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 |