatives
2.9 >>> The Derivative as a Function

3 >>> Differentiation Rules
3.1 >>> Derivatives of Polynomials and Exponential Functions
3.2 >>> The Product and Quotient Rules
3.3 >>> Rates of Change in the Natural and Social Sciences
3.4 >>> Derivatives of Trigonometric Functions
3.5 >>> The Chain Rule
3.6 >>> Implicit Differentiation
3.7 >>> Higher Derivatives
3.8 >>> Derivatives of Logarithmic Functions
3.9 >>> Hyperbolic Functions
3.10 >>> Related Rates
3.11 >>> Linear Approximations and Differentials

4 >>> Applications of Differentiation
4.1 >>> Maximum and Minimum Values
4.2 >>> The Mean Value Theorem
4.3 >>> How Derivatives Affect the Shape of a Graph
4.4 >>> Indeterminate Forms and L'Hospital's Rule
4.5 >>> Summary of Curve Sketching
4.6 >>> Graphing with Calculus and Calculators
4.7 >>> Optimization Problems
4.8 >>> Applications to Business and Economics
4.9 >>> Newton's Method
4.10 >>> Antiderivatives

5 >>> Integrals
5.1 >>> Areas and Distances
5.2 >>> The Definite Integral
5.3 >>> The Fundamental Theorem of Calculus
5.4 >>> Indefinite Integrals and the Net Change Theorem
5.5 >>> The Substitution Rule
5.6 >>> The Logarithm Defined as an Integral

6 >>> Applications of Integration
6.1 >>> Areas between Curves
6.2 >>> Volumes
6.3 >>> Volumes by Cylindrical Shells
6.4 >>> Work
6.5 >>> Average Value of a Function

7 >>> Techniques of Integration
7.1 >>> Integration by Parts
7.2 >>> Trigonometric Integrals
7.3 >>> Trigonometric Substitution
7.4 >>> Integration of Rational Functions by Partial Fractions
7.5 >>> Strategy for Integration
7.6 >>> Integration Using Tables and Computer Algebra Systems
7.7 >>> Approximate Integration
7.8 >>> Improper Integrals

8 >>> Further Applications of Integration
8.1 >>> Arc Length
8.2 >>> Area of a Surface of Revolution
8.3 >>> Applications to Physics and Engineering
8.4 >>> Applications to Economics and Biology
8.5 >>> Probability

9 >>> Differential Equations
9.1 >>> Modeling with Differential Equations
9.2 >>> Direction Fields and Euler's Method
9.3 >>> Separable Equations
9.4 >>> Exponential Growth and Decay
9.5 >>> The Logistic Equation
9.6 >>> Linear Equations
9.7 >>> Predator-Prey Systems

10 >>> Parametric Equations and Polar Coordinates
10.1 >>> Curves Defined by Parametric Equations
10.2 >>> Calculus with Parametric Curves
10.3 >>> Polar Coordinates
10.4 >>> Areas and Lengths in Polar Coordinates
10.5 >>> Conic Sections
10.6 >>> Conic Sections in Polar Coordinates

11 >>> Infinite Sequences and Series
11.1 >>> Sequences
11.2 >>> Series
11.3 >>> The Integral Test and Estimates of Sums
11.4 >>> The Comparison Tests
11.5 >>> Alternating Series
11.6 >>> Absolute Convergence and the Ratio and Root Tests
11.7 >>> Strategy for Testing Series
11.8 >>> Power Series
11.9 >>> Representations of Functions as Power Series
11.10 >>> Taylor and Maclaurin Series
11.11 >>> The Binomial Series
11.12 >>> Applications of Taylor Polynomials

12 >>> Vectors and the Geometry of Space
12.1 >>> Three-Dimensional Coordinate Systems
12.2 >>> Vectors
12.3 >>> The Dot Product
12.4 >>> The Cross Product
12.5 >>> Equations of Lines and Planes
12.6 >>> Cylinders and Quadric Surfaces
12.7 >>> Cylindrical and Spherical Coordinates

13 >>> Vector Functions
13.1 >>> Vector Functions and Space Curves
13.2 >>> Derivatives and Integrals of Vector Functions
13.3 >>> Arc Length and Curvature
13.4 >>> Motion in Space: Velocity and Acceleration

14 >>> Partial Derivatives
14.1 >>> Functions of Several Variables
14.2 >>> Limits and Continuity
14.3 >>> Partial Derivatives
14.4 >>> Tangent Planes and Linear Approximations
14.5 >>> The Chain Rule
14.6 >>> Directional Derivatives and the Gradient Vector
14.7 >>> Maximum and Minimum Values
14.8 >>> Lagrange Multipliers

15 >>> Multiple Integrals
15.1 >>> Double Integrals over Rectangles
15.2 >>> Iterated Integrals
15.3 >>> Double Integrals over General Regions
15.4 >>> Double Integrals in Polar Coordinates
15.5 >>> Applications of Double Integrals
15.6 >>> Surface Area
15.7 >>> Triple Integrals
15.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates
15.9 >>> Change of Variables in Multiple Integrals

16 >>> Vector Calculus
16.1 >>> Vector Fields
16.2 >>> Line Integrals
16.3 >>> The Fundamental Theorem for Line Integrals
16.4 >>> Green's Theorem
16.5 >>> Curl and Divergence
16.6 >>> Parametric Surfaces and their Areas
16.7 >>> Surface Integrals
16.8 >>> Stokes' Theorem
16.9 >>> The Divergence Theorem
16.10 >>> Summary

17 >>> Second-Order Differential Equations
17.1 >>> Second-Order Linear Equations
17.2 >>> Nonhomogeneous Linear Equations
17.3 >>> Applications of Second-Order Differential Equations
17.4 >>> Series Solutions

