| 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 Nonlinear Models | |
| 2.1 Quadratic Functions and Models | Online tutorial for Section 2.1 |
| 2.2 Exponential Functions and Models | Online tutorial for Section 2.2 |
| 2.3 Logarithmic Functions and Models | Online tutorial for Section 2.3 |
| 2.4 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 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 |
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Chapter 3 Introduction to the Derivative |
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| Online: Sketching the Graph of the Derivative |
| Online: Continuity and Differentiability |
Online 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
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| Chapter 4 Techniques of Differentiation |
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Video for Section 4.3 (Prof X-Squared): Product and Quotient Rules
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Videos for Section 4.4 (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 4 |
| 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 5 Applications of the Derivative |
| 5.1 Maxima and Minima | Online tutorial for Section 5.1 Game version |
| 5.2 Applications of Maxima and Minima | Online tutorial for Section 5.2 |
| 5.3 The Second Derivative and Analyzing Graphs |
Online tutorial for Section 5.3 |
| 5.4 Related Rates |
Online tutorial for Section 5.4 |
| 5.5 Elasticity of Demand |
| Case Study: Production Lot Size Management |
Online 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
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| Chapter 6 The Integral |
| 6.1 The Indefinite Integral |
| 6.2 Substitution |
Online tutorial for Section 6.2 Game version |
| 6.3 The Definite Integral: Numerical and Graphical Approaches |
Online tutorial for Section 6.3 Game version |
| 6.4 The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus |
Online tutorial for Section 6.4 |
| Online: Numerical Integration |
| Case Study: Spending on Housing Construction |
Online 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 |
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| Chapter 7 Further Techniques and Applications of the Integral |
| 7.1 Integration by Parts |
Videos for Section 7.1 (Prof X-Squared): Part 1 Part 2
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| 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 |
Online Resources for Chapter 7 |
| Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials
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| 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 Online Material on Regression |
| 8.6 Double Integrals |
| Case Study: Modeling College Population |
Online 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 |
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| 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 |
| 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 9 |
| Chapter Summary | Online version of this chapter | Chapter True/False Quiz |
Math Tools for Chapter 9 |
| Steve Costenoble's Steve Costenoble's Java Graphing Utility | Function Evaluator & Grapher | Excel Grapher | Excel Derivative Grapher |
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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 |
