Chapter 0 Algebra Review | |
0.1 Real Numbers |
Online tutorial for Section 0.1 |
0.2 Exponents and Radicals |
Online tutorial for Section 0.2 |
0.3 Multiplying and Factoring Algebraic Equations |
Online tutorial for Section 0.3 |
0.4 Rational Expressions |
Online tutorial for Section 0.4 |
0.5 Solving Polynomial Equations |
Online tutorial for Section 0.5 |
0.6 Solving Miscellaneous Equations |
0.7 The Coordinate Plane |
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Chapter 1 Functions and Linear Models | |
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Online: New Functions from Old: Scaled and Shifted Functions |
Online: Fitting Functions to Data: Linear and Exponential Regression |
Online Resources for Chapter 1 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 1 |
Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Steve Costenoble's Java Graphing Utility |
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Chapter 2 Systems of Linear Equations and Matrices |
2.1 Systems of Two Linear Equations in Two Unknowns | Online tutorial for Section 2.1 |
2.2 Using Matrices to Solve Systems of Equations |
Online tutorial for Section 2.2 Game version |
2.3 Applications of Systems of Linear Equations |
Online tutorial for Section 2.3 |
Case Study: Hybrid Cars—Optimizing the Degree of Hybridization |
Online Resources for Chapter 2 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 2 |
Pivot and Gauss-Jordan Tool | Excel Pivot and Gauss-Jordan Tool | Graphing Calculator Pivot Program (TI-82/83/84/85/86) | Free Mac Gauss-Jordan Program |
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Chapter 3 Matrix Algebra |
3.1 Matrix Addition and Scalar Multiplication |
Online tutorial for Section 3.1 Game version |
3.2 Matrix Multiplication |
Online tutorial for Section 3.2 Game version |
3.3 Matrix Inversion |
Online tutorial for Section 3.3 |
3.4 Game Theory |
Online tutorial for Section 3.4 Game version |
3.5 Input-Output Models |
Online tutorial for Section 3.5 |
Case Study: Projecting Market Share |
Online Resources for Chapter 3 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 3 |
Matrix Algebra Tool | Online Game Theory Utility | Free Mac Matrix Algebra Program |
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Chapter 4 Linear Programming |
4.1 Graphing Linear Inequalities |
4.2 Solving Linear Programming Problems Graphically |
Online tutorial for Section 4.2
Game version |
4.3 The Simplex Method: Solving Standard Maximization Problems |
Online tutorial for Section 4.3
Game version |
4.4 The Simplex Method: Solving General Linear Programming Problems |
Online tutorial for Section 4.4
Game version |
4.5 The Simplex Method and Duality (Optional) |
Case Study: The Diet Problem |
Diet Problem Solver |
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Online Resources for Chapter 4 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 4 |
Linear Programming Grapher | Excel Row Operation and Pivoting Utility | Simplex Method Tool | Row Operation and Pivoting Utility | Graphing Calculator Pivot Program (TI-82/83/84/85/86) | Diet Problem Solver |
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Chapter 5 Mathematics of Finance |
5.1 Simple Interest |
5.2 Compound Interest |
5.3 Annuities, Loans, and Bonds |
Case Study: Adjustable Rate and Subprime Mortgages |
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Online Resources for Chapter 5 |
Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials |
Math Tools for Chapter 5 |
Time Value of Money Utility
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Chapter 6 Sets and Counting |
6.1 Set Operations |
6.2 Cardinality |
6.3 The Addition and Multiplication Principles |
Online tutorial for Section 6.3 Game version |
6.4 Permutations and Combinations |
Online tutorial for Section 6.4 Game version |
Case Study: Designing a Puzzle |
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Online Resources for Chapter 6 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises |
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Chapter 7 Probability |
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Online Resources for Chapter 7 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises |
Math Tools for Chapter 7 |
Online Markov System Simulation (Visual Simulation) | Matrix Algebra Tool | Online Markov System Computation Utility (Computes Powers of Transition Matrix) |
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Chapter 8 Random Variables and Statistics |
8.1 Random Variables and Distributions |
Online tutorial for Section 8.1 |
8.2 Bernoulli Trials and Binomial Random Variables |
Online tutorial for Section 8.2 |
8.3 Measures of Central Tendency |
Online tutorial for Section 8.3 |
8.4 Measures of Dispersion |
Online tutorial for Section 8.4 |
8.5 Normal Distributions |
Online: Sampling Distributions and the Central Limit Theorem |
Online: Confidence Intervals |
Online: Calculus & Statistics |
Online: Fitting Functions to Data: Regression |
Case Study: Spotting Tax Fraud with Benford's Law |
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Online Resources for Chapter 8 |
Chapter Summary | | Chapter True/False Quiz | Chapter Review Exercises |
Math Tools for Chapter 8 |
Histogram and Probability Distribution Generator | Probability Distribution Generator and Grapher for Bernoulli Trials | Normal Distribution Utility | Normal Distribution Table |
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Chapter 9 Nonlinear Models | |
9.1 Quadratic Functions and Models | Online tutorial for Section 9.1 |
9.2 Exponential Functions and Models | Online tutorial for Section 9.2 |
9.3 Logarithmic Functions and Models | Online tutorial for Section 9.3 |
9.4 Logistic Functions and Models |
Online: Inverse Fuctions |
Online: Fitting Functions to Data: Linear and Exponential Regression |
Online: Using and Deriving
Algebraic Properties of Logarithms |
Case Study: Checking Up on Malthus | Wheat Production Data (Excel) |