18 >>> Appendix A: Numbers, Inequalities, and Absolute Values
19 >>> Appendix B: Coordinate Geometry and Lines
20 >>> Appendix C: Graphs of Second-Degree Equations
21 >>> Appendix D: Trigonometry
22 >>> Appendix E: Sigma Notation
23 >>> Appendix F: Proofs of Theorems
24 >>> Appendix G: Complex Numbers
25 >>> Appendix H: Answers to Odd-Numbered Exercises


TitleText('Calculus: Early Transcendentals')
EditionText('6')
AuthorText('Stewart')

1 >>> Functions and Models
1.1 >>> Four Ways to Represent a Function
1.2 >>> Mathematical Models: A Catalog of Essential Functions
1.3 >>> New Functions from Old Functions
1.4 >>> Graphing Calculators and Computers
1.5 >>> Exponential Functions
1.6 >>> Inverse Functions and Logarithms

2 >>> Limits and Derivatives
2.1 >>> The Tangent and Velocity Problems
2.2 >>> The Limit of a Function
2.3 >>> Calculating Limits Using the Limit Laws
2.4 >>> The Precise Definition of a Limit
2.5 >>> Continuity
2.6 >>> Limits at Infinity; Horizontal Asymptotes
2.7 >>> Derivatives and Rates of Change
2.8 >>> The Derivative as a Function

3 >>> Differentiation Rules
3.1 >>> Derivatives of Polynomials and Exponential Functions
3.2 >>> The Product and Quotient Rules
3.3 >>> Derivatives of Trigonometric Functions
3.4 >>> The Chain Rule
3.5 >>> Implicit Differentiation
3.6 >>> Derivatives of Logarithmic Functions
3.7 >>> Rates of Change in the Natural and Social Sciences
3.8 >>> Exponential Growth and Decay
3.9 >>> Related Rates
3.10 >>> Linear Approximations and Differentials
3.11 >>> Hyperbolic Functions

4 >>> Applications of Differentiation
4.1 >>> Maximum and Minimum Values
4.2 >>> The Mean Value Theorem
4.3 >>> How Derivatives Affect the Shape of a Graph
4.4 >>> Indeterminate Forms and L'Hospital's Rule
4.5 >>> Summary of Curve Sketching
4.6 >>> Graphing with Calculus and Calculators
4.7 >>> Optimization Problems
4.8 >>> Newton's Method
4.9 >>> Antiderivatives

5 >>> Integrals
5.1 >>> Areas and Distances
5.2 >>> The Definite Integral
5.3 >>> The Fundamental Theorem of Calculus
5.4 >>> Indefinite Integrals and the Net Change Theorem
5.5 >>> The Substitution Rule

6 >>> Applications of Integration
6.1 >>> Areas between Curves
6.2 >>> Volumes
6.3 >>> Volumes by Cylindrical Shells
6.4 >>> Work
6.5 >>> Average Value of a Function

7 >>> Techniques of Integration
7.1 >>> Integration by Parts
7.2 >>> Trigonometric Integrals
7.3 >>> Trigonometric Substitution
7.4 >>> Integration of Rational Functions by Partial Fractions
7.5 >>> Strategy for Integration
7.6 >>> Integration Using Tables and Computer Algebra Systems
7.7 >>> Approximate Integration
7.8 >>> Improper Integrals

8 >>> Further Applications of Integration
8.1 >>> Arc Length
8.2 >>> Area of a Surface of Revolution
8.3 >>> Applications to Physics and Engineering
8.4 >>> Applications to Economics and Biology
8.5 >>> Probability

9 >>> Differential Equations
9.1 >>> Modeling with Differential Equations
9.2 >>> Direction Fields and Euler's Method
9.3 >>> Separable Equations
9.4 >>> Models for Population Growth
9.5 >>> Linear Equations
9.6 >>> Predator-Prey Systems

10 >>> Parametric Equations and Polar Coordinates
10.1 >>> Curves Defined by Parametric Equations
10.2 >>> Calculus with Parametric Curves
10.3 >>> Polar Coordinates
10.4 >>> Areas and Lengths in Polar Coordinates
10.5 >>> Conic Sections
10.6 >>> Conic Sections in Polar Coordinates

11 >>> Infinite Sequences and Series
11.1 >>> Sequences
11.2 >>> Series
11.3 >>> The Integral Test and Estimates of Sum
11.4 >>> The Comparison Tests
11.5 >>> Alternating Series
11.6 >>> Absolute Convergence and the Ratio and Root Tests
11.7 >>> Strategy for Testing Series
11.8 >>> Power Series
11.9 >>> Representations of Functions as Power Series
11.10 >>> Taylor and Maclaurin Series
11.11 >>> Applications of Taylor Polynomials

12 >>> Vectors and the Geometry of Space
12.1 >>> Three-Dimensional Coordinate Systems
12.2 >>> Vectors
12.3 >>> The Dot Product
12.4 >>> The Cross Product
12.5 >>> Equations of Lines and Planes
12.6 >>> Cylinders and Quadric Surfaces

13 >>> Vector Functions
13.1 >>> Vector Functions and Space Curves
13.2 >>> Derivatives and Integrals of Vector Functions
13.3 >>> Arc Length and Curvature
13.4 >>> Motion in Space: Velocity and Acceleration

14 >>> Partial Derivatives
14.1 >>> Functions of Several Variables
14.2 >>> Limits and Continuity
14.3 >>> Partial Derivatives
14.4 >>> Tangent Planes and Linear Approximations
14.5 >>> The Chain Rule
14.6 >>> Directional Derivatives and the Gradient Vector
14.7 >>> Maximum and Minimum Values
14.8 >>> Lagrange Multipliers

