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Chapter 0 Precalculus review
0.1 Real numbers0.1 Tutorial | Adaptive game tutorial
0.3 Multiplying and factoring algebraic equations0.3 Tutorial | Adaptive game tutorial
0.4 Rational expressions 0.4 Tutorial | Adaptive game tutorial
0.5 Solving polynomial equations0.5 Tutorial | Adaptive game tutorial
0.6 Solving miscellaneous equations0.6 Tutorial | Adaptive game tutorial
0.7 The coordinate plane
0.8 Logarithms0.8 Tutorial | Adaptive game tutorial

Chapter 1 Functions and applications
1.1 Functions from the numerical, algebraic, and graphical viewpoints1.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 1.1: Introduction to functions
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1.2 Functions and models1.2 Tutorial | Game tutorial |
Videos
 Videos for Section 1.2: Part A: Cost, revenue, and profit models Part B: Demand, supply and time-change models
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1.3 Linear functions and models1.3 Tutorial | Game tutorial | |
1.4 Linear regression1.4 Tutorial | Game tutorial |
Videos
 Videos for Section 1.4: Part A: Sum of Squares Error Part B: The regression line
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Online: New functions from old: Scaled and shifted functions
Online: Fitting curves to data: Linear and exponential regression
Case study:  Modeling spending on Internet advertising

Chapter 1 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 1 tools
Function evaluator and grapher | Excel grapher | Simple regression utility

Chapter 2 Nonlinear functions and models
2.1 Quadratic functions and models2.1 Tutorial | Game tutorial |
Video
 Video  for Section 2.1: Quadratic functions and models
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Practice/visualize
 Practice/visualize for Section 2.1: Quadratic function Features and graph of a quadratic function Calculating revenue and profit from demand and cost
2.2 Exponential functions and models2.2 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 2.2: Exponential functions and models
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2.3 Logarithmic functions and models2.3 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 2.3: Logarithmic functions and models
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2.4 Logistic functions and models
Video
 Video  for Section 2.4: Logistic functions and models
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Practice/visualize
 Practice/visualize for Section 2.4: Logistic function: Basics Logistic model: Epidemics Graph of a logarithmic function
Online: Inverse functions
Online: Fitting curves to data: linear and exponential regression
Online: Using and Deriving Algebraic Properties of Logarithms
Case study:  Checking up on MalthusWheat production data

Chapter 2 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 2 tools
Function evaluator and grapher | Excel grapher | Simple regression utility

Chapter 3 Mathematics of finance
3.1 Simple interest3.1 Tutorial | Game tutorial |
3.2 Compound interest3.2 Tutorial | Game tutorial |
3.3 Annuities, loans, and bonds3.3 Tutorial | Game tutorial |
Case study:  Adjustable rate and subprime mortgages

Chapter 3 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 3 tools
Time value of money utility

Chapter 4 Systems of linear equations and matrices
4.1 Systems of two linear equations in two unknowns 4.1 Tutorial | Game tutorial |
Videos
 Videos for Section 4.1: Part A: Solving graphically Part B: Solving by elimination Part C: Applications
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4.2 Using matrices to solve systems of equations 4.2 Tutorial | Game tutorial | |
4.3 Applications of systems of linear equations 4.3 Tutorial | Game tutorial |
Videos
 Videos for Section 4.3: Part A: Setting up applications Part B: Traffic flow
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Practice/visualize
 Practice/visualize for Section 4.3: Solving a blending problem Solving a traffic-flow problem
Case study:  Hybrid cars: Optimizing the degree of hybridization

Chapter 4 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 4 tools
Pivot and Gauss-Jordan tool | Excel pivot and Gauss-Jordan tool | Pivot program for graphing calculator (TI-82/83/84/85/86)

Chapter 5 Matrix algebra
5.1 Matrix addition and scalar multiplication5.1 Tutorial | Game tutorial |
Video
 Video  for Section 5.1: Matrix addition and scalar multiplication
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Practice/visualize
 Practice/visualize for Section 5.1: Matrix elements Matrix addition and subtraction Calculating change in sales using matrix subtraction Matrix transposition
5.2 Matrix multiplication5.2 Tutorial | Game tutorial |
Video
 Video  for Section 5.2: Matrix multiplication
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5.3 Matrix inversion5.3 Tutorial | Game tutorial |
Video
 Video  for Section 5.3: Matrix inversion
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Practice/visualize
 Practice/visualize for Section 5.3: Finding a matrix inverse Determinant and inverse of a 2 × 2 matrix Solving systems of equations with matrix inverses
5.4 Game theory5.4 Tutorial | Game tutorial | |
Practice/visualize
 Practice/visualize for Section 5.4: Expected payoff of a game Optimal counterstrategy Strictly determined game
5.5 Input-output models5.5 Tutorial |
Practice/visualize
 Practice/visualize for Section 5.5: Input-output model
Online: Determinants and Cramer's Rule (pdf only)
Case study:  Projecting market share

