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Applied Calculus 4e
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| You can get back here from anywhere by pressing the"Everything for Calculus" link. | ||
| 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 | Free Mac Grapher | |
| 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 | Free Mac Grapher | |
| 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 |
| 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 | Excel Derivative Grapher | Simple Regression Utility | Download Free Mac Grapher | |
| Chapter 4 Techniques of Differentiation | |
| 4.1 The Product and Quotient Rules | On-line tutorial for Section 4.1 |
| 4.2 The Chain Rule | On-line tutorial for Section 4.2 |
| 4.3 Derivatives of Logarithmic and Exponential Functions | On-line tutorial for Section 4.3 |
| 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 | |
| Function Evaluator & Grapher | Excel First- and Second-Derivative Graphing Utility | Free Mac Grapher | |
| 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 | |
| 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) |
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| 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 | |