15 >>> Multiple Integrals
15.1 >>> Double Integrals over Rectangles
15.2 >>> Iterated Integrals
15.3 >>> Double Integrals over General Regions
15.4 >>> Double Integrals in Polar Coordinates
15.5 >>> Applications of Double Integrals
15.6 >>> Triple Integrals
15.7 >>> Triple Integrals in Cylindrical Coordinates
15.8 >>> Triple Integrals in Spherical Coordinates
15.9 >>> Change of Variables in Multiple Integrals

16 >>> Vector Calculus
16.1 >>> Vector Fields
16.2 >>> Line Integrals
16.3 >>> The Fundamental Theorem for Line Integrals
16.4 >>> Green's Theorem
16.5 >>> Curl and Divergence
16.6 >>> Parametric Surfaces and their Areas
16.7 >>> Surface Integrals
16.8 >>> Stokes' Theorem
16.9 >>> The Divergence Theorem
16.10 >>> Summary

17 >>> Second-Order Differential Equations
17.1 >>> Second-Order Linear Equations
17.2 >>> Nonhomogeneous Linear Equations
17.3 >>> Applications of Second-Order Differential Equations
17.4 >>> Series Solutions

18 >>> Appendix A:  Numbers, Inequalities, and Absolute Values
19 >>> Appendix B: Coordinate Geometry and Lines
20 >>> Appendix C: Graphs of Second-Degree Equations
21 >>> Appendix D: Trigonometry
22 >>> Appendix E: Sigma Notation
23 >>> Appendix F: Proofs of Theorems
24 >>> Appendix G: The Logarithm Defined as an Integral
25 >>> Appendix H: Complex Numbers
26 >>> Appendix I: Answers to Odd-Numbered Exercises

TitleText('College Algebra')
EditionText('3')
AuthorText('Stewart, Redlin, Watson')

1 >>> Basic Algebra
1.1 >>> What is Algebra?
1.2 >>> Real Numbers
1.3 >>> Exponentials and Radicals
1.4 >>> Algebraic Equations
1.5 >>> Fractional Expressions
1.6 >>> Basic Equations
2 >>> Coordinates and Graphs
2.1 >>> The Coordinate Plane
2.2 >>> Graphs of Equations
2.3 >>> Graphing Calculators and Computers
2.4 >>> Lines
3 >>> Equations and Inequalities
3.1 >>> Algebraic and Graphical Solutions of Equations
3.2 >>> Modeling with Equations
3.3 >>> Quadratic Equations
3.4 >>> Complex Numbers
3.5 >>> Other Equations
3.6 >>> Linear Inequalities
3.7 >>> Nonlinear Inequalities
3.8 >>> Absolute Value
4 >>> Functions
4.1 >>> What is a Function?
4.2 >>> Graphs of Functions
4.3 >>> Applied Functions: Variation
4.4 >>> Average Rate of Change: Increasing and Decreasing Functions
4.5 >>> Transformations of Functions
4.6 >>> Extreme Values of Functions
4.7 >>> Combining Functions
4.8 >>> One-to-One Functions and Their Inverses
5 >>> Polynomial and Rational Functions
5.1 >>> Polynomial Functions and Their Graphs
5.2 >>> Dividing Polynomials
5.3 >>> Real Zeros of Polynomials
5.4 >>> The Fundamental Theorem of Algebra
5.5 >>> Rational Functions
6 >>> Exponential and Logarithmic Functions
6.1 >>> Exponential Functions
6.2 >>> The Natural Exponential Function
6.3 >>> Logistic Functions
6.4 >>> Laws of Logarithms
6.5 >>> Exponential and Logarithmic Equations
6.6 >>> Applications of Exponential and Logarithmic Functions
7 >>> Systems of Equations and Inequalities
7.1 >>> Systems of Equations
7.2 >>> Pairs of Lines
7.3 >>> Systems of Linear Equations
7.4 >>> The Algebra of Matrices
7.5 >>> Inverses of Matrices and Matrix Equations
7.6 >>> Determinants and Cramer's Rule
7.7 >>> Systems of Inequalities
7.8 >>> Partial Fractions
8 >>> Conic Sections
8.1 >>> Parabolas
8.2 >>> Ellipses
8.3 >>> Hyperbolas
8.4 >>> Shifted Conics
9 >>> Sequences and Series
9.1 >>> Sequences and Summation Notation
9.2 >>> Arithmetic Sequences
9.3 >>> Geometric Sequences
9.4 >>> Annuities and Installment Buying
9.5 >>> Mathematical Induction
9.6 >>> The Binomial Theorem
10 >>> Counting and Probability
10.1 >>> Counting Principles
10.2 >>> Permutations and Combinations
10.3 >>> Probability
10.4 >>> Expected Value

TitleText('Precalculus')
EditionText('3')
AuthorText('Stewart, Redlin, Watson')

1 >>> Fundamentals
1.1 >>> Real Numbers
1.2 >>> Exponents and Radicals
1.3 >>> Algebraic Expressions
1.4 >>> Fractional Expressions
1.5 >>> Equations
1.6 >>> Problem Solving with Equations
1.7 >>> Inequalities
1.8 >>> Coordinate Geometry
1.9 >>> Graphing Calculators and Computers
1.10 >>> Lines

2 >>> Functions
2.1 >>> What is a Function?
2.2 >>> Graphs of Functions
2.3 >>> Applied Functions
2.4 >>> Transformations of Functions
2.5 >>> Extreme Values of Functions
2.6 >>> Combining Functions
2.7 >>> One-to-One Functions and Their Inverses