Online Resources for Chapter 9 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 9 |
Function Evaluator & Grapher | Excel Grapher | Regression Utility | Steve Costenoble's Steve Costenoble's Java Graphing Utility |
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Chapter 10 Introduction to the Derivative |
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Online: Sketching the Graph of the Derivative |
Online: Continuity and Differentiability |
Online Resources for Chapter 10 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Additional exercises for derivatives of powers, sums, and constant multiples | Chapter Excel Tutorials |
Math Tools for Chapter 10 |
Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Steve Costenoble's Steve Costenoble's Java Graphing Utility | Excel Derivative Grapher
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Chapter 11 Techniques of Differentiation |
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Video for Section 11.3 (Prof X-Squared): Product and Quotient Rules
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Videos for Section 11.4 (Prof X-Squared): Chain Rule Part 1 Chain Rule Part 2
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Online: Linear Approximation and Error Estimation |
Online: Proof of the Power Rule |
Online: Proof of the Quotient Rule |
Online: Proof of the Chain Rule |
Online Resources for Chapter 11 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Exercises for derivatives of powers, sums, and constant multiples | Exercises for product and quotient rules | Chapter Review Exercises
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Chapter 12 Applications of the Derivative |
12.1 Maxima and Minima |
5.1 Maxima and Minima | Online tutorial for Section 12.1 Game version |
12.2 Applications of Maxima and Minima | Online tutorial for Section 12.2 |
12.3 The Second Derivative and Analyzing Graphs |
Online tutorial for Section 12.3 |
12.4 Related Rates |
Online tutorial for Section 12.4 |
12.5 Elasticity of Demand |
Case Study: Production Lot Size Management |
Online Resources for Chapter 12 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 12 |
Steve Costenoble's Java Graphing Utility | Function Evaluator & Grapher | Excel First- and Second-Derivative Graphing Utility | Free Mac Grapher |
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Chapter 13 The Integral |
13.1 The Indefinite Integral |
13.2 Substitution |
Online tutorial for Section 13.2 Game version |
13.3 The Definite Integral: Numerical and Graphical Approaches |
Online tutorial for Section 13.3 Game version |
13.4 The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus |
Online tutorial for Section 13.4 |
Online: Numerical Integration |
Case Study: Spending on Housing Construction |
Online Resources for Chapter 13 |
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 13 |
Numerical Integration Utility | Graphing Calculator Programs for Numerical Integration | Excel Riemann Sum Grapher |
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Chapter 14 Further Techniques and Applications of the Integral |
14.1 Integration by Parts |
Videos for Section 7.1 (Prof X-Squared): Part 1 Part 2
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14.2 Area Between Two Curves and Applications |
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 |
Case Study: Estimating Tax Revenues |
Online Resources for Chapter 14 |
Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials |
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Chapter 15 Functions of Several Variables |
15.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints |
15.2 Three Dimensional Space and the Graph of a Function of Two Variables |
15.3 Partial Derivatives |
15.4 Maxima and Minima |
15.5 Constrained Maxima and Minima Applications | Also See Online Material on Regression |
15.6 Double Integrals |
Case Study: Modeling College Population |
Online Resources for Chapter 15 |
Chapter Summary | Chapter True/False Quiz |
Math Tools for Chapter 15 |
Surface Graphing Utility |
Excel Surface Graphing Utility | Linear Multiple Regression Utility |
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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 |
Case Study: Predicting Airline Empty Seat Volume |
Download data |
Online Resources for Chapter 16 |
Chapter Summary | Online version of this chapter | Chapter True/False Quiz |
Math Tools for Chapter 16 |
Steve Costenoble's Java Graphing Utility | Function Evaluator & Grapher | Excel Grapher | Excel Derivative Grapher |
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Online Chapter: Trigonometric Functions and Calculus (Text and Complete Exercise Sets Online; brings together material in Chapters 10, 12, and 14) |
Introduction |
Modeling with the Sine Function |
The Six Trigonometric Functions |
Derivatives of Trigonometric Functions |
Integrals of Trigonometric Functions |
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Chapter P: Calculus Applied to Probability and Statistics (Text and Complete Exercise Sets Online; a complete text version of this chapter can be downloaded here in pdf format) |
Introduction |
CP.1 Continuous Random Variables and Histograms |
CP.2 Probability Density Functions: Uniform, Exponential, Normal, and Beta |
CP.3 Mean, Median, Variance and Standard Deviation |
Case Study: Creating a Family Trust |
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Appendix A: Logic (Also see on-line full chapter version below.) | Answers to Odd-numbered Exercises in Textbook |
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Appendix B: Table: Area Under a Normal Curve |
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Chapter L: Introduction to Logic (Text and Complete Exercise Sets Online; a complete text version of this chapter can be downloaded here in pdf format) |
Introduction |
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 |