Chapter 5 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 5 tools
Pivot program for graphing calculator (TI-82/83/84/85/86) | Matrix algebra tool

Chapter 6 Linear programming
6.1 Graphing linear inequalities6.1 Tutorial | Game tutorial |
Video
 Video  for Section 6.1: Graphing linear inequalities
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Practice/visualize
 Practice/visualize for Section 6.1: Graphing single inequalities Graphing two simultaneous inequalities Finding corner points of the solution set
6.2 Solving linear programming problems graphically6.2 Tutorial | Game tutorial |
Video
 Video  for Section 6.2: Solving linear programming problems graphically
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Practice/visualize
 Practice/visualize for Section 6.2: Solving a linear programming problem graphically
6.3 The simplex method: Solving standard maximization problems6.3 Tutorial | Game tutorial |
Video
 Video  for Section 6.3: The simplex method: Standard maximization problems
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Practice/visualize
 Practice/visualize for Section 6.3: Simplex method (standard LP problem)
6.4 The simplex method: Solving general linear programming problems6.4 Tutorial | Game tutorial |
Video
 Video  for Section 6.4: The simplex method: General LP problems
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Practice/visualize
 Practice/visualize for Section 6.4: Simplex method (nonstandard maximize problem)
6.5 The simplex method and duality
Case study:  The diet problemDiet problem solver

Chapter 6 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 6 tools
Linear programming grapher | Simplex method tool | Pivot and Gauss-Jordan tool | Excel pivot and Gauss-Jordan tool | Pivot program for graphing calculator (TI-82/83/84/85/86) | Diet problem solver | Linear programming grapher app (Android) | Linear programming grapher app for iPhone, iPad, and iPod touch

Chapter 7 Sets and counting
7.1 Set operations7.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 7.1: Set operations
7.2 Cardinality7.2 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 7.2: Cardinality
7.3 Decision algorithms: The addition and multiplication principles 7.3 Tutorial | Game tutorial |
Video
 Video  for Section 7.3: Addition and multiplication principles
7.4 Permutations and combinations7.4 Tutorial | Game tutorial |
Video
 Video  for Section 7.4: Permutations and combinations
Case study:  Designing a puzzle

Chapter 7 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises

Chapter 8 Probability
8.1 Sample spaces and events8.1 Tutorial | Game tutorial |
Video
 Video  for Section 8.1: Sample spaces and events
8.2 Relative frequency8.2 Tutorial | Game tutorial |
Video
 Video  for Section 8.2: Relative frequency
8.3 Probability and probability models8.3 Tutorial | Game tutorial |
Videos
 Videos for Section 8.3: Probability models Part A Probability models Part B
8.4 Probability and counting techniques
8.5 Conditional probability and independence8.5 Tutorial | Game tutorial |
Videos
 Videos for Section 8.5: Conditional probability Part A Conditional probability Part B
8.6 Bayes' Theorem and Applications8.6 Tutorial | Game tutorial |
Video
 Video  for Section 8.6: Bayes' theorem and applications
8.7 Markov systems
Video
 Video  for Section 8.7: Markov systems
Case study:  The Monty Hall problemOnline Monty Hall simulation

Chapter 8 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises

Chapter 8 tools
Markov system simulation | Matrix algebra tool | Markov system computation utility

Chapter 9 Random variables and statistics
9.1 Random variables and distributions9.1 Tutorial | Game tutorial |
Video
 Video  for Section 9.1: Random variables and distributions
9.2 Bernoulli trials and binomial random variables9.2 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 9.2: Bernoulli trials and binomial random variables
9.3 Measures of central tendency9.3 Tutorial
9.4 Measures of dispersion9.4 Tutorial
9.5 Normal distributions
Online: Sampling distributions and the Central Limit Theorem
Online: Confidence intervals
Online: Calculus applied to statistics (online chapter)
Online: Fitting curves to data: Linear and exponential regression
Case study:  Spotting tax fraud with Benford's law

Chapter 9 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises

Chapter 9 tools
Histogram utility | Binomial distribution utility | Normal distribution utility | Normal distribution table