3 >>> Polynomials and Rational Functions
3.1 >>> Polynomial Functions and Their Graphs
3.2 >>> Real Zeros of Polynomials
3.3 >>> Complex Numbers
3.4 >>> Complex Roots and The Fundamental Theorem of Algebra
3.5 >>> Rational Functions
4 >>> Exponential and Logarithmic Functions
4.1 >>> Exponential Functions
4.2 >>> The Natural Exponential Function
4.3 >>> Logarithmic Functions
4.4 >>> Laws of Logarithms
4.5 >>> Exponential and Logarithmic Equations
4.6 >>> Applications of Exponential and Logarithmic Equations
5 >>> Trigonometric Functions
5.1 >>> The Unit Circle
5.2 >>> Trigonometric Functions of Real Numbers
5.3 >>> Trigonometric Graphs
5.4 >>> More Trigonometric Graphs
6 >>> Trigonometric Functions of Angles
6.1 >>> Angle Measure
6.2 >>> Trigonometry of Right Triangles
6.3 >>> Trigonometric Functions of Angles
6.4 >>> The Law of Sines
6.5 >>> The Law of Cosines
7 >>> Analytic Trigonometry
7.1 >>> Trigonometric Identities
7.2 >>> Addition and Subtraction Formulas
7.3 >>> Double-Angle, Half-Angle, and Product-Sum Formulas
7.4 >>> Inverse Trigonometric Functions
7.5 >>> Trigonometric Equations
7.6 >>> Trigonometric Form of Complex Numbers; DeMoivre's Theorem
7.7 >>> Vectors
8 >>> Systems of Equations and Inequalities
8.1 >>> Systems of Equations
8.2 >>> Pairs of Lines
8.3 >>> Systems of Linear Equations
8.4 >>> The Algebra of Matrices
8.5 >>> Inverses of Matrices and Matrix Equations
8.6 >>> Determinants and Cramer's Rule
8.7 >>> Systems of Inequalities
8.8 >>> Partial Fractions
9 >>> Topics in Analytic Geometry
9.1 >>> Parabolas
9.2 >>> Ellipses
9.3 >>> Hyperbolas
9.4 >>> Shifted Conics
9.5 >>> Rotation of Axes
9.6 >>> Polar Coordinates
9.7 >>> Polar Equations of Conics
9.8 >>> Parametric Equations
10 >>> Sequences and Series
10.1 >>> Sequences and Summation Notation
10.2 >>> Arithmetic Sequences
10.3 >>> Geometric Sequences
10.4 >>> Annuities and Installment Buying
10.5 >>> Mathematical Induction
10.6 >>> The Binomial Theorem
11 >>> Counting and Probability
11.1 >>> Counting Principles
11.2 >>> Permutations and Combinations
11.3 >>> Probability
11.4 >>> Expected Value


TitleText('Functions Modeling Change')
EditionText('3')
AuthorText('Connally')

1 >>> Linear Functions and Change
1.1 >>> Functions and Function Notation
1.2 >>> Rate of Change
1.3 >>> Linear Functions
1.4 >>> Formulas for Linear Functions
1.5 >>> Geometric Properties of Linear Functions
1.6 >>> Fitting Linear Functions to Data
2 >>> Functions
2.1 >>> Input and Output
2.2 >>> Domain and Range
2.3 >>> Piecewise Defined Functions
2.4 >>> Composite and Inverse Functions
2.5 >>> Concavity
2.6 >>> Quadratic Functions
3 >>> Exponential Functions
3.1 >>> Introduction to the Family of Exponential Functions
3.2 >>> Comparing Exponential and Linear Functions
3.3 >>> Graphs of Exponential Functions
3.4 >>> Continuous Growth and the Number e
3.5 >>> Compound Interest
4 >>> Logarithmic Functions
4.1 >>> Logarithms and their Properties
4.2 >>> Logarithms and Exponential Models
4.3 >>> The Logarithmic Function
4.4 >>> Logarithmic Scales
5 >>> Transformations of Functions and their Graphs
5.1 >>> Vertical and Horizontal Shifts
5.2 >>> Reflections and Symmetry
5.3 >>> Vertical Stretches and Compressions
5.4 >>> Horizontal Stretches and Compressions
5.5 >>> The Family of Quadratic Functions
6 >>> Trigonometric Functions
6.1 >>> Introduction to Periodic Functions
6.2 >>> The Sine and Cosine Functions
6.3 >>> Radians
6.4 >>> Graphs of the Sine and Cosine
6.5 >>> Sinusoidal Functions
6.6 >>> Other Trigonometric Functions
6.7 >>> Inverse Trigonometric Functions
7 >>> Trigonometry
7.1 >>> General Triangles: Laws of Sines and Cosines
7.2 >>> Trigonometric Identities
7.3 >>> Sum and Difference Formulas for Sine and Cosine
7.4 >>> Trigonometric Models
7.5 >>> Polar Coordinates
7.6 >>> Complex Numbers and Polar Coordinates
8 >>> Compositions, Inverses and Combinations of Functions
8.1 >>> Composition of Functions
8.2 >>> Inverse Functions
8.3 >>> Combinations of Functions
9 >>> Polynomial and Rational Functions
9.1 >>> Power Functions
9.2 >>> Polynomial Functions
9.3 >>> The Short-Run Behavior of Polynomials
9.4 >>> Rational Functions
9.5 >>> The Short-Run Behavior of Rational Functions
9.6 >>> Comparing Power, Exponential and Log Functions
9.7 >>> Fitting Exponentials and Polynomials to Data
10 >>> Vector and Matrices
10.1 >>> Vectors
10.2 >>> The Components of a Vector
10.3 >>> Application of Vectors
10.4 >>> The Dot Product
10.5 >>> Matrices
11 >>> Sequences and Series
11.1 >>> Sequences
11.2 >>> Defining Functions Using Sums: Arithmetic Series
11.3 >>> Finite Geometric Series
11.4 Infinite Geometric Series
12 >>> Parametric Equations and Conic Sections
12.1 >>> Parametric Equations
12.2 >>> Implicitly Defined Curves and Circles
12.3 >>> Ellipses
12.4 >>> Hyperbolas
12.5 >>> Geometric Properties of Conic Sections
12.6 >>> Hyperbolic Functions

