| Chapter 0 Algebra Review |  |
| 0.1 Real Numbers |
On-line tutorial for Section 0.1 |
| 0.2 Exponents and Radicals |
On-line tutorial for Section 0.2 |
| 0.3 Multiplying and Factoring Algebraic Equations |
On-line tutorial for Section 0.3 |
| 0.4 Rational Expressions |
On-line tutorial for Section 0.4 |
| 0.5 Solving Polynomial Equations |
On-line tutorial for Section 0.5 |
| 0.6 Solving Miscellaneous Equations |
|
| Chapter 1 Functions and Linear Models | |
| 1.1 Functions from the Numerical and Algebraic Viewpoints | On-line tutorial for Section 1.1 |
| 1.2 Functions from the Graphical Viewpoint | On-line tutorial for Section 1.2 |
| 1.3 Linear Functions | On-line tutorial for Section 1.3 |
| 1.4 Linear Models |
On-line tutorial for Section 1.4 |
| 1.5 Linear Regression | On-line tutorial for Section 1.5 |
| On-Line: New Functions from Old: Scaled and Shifted Functions |
| On-Line: Fitting Functions to Data: Linear and Exponential Regression |
| Case Study: Modeling Spending on Internet Advertising |
On-Line 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 Steve Costenoble's Java Graphing Utility |
|
| Chapter 2 Nonlinear Models | |
| 2.1 Quadratic Functions and Models | On-line tutorial for Section 2.1 |
| 2.2 Exponential Functions and Models | On-line tutorial for Section 2.2 |
| 2.3 Logarithmic Functions and Models | On-line tutorial for Section 2.3 |
| 2.4 Logistic Functions and Models |
| On-Line: Inverse Fuctions |
| On-Line: Fitting Functions to Data: Linear and Exponential Regression |
| On-Line: Using and Deriving
Algebraic Properties of Logarithms |
| Case Study: Checking Up on Malthus |
On-Line Resources for Chapter 2 |
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 2 |
| Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Steve Costenoble's Steve Costenoble's Java Graphing Utility |
|
Chapter 3 Introduction to the Derivative |
| 3.1 Limits: Numerical and Graphical Approaches |
On-line tutorial for Section 3.1 |
| 3.2 Limits and Continuity |
On-line tutorial for Section 3.2 |
| 3.3 Limits: Algebraic Approach |
On-line tutorial for Section 3.3 |
| 3.4 Average Rate of Change |
On-line tutorial for Section 3.4 Game version |
| 3.5 The Derivative: Numerical and Graphical Viewpoints |
On-line tutorial for Section 3.5 Game version |
| 3.6 The Derivative: Algebraic Viewpoint |
On-line tutorial for Section 3.6 Game version |
| 3.7 Derivatives of Powers, Sums, and Constant Multiples |
On-line tutorial for Section 3.7 Game version |
| 3.8 A First Application: Marginal Analysis |
| On-Line: Sketching the Graph of the Derivative |
| On-Line: Proof of the Power Rule |
| On-Line: Continuity and Differentiability |
| Case Study: Reducing Sulfur Emissions |
On-Line Resources for Chapter 3 |
| 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 3 |
| Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Steve Costenoble's Steve Costenoble's Java Graphing Utility | Excel Derivative Grapher
|
|
| Chapter 4 Techniques of Differentiation |
| 4.1 The Product and Quotient Rules |
On-line tutorial for Section 4.1 Game version |
| 4.2 The Chain Rule |
On-line tutorial for Section 4.2 Game version |
| 4.3 Derivatives of Logarithmic and Exponential Functions |
On-line tutorial for Section 4.3 Game version |
| 4.4 Implicit Differentiation |
| On-Line:Linear Approximation and Error Estimation |
| On-Line:Proof of the Quotient Rule |
| On-Line:Proof of the Chain Rule |
| Case Study: Projecting Market Growth |
On-Line Resources for Chapter 4 |
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Additional exercises for product and quotient rules
|
|
| Chapter 5 Applications of the Derivative |
| 5.1 Maxima and Minima | On-line tutorial for Section 5.1 |
| 5.2 Applications of Maxima and Minima | On-line tutorial for Section 5.2 |
| 5.3 The Second Derivative and Analyzing Graphs |
On-line tutorial for Section 5.3 |
| 5.4 Related Rates |
On-line tutorial for Section 5.4 |
| 5.5 Elasticity of Demand |
| Case Study: Production Lot Size Management |
On-Line Resources for Chapter 5 |
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 5 |
| Steve Costenoble's Steve Costenoble's Java Graphing Utility | Function Evaluator & Grapher | Excel First- and Second-Derivative Graphing Utility
|
|
| Chapter 6 The Integral |
| 6.1 The Indefinite Integral |
On-line tutorial for Section 6.1 |
| 6.2 Substitution |
On-line tutorial for Section 6.2 |
| 6.3 The Definite Integral: Numerical and Graphical Approaches |
On-line tutorial for Section 6.3 |
| 6.4 The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus |
On-line tutorial for Section 6.4 |
| On-Line: Numerical Integration |
| Case Study: Wage Inflation |
On-Line Resources for Chapter 6 |
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials |
Math Tools for Chapter 6 |
| Numerical Integration Utility | Graphing Calculator Programs for Numerical Integration | Excel Riemann Sum Grapher |
|
| Chapter 7 Further Techniques and Applications of the Integral |
| 7.1 Integration by Parts |
| 7.2 Area Between Two Curves and Applications |
| 7.3 Averages and Moving Averages |
| 7.4 Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams |
| 7.5 Improper Integrals and Applications |
| 7.6 Differential Equations and Applications |
| Case Study: Estimating Tax Revenues |
On-Line Resources for Chapter 7 |
| Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials
|
|
| Chapter 8 Functions of Several Variables |
| 8.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints |
| 8.2 Three Dimensional Space and the Graph of a Function of Two Variables |
| 8.3 Partial Derivatives |
| 8.4 Maxima and Minima |
| 8.5 Constrained Maxima and Minima Applications | Also See On-Line Material on Regression |
| 8.6 Double Integrals |
| Case Study: Constructing a Best Fit Demand Curve |
On-Line Resources for Chapter 8 |
| Chapter Summary | Chapter True/False Quiz |
Math Tools for Chapter 8 |
| Surface Graphing Utility |
Excel Surface Graphing Utility | Linear Multiple Regression Utility |
|
| Chapter 9 Trigonometric Models |
| 9.1 Trigonometric Functions, Models, and Regression |
| 9.2 Derivatives of Trigonometric Functions and Applications |
| 9.3 Integrals of Trigonometric Functions and Applications |
| On-Line: Proofs of Some Trigonometric Limits |
| On-Line: New Functions from Old: Scaled and Shifted Functions |
| Case Study: Predicting Cocoa Inventories |
On-Line Resources for Chapter 9 |
| Chapter Summary | On-line version of this chapter |
Math Tools for Chapter 9 |
| Steve Costenoble's Steve Costenoble's Java Graphing Utility | Function Evaluator & Grapher | Excel Grapher | Excel Derivative Grapher |
|
Chapter P: Calculus Applied to Probability and Statistics
(Text and Complete Exercise Sets On-Line; 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 |