Chapter 10 Introduction to the derivative
10.1 Limits: numerical and graphical viewpoints10.1 Tutorial | Game tutorial |
Videos
 Videos for Section 10.1: Limits: Numerical viewpoint Limits: Graphical viewpoint
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10.2 Limits and continuity10.2 Tutorial | Game tutorial |
Video
 Video  for Section 10.2: Limits and continnutiy
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10.3 Limits and continuity: algebraic viewpoint10.3 Tutorial | Game tutorial |
Videos
 Videos for Section 10.3: A: How to calculate limits algebraically B: Limits at infinity
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Practice/visualize
 Practice/visualize for Section 10.3: Calculating a limit algebraically The determinate form k/0
10.4 Average rate of change10.4 Tutorial | Game tutorial |
Video
 Video  for Section 10.4: Average rates of change
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10.5 The derivative: numerical and graphical viewpoints10.5 Tutorial | Game tutorial |
Videos
 Videos for Section 10.5: Part A: The derivative: numerical approach Part B: The derivative: geometric approach
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10.6 The derivative: algebraic viewpoint10.6 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 10.6: The derivative: algebraic approach
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Practice/visualize
 Practice/visualize for Section 10.6: Calculating the derivative algebraically
Online: Sketching the graph of the derivative
Online: Continuity and differentiability
Case study:  Reducing sulfur emissions

Chapter 10 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 10 tools
Function evaluator and grapher | Excel grapher | Excel first and second derivative graphing utility

Chapter 11 Techniques of differentiation
11.1 Derivatives of powers, sums, and constant multiples11.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 11.1: Derivatives of powers, sums, and constant multiples
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Practice/visualize
 Practice/visualize for Section 11.1: Derivatives of powers of x Derivatives of sums and constant multiples
11.2 A first application: Marginal analysis11.2 Tutorial | Game tutorial |
Video
 Video  for Section 11.2: Marginal analysiss
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Practice/visualize
 Practice/visualize for Section 11.2: Calculating marginal cost Visualize average and marginal cost
11.3 The product and quotient rules11.3 Tutorial | Adaptive game tutorial |
Videos
 Videos for Section 11.3: The product and quotient rules Prof X Squared's video
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Practice/visualize
 Practice/visualize for Section 11.3: Practice product and quotient rule
11.4 The chain rule11.4 Tutorial | Adaptive game tutorial |
Videos
 Videos for Section 11.4: The chain rule Prof X Squared's video Part A Prof X Squared's video Part B
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Practice/visualize
 Practice/visualize for Section 11.4: Derivatives using the chain rule
11.5 Derivatives of logarithmic and exponential functions11.5 Tutorial | Game tutorial |
Video
 Video  for Section 11.5: Derivatives of logarithmic and exponential functions
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Practice/visualize
 Practice/visualize for Section 11.5: Derivatives of logarithms of functions Derivatives of exponentials of functions
11.6 Implicit differentiation
Practice/visualize
 Practice/visualize for Section 11.6: Implicit differentiation Logarithmic differentiation
Online: Linear approximation and error estimation
Online: Proof of the power rule
Online: Proof of the quotient rule
Online: Proof of the chain rule
Case study:  Projecting market growth

Chapter 11 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Additional exercises for derivatives of powers, sums, and constant multiples | Additional exercises for the product and quotient rules

Chapter 11 tools
Function evaluator and grapher | Excel grapher | Excel first and second derivative graphing utility

Chapter 12 Further applications of the derivative
12.1 Maxima and minima12.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 12.1: Maxima and minima
12.2 Applications of maxima and minima12.2 Tutorial | Game tutorial |
Video
 Video  for Section 12.2: Applications of maxima and minima
|
Practice/visualize
 Practice/visualize for Section 12.2: Applied optimization
12.3 Higher order derivatives: Acceleration and concavity12.3 Tutorial | Game tutorial |
Video
 Video  for Section 12.3: Higher order derivatives: Acceleration and concavity
12.4 Analyzing graphs12.4 Tutorial |
Video
 Video  for Section 12.4: Analyzing graphs
12.5 Related rates12.5 Tutorial | Game tutorial |
Video
 Video  for Section 12.5: Related rates
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Practice/visualize
 Practice/visualize for Section 12.5: Related rates: Distinuishing between Q and dQ/dt Related rates: The rising rocket
12.6 Elasticity 12.6 Tutorial | Game tutorial |
Video
 Video  for Section 12.6: Elasticity
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Practice/visualize
 Practice/visualize for Section 12.6: Calculating elasticity (linear demand equation) Calculating and interpreting elasticity (quadratic demand equation)
Case study:  Production lot size management