TitleText('Functions Modeling Change')
EditionText('4')
AuthorText('Connally')

1 >>> Linear Functions and Change
1.1 >>> Functions and Function Notation
1.2 >>> Rate of Change
1.3 >>> Linear Functions
1.4 >>> Formulas for Linear Functions
1.5 >>> Geometric Properties of Linear Functions
1.6 >>> Fitting Linear Functions to Data
2 >>> Functions
2.1 >>> Input and Output
2.2 >>> Domain and Range
2.3 >>> Piecewise Defined Functions
2.4 >>> Composite and Inverse Functions
2.5 >>> Concavity
3 >>> Quadratic Functions
3.1 >>> Introduction to the Family of Quadratic Functions
3.2 >>> The Vertex of a Parabola
4 >>> Exponential Functions
4.1 >>> Introduction to the Family of Exponential Functions
4.2 >>> Comparing Exponential and Linear Functions
4.3 >>> Graphs of Exponential Functions
4.4 >>> Applications to Compound Interest
4.5 >>> The Number e
5 >>> Logarithmic Functions
5.1 >>> Logarithms and their Properties
5.2 >>> Logarithms and Exponential Models
5.3 >>> The Logarithmic Function
5.4 >>> Logarithmic Scales
6 >>> Transformations of Functions and Their Graphs
6.1 >>> Vertical and Horizontal Shifts
6.2 >>> Reflections and Symmetry
6.3 >>> Vertical Stretches and Compressions
6.4 >>> Horizontal Stretches and Compressions
6.5 >>> Combining Transformations
7 >>> Trigonometric in Circles and Triangles
7.1 >>> Introduction to Periodic Functions
7.2 >>> The Sine and Cosine Functions
7.3 >>> Graphs of Sine and Cosine
7.4 >>> The Tangent Function
7.5 >>> Right Triangles: Inverse Trigonometric Functions
7.6 >>> Non-Right Triangles
8 >>> The Trigonometric Functions
8.1 >>> Radians and Arc Length
8.2 >>> Sinusoidal Functions and Their Graphs
8.3 >>> Trigonometric Functions: Relationships and Graphs
8.4 >>> Trigonometric Equations and Inverse Functions
8.5 >>> Polar Coordinates
8.6 >>> Complex Numbers and Polar Coordinates
9 >>> Trigonometric Identities and Their Applications
9.1 >>> Identities, Expressions and Equations
9.2 >>> Sum and Difference Formulas for Sine and Cosine
9.3 >>> Trigonometric Models
10 >>> Compositions, Inverses and Combinations of Functions
10.1 >>> Composition of Functions
10.2 >>> Invertibility and Properties of Inverse Functions
10.3 >>> Combinations of Functions
11 >>> Polynomial and Rational Functions
11.1 >>> Power Functions
11.2 >>> Polynomial Functions
11.3 >>> The Short-Run Behavior of Polynomials
11.4 >>> Rational Functions
11.5 >>> The Short-Run Behavior of Rational Functions
11.6 >>> Comparing Power, Exponential and Log Functions
11.7 >>> Fitting Exponentials and Polynomials to Data
12 >>> Vector and Matrices
12.1 >>> Vectors
12.2 >>> The Components of a Vector
12.3 >>> Application of Vectors
12.4 >>> The Dot Product
12.5 >>> Matrices
13 >>> Sequences and Series
13.1 >>> Sequences
13.2 >>> Defining Functions Using Sums: Arithmetic Series
13.3 >>> Finite Geometric Series
13.4 Infinite Geometric Series
14 >>> Parametric Equations and Conic Sections
14.1 >>> Parametric Equations
14.2 >>> Implicitly Defined Curves and Circles
14.3 >>> Ellipses
14.4 >>> Hyperbolas
14.5 >>> Geometric Properties of Conic Sections
14.6 >>> Hyperbolic Functions

TitleText('Calculus')
EditionText('4')
AuthorText('Hughes-Hallett')

