Chapter 0 Precalculus review 
0.1 Real numbers   0.1 Tutorial  Adaptive game tutorial 

0.2 Exponents and radicals   0.2 Tutorial  Adaptive game tutorial 

0.3 Using exponent identities   0.3 Tutorial  Adaptive game tutorial 

0.4 Multiplying and factoring algebraic expressions   0.4 Tutorial  Adaptive game tutorial 
0.5 Rational expressions   0.5 Tutorial  Adaptive game tutorial 
0.6 Solving polynomial equations   0.6 Tutorial  Adaptive game tutorial 
0.7 Solving miscellaneous equations  
0.8 The coordinate plane   0.8 Tutorial  Adaptive game tutorial 
0.9 Logarithms  

Chapter 1 Functions and applications 
1.1 Functions from the numerical, algebraic, and graphical viewpoints   1.1 Tutorial  Adaptive game tutorial 


1.2 Functions and models   1.2 Tutorial  Adaptive game tutorial 


1.3 Linear functions and models   1.3 Tutorial  Adaptive game tutorial 


1.4 Linear regression   1.4 Tutorial  Game tutorial 


Online: New functions from old: Scaled and shifted functions   Tutorial for this section  Adaptive game tutorial 
Online: Fitting curves to data: Linear and exponential regression  
Case study: Modeling YouTube viewership  


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 models   2.1 Tutorial  Game tutorial 


2.2 Exponential functions and models   2.2 Tutorial  Adaptive game tutorial 


2.3 The number e and exponential growth and decay  


2.4 Logistic and logarithmic functions and models   2.4 Tutorial  Game tutorial 


Online: Inverse functions  
Online: Fitting curves to data: linear and exponential regression  
Online: Using and Deriving Algebraic Properties of Logarithms  
Case study: Projecting market growth  


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 interest   3.1 Tutorial  Game tutorial 

3.2 Compound interest   3.2 Tutorial  Game tutorial 

3.3 Annuities, loans, and bonds   3.3 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 


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 


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 GaussJordan tool  Excel pivot and GaussJordan tool  Pivot program for graphing calculator (TI82/83/84/85/86) 

Chapter 5 Matrix algebra 
5.1 Matrix addition and scalar multiplication   5.1 Tutorial  Game tutorial 


5.2 Matrix multiplication   5.2 Tutorial  Game tutorial 


5.3 Matrix inversion   5.3 Tutorial  Game tutorial 


5.4 Game theory   5.4 Tutorial  Game tutorial 


5.5 Inputoutput models   5.5 Tutorial 

Online: Determinants and Cramer's Rule (pdf only)  
Case study: Social network analysis  


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

Chapter 5 tools 
Pivot program for graphing calculator (TI82/83/84/85/86)  Matrix algebra tool 

Chapter 6 Linear programming 
6.1 Graphing linear inequalities   6.1 Tutorial  Game tutorial 


6.2 Solving linear programming problems graphically   6.2 Tutorial  Game tutorial 


6.3 The simplex method: Solving standard maximization problems   6.3 Tutorial  Adaptive game tutorial 


6.4 The simplex method: Solving general linear programming problems   6.4 Tutorial  Adaptive game tutorial 


6.5 The simplex method and duality  
Case study: The diet problem   Diet 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 GaussJordan tool  Excel pivot and GaussJordan tool  Pivot program for graphing calculator (TI82/83/84/85/86)  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 operations   7.1 Tutorial  Adaptive game tutorial 


7.2 Cardinality   7.2 Tutorial  Adaptive game tutorial 


7.3 Decision algorithms: The addition and multiplication principles   7.3 Tutorial  Adaptive game tutorial 


7.4 Permutations and combinations   7.4 Tutorial  Adaptive game tutorial 


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 events   8.1 Tutorial  Game tutorial 

8.2 Relative frequency   8.2 Tutorial  Game tutorial 

8.3 Probability and probability models   8.3 Tutorial  Game tutorial 

8.4 Probability and counting techniques  
8.5 Conditional probability and independence   8.5 Tutorial  Game tutorial 

8.6 Bayes' Theorem and Applications   8.6 Tutorial  Game tutorial 

8.7 Markov systems  

Case study: The Monty Hall problem   Online 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 distributions   9.1 Tutorial  Game tutorial 

9.2 Bernoulli trials and binomial random variables   9.2 Tutorial  Adaptive game tutorial 


9.3 Measures of central tendency   9.3 Tutorial 
9.4 Measures of dispersion   9.4 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 viewpoints   10.1 Tutorial  Game tutorial 


10.2 Limits: algebraic viewpoint   10.2 Tutorial  Game tutorial 


10.3 Limits and continuity   10.3 Tutorial  Game tutorial 


10.4 Average rate of change   10.4 Tutorial  Adaptive game tutorial 


10.5 The derivative: numerical and graphical viewpoints   10.5 Tutorial  Game tutorial 


10.6 The derivative: algebraic viewpoint   10.6 Tutorial  Adaptive game tutorial 


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 multiples   11.1 Tutorial  Adaptive game tutorial 


11.2 A first application: Marginal analysis   11.2 Tutorial  Game tutorial 


11.3 The product and quotient rules   11.3 Tutorial  Adaptive game tutorial 


11.4 The chain rule   11.4 Tutorial  Adaptive game tutorial 


11.5 Derivatives of logarithmic and exponential functions   11.5 Tutorial  Adaptive game tutorial 


11.6 Implicit 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: Tracking the covid19 epidemic in the U.S.   COVID19 data (Excel) 


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 minima   12.1 Tutorial  Adaptive game tutorial 


12.2 Applications of maxima and minima   12.2 Tutorial  Game tutorial 


12.3 Higher order derivatives: Acceleration and concavity   12.3 Tutorial  Game tutorial 


12.4 Analyzing graphs   12.4 Tutorial  Adaptive game tutorial 


12.5 Related rates   12.5 Tutorial  Game tutorial 


12.6 Elasticity   12.6 Tutorial  Game tutorial 


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 integral   13.1 Tutorial  Game tutorial 


13.2 Substitution   13.2 Tutorial  Game tutorial 


13.3 The definite integral: Numerical and graphical viewpoints   13.3 Tutorial  Game tutorial 


13.4 The definite integral: Algebraic viewpoint and the fundamental theorem of calculus   13.4 Tutorial  Game tutorial 


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 (TI82/83/84/85/86)  Excel Riemann sum grapher 

Chapter 14 Further integration techniques and applications of the integral 
14.1 Integration by parts   14.1 Tutorial  Game tutorial 


14.2 Area between two curves   14.2 Tutorial  Game tutorial 

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  

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 (TI82/83/84/85/86)  Excel Riemann sum grapher 

Chapter 15 Functions of several variables 
15.1 Functions of several variables from the numerical, algebraic, and graphical viewpoints   15.1 Tutorial  Adaptive game tutorial 


15.2 Partial derivatives  

15.3 Maxima and minima  

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   16.1 Tutorial  Adaptive game tutorial 
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  
Case study: Predicting airline empty seat volume   Empty seat miles data (Excel) 


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  

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 