Chapter 12 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 12 tools
Function evaluator and grapher | Excel grapher | Excel first and second derivative graphing utility

Chapter 13 The integral
13.1 The indefinite integral13.1 Tutorial | Game tutorial |
Videos
 Videos for Section 13.1: The indefinite integral The indefinite integral: Applications
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13.2 Substitution13.2 Tutorial | Game tutorial |
Videos
 Videos for Section 13.2: Substitution: Part A Substitution Part B: Shortcuts
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13.3 The definite integral: Numerical and graphical viewpoints13.3 Tutorial | Game tutorial |
Video
 Video  for Section 13.3: The definite integral: Numerical and graphical viewpoints
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13.4 The definite integral: Algebraic viewpoint and the fundamental theorem of calculus13.4 Tutorial | Game tutorial |
Video
 Video  for Section 13.4: The definite integral: Fundamental theorem of calculus<
|
Online: Numerical integration
Case study:  Spending on housing construction

Chapter 13 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 13 tools
Numerical integration utility and grapher | Graphing calculator programs for numerical integration (TI-82/83/84/85/86) | Excel Riemann sum grapher

Chapter 14 Further integration techniques and applications of the integral
14.1 Integration by parts14.1 Tutorial | Game tutorial |
Videos
 Videos for Section 14.1: Prof X Squared's video Part A Prof X Squared's video Part B
14.2 Area between two curves and applications14.2 Tutorial | Game tutorial |
Practice/visualize
 Practice/visualize for Section 14.2: Area between curves Area between crossing curves
14.3 Averages and moving averages
14.4 Applications to business and economics: Consumers' and producers' surplus and continuous income streams
14.5 Improper integrals and applications
14.6 Differential equations and applications
Practice/visualize
 Practice/visualize for Section 14.6: First order linear differential equation
Online: Linear differential equations
Case study:  Estimating tax revenues

Chapter 14 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 14 tools
Numerical integration utility and grapher | Graphing calculator programs for numerical integration (TI-82/83/84/85/86) | Excel Riemann sum grapher

Chapter 15 Functions of several variables
15.1 Functions of several variables from the numerical, algebraic, and graphical viewpoints
Videos
 Videos for Section 15.1: Functions of several variables Using a spreadhseet
15.2 Partial derivatives
Video
 Video  for Section 15.2: Partial derivatives
15.3 Maxima and minima
Videos
 Videos for Section 15.3: Maxima and minima:Part A Maxima and minima:Part B Maxima and minima: Applications
15.4 Constrained maxima and minima and applications
15.5 Double integrals and applications
Online: Chain rule for functions of several variables (pdf only)
Online: Extreme Values: Boundaries and the Extreme Value Theorem (pdf only)
Case study:  Modeling college population

Chapter 15 resources
Chapter summary | Chapter true/false quiz

Chapter 15 tools
Surface graphing utility | Excel surface graphing utility | Multiple regression utility

Chapter 16 Trigonometric models
16.1 Trigonometric functions, models, and regression
16.2 Derivatives of trigonometric functions and applications
16.3 Integrals of trigonometric functions and applications
Online: Proofs of some trigonometric limits
Online: New functions from old: Scaled and shifted functions

Chapter 16 resources
Chapter summary | Chapter true/false quiz | Chapter Excel tutorials | Online version of this chapter

Chapter 16 tools
Function evaluator and grapher | Excel grapher

Chapter L: Introduction to logic
An expanded version of Appendix A in the textbook. A complete text version of this chapter can be downloaded here.
L.1 Statements and logical operators
L.2 Logical equivalence, tautologies and contradictions
L.3 The conditional and the biconditional
L.4 Tautological implications and tautological equivalences
L.5 Rules of inference
L.6 Arguments and proofs
L.7 Predicate calculus

Chapter S: Sequences, series, and Taylor series
Text and exercises online
S.1 Taylor polynomials
S.2 Infinite sequences
S.3 Infinite series
Practice/visualize
 Practice/visualize for Section S.3: Telescoping series
S.4 Taylor series
S.5 Applications of Taylor series
Chapter S Case study:  Predicting sales

Chapter P: Calculus applied to probability and statistics
Text and exercises online; a complete text version of this chapter can be downloaded here.
P.1 Continuous random variables and histograms
P.2 Probability density functions: Uniform, exponential, normal, and beta
P.3 Mean, median, variance and standard deviation
Chapter P Case study:  Creating a family trust