1 >>> A Library of Functions
1.1 >>> Functions and Change
1.2 >>> Exponential Functions
1.3 >>> New Functions from Old
1.4 >>> Logarithmic Functions
1.5 >>> Trigonometric Functions
1.6 >>> Powers, Polynomials, and Rational Functions
1.7 >>> Introduction to Continuity
1.8 >>> Limits
2 >>> Key Concept: The Derivative
2.1 >>> How do we measure speed?
2.2 >>> The Derivative at a Point
2.3 >>> The Derivative Function
2.4 >>> Interpretations of the Derivative
2.5 >>> The Second Derivative
2.6 >>> Differentiability
3 >>> Shortcuts to Differentiation
3.1 >>> Powers and Polynomials
3.2 >>> The Exponential Function
3.3 >>> The Product and Quotient Rules
3.4 >>> The Chain Rule
3.5 >>> The Trigonometric Functions
3.6 >>> The Chain Rule and Inverse Functions
3.7 >>> Implicit Functions
3.8 >>> Hyperbolic Functions
3.9 >>> Linear Approximation and the Derivative
3.10 >>> Theorems About Differentiable Functions
4 >>> Using the Derivative
4.1 >>> Using First and Second Derivatives
4.2 >>> Families of Curves
4.3 >>> Optimization
4.4 >>> Applications to Marginality
4.5 >>> Optimization and Modeling
4.6 >>> Rates and Related Rates
4.7 >>> L'Hopital's Rule, Growth, and Dominance
4.8 >>> Parametric Equations
5 >>> Key Concept: The Definite Integral
5.1 >>> How do we measure distance traveled?
5.2 >>> The Definite Integral
5.3 >>> The Fundamental Theorem and Interpretations
5.4 >>> Theorems About Definite Integrals
6 >>> Constructing Antiderivatives
6.1 >>> Antiderivatives Graphically and Numerically
6.2 >>> Constructing Antiderivatives Analytically
6.3 >>> Differential Equations
6.4 >>> Second Fundamental Theorem of Calculus
6.5 >>> The Equations of Motion
7 >>> Integration
7.1 >>> Integration by Substitution
7.2 >>> Integration by Parts
7.3 >>> Tables of Integrals
7.4 >>> Algebraic Identities and Trigonometric Substitutions
7.5 >>> Approximating Definite Integrals
7.6 >>> Approximation Errors an Simpson's Rule
7.7 >>> Improper Integrals
7.8 >>> Comparison of Improper Integrals
8 >>> Using the Definite Integral
8.1 >>> Areas and Volumes
8.2 >>> Applications to Geometry
8.3 >>> Area and Arc Length in Polar Coordinates
8.4 >>> Density and Center of Mass
8.5 >>> Applications to Physics
8.6 >>> Applications to Economics
8.7 >>> Distribution Functions
8.8 >>> Probability, Mean, and Median
9 >>> Sequences and Series
9.1 >>> Sequences
9.2 >>> Geometric Series
9.3 >>> Convergence of Series
9.4 >>> Tests for Convergence
9.5 >>> Power Series and Interval of Convergence
10 >>> Approximating Functions Using Series
10.1 >>> Taylor Polynomials
10.2 >>> Taylor Series
10.3 >>> Finding and Using Taylor Series
10.4 >>> The Error in Taylor Polynomial Approximations
10.5 >>> Fourier Series
11 >>> Differential Equations
11.1 >>> What is a differential equation?
11.2 >>> Slope Fields
11.3 >>> Euler's Method
11.4 >>> Separation of Variables
11.5 >>> Growth and Decay
11.6 >>> Applications and Modeling
11.7 >>> Models of Population Growth
11.8 >>> Systems of Differential Equations
11.9 >>> Analyzing the Phase Plane
11.10 >>> Second-Order Differential Equations: Oscillations
11.11 >>> Linear Second-Order Differential Equations
12 >>> Functions of Several Variables
12.1 >>> Functions of Two Variables
12.2 >>> Graphs of Functions of Two Variables
12.3 >>> Control Diagrams
12.4 >>> Linear Functions
12.5 >>> Functions of Three Variables
12.6 >>> Limits and Continuity
13 >>> A Fundamental Tool: Vectors
13.1 >>> Displacement Vectors
13.2 >>> Vectors in General
13.3 >>> The Dot Product
13.4 >>> The Cross Product
14 >>> Differentiating Functions of Several Variables
14.1 >>> The Partial Derivative
14.2 >>> Computing Partial Derivatives Algebraically
14.3 >>> Local Linearity and the Differential
14.4 >>> Gradients and Directional Derivatives in the Plane
14.5 >>> Gradients and Directional Derivatives in Space
14.6 >>> The Chain Rule
14.7 >>> Second-Order Partial Derivatives
14.8 >>> Differentiability
15 >>> Optimization: Local and Global Extrema
15.1 >>> Local Extrema
15.2 >>> Optimization
15.3 >>> Constrained Optimization: Lagrange Multipliers
16 >>> Integrating Functions of Several Variables
16.1 >>> The Definite Integral of a Function of Two Variables
16.2 >>> Iterated Integrals
16.3 >>> Triple Integrals
16.4 >>> Double Integrals in Polar Coordinates
16.5 >>> Integrals in Cylindrical and Spherical Coordinates
16.6 >>> Applications of Integration to Probability
16.7 >>> Change of Variables in Multiple Integral
17 >>> Parameterization and Vector Fields
17.1 >>> Parameterized Curves
17.2 >>> Motion, Velocity, and Acceleration
17.3 >>> Vector Fields
17.4 >>> The Flow of a Vector Field
17.5 >>> Parameterized Surfaces
18 >>> Line Integrals
18.1 >>> The Idea of a Line Integral
18.2 >>> Computing Line Integrals Over Parameterized Curves
18.3 >>> Gradient Fields and Path-Independent Fields
18.4 >>> Path-Independent Vector Fields and Green's Theorem
19 >>> Flux Integrals
19.1 >>> The Idea of a Flux Integral
19.2 >>> Flux Integrals for Graphs, Cylinders, and Spheres
19.3 >>> Flux Integrals over Parameterized Surfaces
20 >>> Calculus of Vector Fields
20.1 >>> The Divergence of a Vector Field
20.2 >>> The Divergence Theorem
20.3 >>> The Curl of a Vector Field
20.4 >>> Stokes' Theorem
20.5 >>> The Three Fundamental Theorems

TitleText('Calculus')
EditionText('5')
AuthorText('Hughes-Hallett')

1 >>> A Library of Functions
1.1 >>> Functions and Change
1.2 >>> Exponential Functions
1.3 >>> New Functions From Old
1.4 >>> Logarithmic Functions
1.5 >>> Trigonometric Functions
1.6 >>> Powers, Polynomials and Rational Functions
1.7 >>> Introduction to Continuity
1.8 >>> Limits
2 >>> Key Concept: The Derivative
2.1 >>> How Do We Measure Speed
2.2 >>> The Derivative at a Point
2.3 >>> The Derivative Function
2.4 >>> Interpretations of the Derivative
2.5 >>> The Second Derivative
2.6 >>> Differentiability
3 >>> Short-Cuts to Differentiation
3.1 >>> Powers and Polynomials
3.2 >>> The Exponential Function
3.3 >>> The Product and Quotient Rules
3.4 >>> The Chain Rule
3.5 >>> The Trigonometric Functions
3.6 >>> The Chain Rule and Inverse Functions
3.7 >>> Implicit Functions
3.8 >>> Hyperbolic Functions
3.9 >>> Linear Approximation and the Derivative
3.10 >>> Theorems About Differentiable Functions
4 >>> Using the Derivative
4.1 >>> Using First and Second Derivatives
4.2 >>> Optimization
4.3 >>> Families of Functions
4.4 >>> Optimization, Geometry and Modeling
4.5 >>> Applications to Marginality
4.6 >>> Rates and Related Rates
4.7 >>> L'Hopital's Rule, Growth and Dominance
4.8 >>> Parametric Equations
5 >>> Key Concept: The Definite Integral
5.1 >>> How Do We Measure Distance Traveled
5.2 >>> The Definite Integral
5.3 >>> The Fundamental Theorem and Interpretations
5.4 >>> Theorems about Definite Integrals
6 >>> Constructing Antiderivatives
6.1 >>> Antiderivatives Graphically and Numerically
6.2 >>> Constructing Antiderivatives Analytically
6.3 >>> Differential Equations
6.4 >>> The Second Fundamental Theorem of Calculus
6.5 >>> The Equations of Motion
7 >>> Integration
7.1 >>> Integration by Substitution
7.2 >>> Integration by Parts
7.3 >>> Tables of Integrals
7.4 >>> Algebraic Identities and Trigonometric Substitutions
7.5 >>> Approximating Definite Integrals
7.6 >>> Approximation Errors and Simpson's Rule
7.7 >>> Improper Integrals
7.8 >>> Comparison of Improper Integrals
8 >>> Using the Definite Integral
8.1 >>> Areas and Volumes
8.2 >>> Applications to Geometry
8.3 >>> Area and Arc Length in Polar Coordinates
8.4 >>> Density and Center of Mass
8.5 >>> Applications to Physics
8.6 >>> Applications to Economics
8.7 >>> Distribution Functions
8.8 >>> Probability, Mean and Median
9 >>> Sequences and Series
9.1 >>> Sequences
9.2 >>> Geometric Series
9.3 >>> Convergence of Series
9.4 >>> Tests for Convergence
9.5 >>> Power Series and Interval of Convergence
10 >>> Approximating Functions Using Series
10.1 >>> Taylor Polynomials
10.2 >>> Taylor Series
10.3 >>> Finding and Using Taylor Series
10.4 >>> The Error in Taylor Polynomial Approximations
10.5 >>> Fourier Series
11 >>> Differential Equations
11.1 >>> What is a Differential Equation
11.2 >>> Slope Fields
11.3 >>> Euler's Method
11.4 >>> Separation of Variables
11.5 >>> Growth and Decay
11.6 >>> Applications and Modeling
11.7 >>> The Logistic Model
11.8 >>> Systems of Differential Equations
11.9 >>> Analyzing the Phase Plane
11.10 >>> Second-Order Differential Equations: Oscillations
11.11 >>> Linear Second-Order Differential Equations
12 >>> Functions of Several Variables
12.1 >>> Functions of Two Variables
12.2 >>> Graphs of Functions of Two Variables
12.3 >>> Control Diagrams
12.4 >>> Linear Functions
12.5 >>> Functions of Three Variables
12.6 >>> Limits and Continuity
13 >>> A Fundamental Tool: Vectors
13.1 >>> Displacement Vectors
13.2 >>> Vectors in General
13.3 >>> The Dot Product
13.4 >>> The Cross Product
14 >>> Differentiating Functions of Several Variables
14.1 >>> The Partial Derivative
14.2 >>> Computing Partial Derivatives Algebraically
14.3 >>> Local Linearity and the Differential
14.4 >>> Gradients and Directional Derivatives in the Plane
14.5 >>> Gradients and Directional Derivatives in Space
14.6 >>> The Chain Rule
14.7 >>> Second-Order Partial Derivatives
14.8 >>> Differentiability
15 >>> Optimization: Local and Global Extrema
15.1 >>> Local Extrema
15.2 >>> Optimization
15.3 >>> Constrained Optimization: Lagrange Multipliers
16 >>> Integrating Functions of Several Variables
16.1 >>> The Definite Integral of a Function of Two Variables
16.2 >>> Iterated Integrals
16.3 >>> Triple Integrals
16.4 >>> Double Integrals in Polar Coordinates
16.5 >>> Integrals in Cylindrical and Spherical Coordinates
16.6 >>> Applications of Integration to Probability
16.7 >>> Change of Variables in Multiple Integral
17 >>> Parameterization and Vector Fields
17.1 >>> Parameterized Curves
17.2 >>> Motion, Velocity, and Acceleration
17.3 >>> Vector Fields
17.4 >>> The Flow of a Vector Field
17.5 >>> Parameterized Surfaces
18 >>> Line Integrals
18.1 >>> The Idea of a Line Integral
18.2 >>> Computing Line Integrals Over Parameterized Curves
18.3 >>> Gradient Fields and Path-Independent Fields
18.4 >>> Path-Independent Vector Fields and Green's Theorem
19 >>> Flux Integrals
19.1 >>> The Idea of a Flux Integral
19.2 >>> Flux Integrals for Graphs, Cylinders, and Spheres
19.3 >>> Flux Integrals over Parameterized Surfaces
20 >>> Calculus of Vector Fields
20.1 >>> The Divergence of a Vector Field
20.2 >>> The Divergence Theorem
20.3 >>> The Curl of a Vector Field
20.4 >>> Stokes' Theorem
20.5 >>> The Three Fundamental Theorems

TitleText('Calculus: Early Transcendentals')
EditionText('1')
AuthorText('Rogawski')

1 >>> Precalculus Review
1.1 >>> Real Numbers, Functions, and Graphs
1.2 >>> Linear and Quadratic Functions
1.3 >>> The Basic Classes of Functions
1.4 >>> Trigonometric Functions
1.5 >>> Inverse Functions
1.6 >>> Exponential and Logarithmic Functions
1.7 >>> Technology: Calculators and Computers
2 >>> Limits
2.1 >>> Limits, Rates of Change, and Tangent Lines
2.2 >>> Limits: A Numerical and Graphical Approach
2.3 >>> Basic Limit Laws
2.4 >>> Limits and Continuity
2.5 >>> Evaluating Limits Algebraically
2.6 >>> Trigonometric Limits
2.7 >>> Intermediate Value Theorem
2.8 >>> The Formal Definition of a Limit
3 >>> Differentiation
3.1 >>> Definition of the Derivative
3.2 >>> The Derivative as a Function
3.3 >>> Product and Quotient Rules
3.4 >>> Rates of Change
3.5 >>> Higher Derivatives
3.6 >>> Trigonometric Functions
3.7 >>> The Chain Rule
3.8 >>> Implicit Differentiation
3.9 >>> Derivatives of Inverse Functions
3.10 >>> Derivatives of General Exponential and Logarithmic Functions
3.11 >>> Related Rates
4 >>> Applications of the Derivative
4.1 >>> Linear Approximation and Applications
4.2 >>> Extreme Values
4.3 >>> The Mean Value Theorem and Monotonicity
4.4 >>> The Shape of a Graph
4.5 >>> Graph Sketching and Asymptotes
4.6 >>> Applied Optimization
4.7 >>> L'Hopital's Rule
4.8 >>> Newton's Method
4.9 >>> Antiderivatives
5 >>> The Integral
5.1 >>> Approximating and Computing Area
5.2 >>> The Definite Integral
5.3 >>> The Fundamental Theorem of Calculus, Part I
5.4 >>> The Fundamental Theorem of Calculus, Part II
5.5 >>> Net or Total Change as the Integral of a Rate
5.6 >>> Substitution Method
5.7 >>> Further Transcendental Functions
5.8 >>> Exponential Growth and Decay
6 >>> Applications of the Integral
6.1 >>> Area Between Two Curves
6.2 >>> Setting Up Integrals: Volumes, Density, Average Value
6.3 >>> Volumes of Revolution
6.4 >>> The Method of Cylindrical Shells
6.5 >>> Work and Energy
7 >>> Techniques of Integration
7.1 >>> Numerical Integration
7.2 >>> Integration by Parts
7.3 >>> Trigonometric Integrals
7.4 >>> Trigonometric Substitution
7.5 >>> Integrals of Hyperbolic and Inverse Hyperbolic Functions
7.6 >>> The Method of Partial Fractions
7.7 >>> Improper Integrals
8 >>> Further Applications of the Integral and Taylor Polynomials
8.1 >>> Arc Length and Surface Area
8.2 >>> Fluid Pressure and Force
8.3 >>> Center of Mass
8.4 >>> Taylor Polynomials
9 >>> Introduction to Differential Equations
9.1 >>> Solving Differential Equations
9.2 >>> Models Involving y'=k(y-b)
9.3 >>> Graphical and Numerical Methods
9.4 >>> The Logistic Equation
9.5 >>> First-Order Linear Equations
10 >>> Infinite Series
10.1 >>> Sequences
10.2 >>> Summing an Infinite Series
10.3 >>> Convergence of Series with Positive Terms
10.4 >>> Absolute and Conditional Convergence
10.5 >>> The Ratio and Root Tests
10.6 >>> Power Series
10.7 >>> Taylor Series
11 >>> Parametric Equations, Polar Coordinates, and Conic Sections
11.1 >>> Parametric Equations
11.2 >>> Arc Length and Speed
11.3 >>> Polar Coordinates
11.4 >>> Area and Arc Length in Polar Coordinates
11.5 >>> Conic Sections
12 >>> Vector Geometry
12.1 >>> Vectors in the Plane
12.2 >>> Vectors in Three Dimensions
12.3 >>> Dot Product and the Angle Between Two Vectors
12.4 >>> The Cross Product
12.5 >>> Planes in Three-Space
12.6 >>> A Survey of Quadric Surfaces
12.7 >>> Cylindrical and Spherical Coordinates
13 >>> Calculus of Vector-Valued Functions
13.1 >>> Vector-Valued Functions
13.2 >>> Calculus of Vector-Valued Functions
13.3 >>> Arc Length and Speed
13.4 >>> Curvature
13.5 >>> Motion in Three-Space
13.6 >>> Planetary Motion According to Kepler and Newton
14 >>> Differentiation in Several Variables
14.1 >>> Functions in Two or More Variables
14.2 >>> Limits and Continuity in Several Variables
14.3 >>> Partial Derivatives
14.4 >>> Differentiability, Linear Approximation, and Tangent Planes
14.5 >>> The Gradient and Directional Derivatives
14.6 >>> The Chain Rule
14.7 >>> Optimization in Several Variables
14.8 >>> Lagrange Multipliers: Optimizing with a Constraint
15 >>> Multiple Integration
15.1 >>> Integrals in Several Variables
15.2 >>> Double Integrals over More General Regions
15.3 >>> Triple Integrals
15.4 >>> Integration in Polar, Cylindrical, and Spherical Coordinates
15.5 >>> Change of Variables
16 >>> Line and Surface Integrals
16.1 >>> Vector Fields
16.2 >>> Line Integrals
16.3 >>> Conservative Vector Fields
16.4 >>> Parametrized Surfaces and Surface Integrals
16.5 >>> Integrals of Vector Fields
17 >>> Fundamental Theorems of Vector Analysis
17.1 >>> Green's Theorem
17.2 >>> Stokes' Theorem
17.3 >>> Divergence Theorem