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by Geoffrey C. Berresford and Andrew M. Rockett

Edition: 3RD 04Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

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This brief edition of Applied Calculus comprises Chapters 1-7 of the complete text plus two sections on differential equations.

Index of Selected Applications

Graphing Calculator Terminology

**1. Functions**

1.1 Real Numbers, Inequalities, and Lines

1.2 Exponents

1.3 Functions

1.4 Functions, Continued

**2. Derivatives and Their Uses**

2.1 Limits and Continuity

2.2 Rates of Change, Slopes, and Derivatives

2.3 Some Differentiation Formulas

2.4 The Product and Quotient Rules

2.5 Higher-Order Derivatives

2.6 The Chain Rule and Generalized Power Rule

2.7 Nondifferentiable Functions

**3. Further Applications of Derivatives**

3.1 Graphing Using the First Derivative

3.2 Graphing Using the First and Second Derivatives

3.3 Optimization

3.4 Further Applications of Optimization

3.5 Optimizing Lot Size and Harvest Size

3.6 Implicit Differentiation and Related Rates

Cumulative Review for Chapters 1-3

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Differentiation of Logarithmic and Exponential Functions

4.4 Two Applications to Economics: Related Rates and Elasticity of Demand

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 Integration Using Logarithmic and Exponential Functions

5.3 Definite Integrals and Areas

5.4 Further Applications of Definite Integrals: Average Value and Area Between Curves

5.5 Two Applications to Economics: Consumers' Surplus and Income Distribution

5.6 Integration by Substitution

**6. Integration Techniques and Differential Equations**

6.1 Integration by Parts

6.2 Integration Using Tables

6.3 Improper Integrals

6.4 Numerical Integration

6.5 Differential Equations

6.6 Further Applications of Differential Equations: Three Models of Growth

**7. Calculus of Several Variables**

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Several Variables

7.4 Least Squares

7.5 Lagrange Multipliers and Constrained Optimization

7.6 Total Differentials and Approximate Changes

7.7 Multiple Integrals

Cumulative Review for Chapters 1-7

Answers to Selected Exercises

Definitions, Formulas, and Properties

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Summary

This brief edition of Applied Calculus comprises Chapters 1-7 of the complete text plus two sections on differential equations.

Table of Contents

Index of Selected Applications

Graphing Calculator Terminology

**1. Functions**

1.1 Real Numbers, Inequalities, and Lines

1.2 Exponents

1.3 Functions

1.4 Functions, Continued

**2. Derivatives and Their Uses**

2.1 Limits and Continuity

2.2 Rates of Change, Slopes, and Derivatives

2.3 Some Differentiation Formulas

2.4 The Product and Quotient Rules

2.5 Higher-Order Derivatives

2.6 The Chain Rule and Generalized Power Rule

2.7 Nondifferentiable Functions

**3. Further Applications of Derivatives**

3.1 Graphing Using the First Derivative

3.2 Graphing Using the First and Second Derivatives

3.3 Optimization

3.4 Further Applications of Optimization

3.5 Optimizing Lot Size and Harvest Size

3.6 Implicit Differentiation and Related Rates

Cumulative Review for Chapters 1-3

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Differentiation of Logarithmic and Exponential Functions

4.4 Two Applications to Economics: Related Rates and Elasticity of Demand

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 Integration Using Logarithmic and Exponential Functions

5.3 Definite Integrals and Areas

5.4 Further Applications of Definite Integrals: Average Value and Area Between Curves

5.5 Two Applications to Economics: Consumers' Surplus and Income Distribution

5.6 Integration by Substitution

**6. Integration Techniques and Differential Equations**

6.1 Integration by Parts

6.2 Integration Using Tables

6.3 Improper Integrals

6.4 Numerical Integration

6.5 Differential Equations

6.6 Further Applications of Differential Equations: Three Models of Growth

**7. Calculus of Several Variables**

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Several Variables

7.4 Least Squares

7.5 Lagrange Multipliers and Constrained Optimization

7.6 Total Differentials and Approximate Changes

7.7 Multiple Integrals

Cumulative Review for Chapters 1-7

Answers to Selected Exercises

Definitions, Formulas, and Properties

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

Index of Selected Applications

Graphing Calculator Terminology

**1. Functions**

1.1 Real Numbers, Inequalities, and Lines

1.2 Exponents

1.3 Functions

1.4 Functions, Continued

**2. Derivatives and Their Uses**

2.1 Limits and Continuity

2.2 Rates of Change, Slopes, and Derivatives

2.3 Some Differentiation Formulas

2.4 The Product and Quotient Rules

2.5 Higher-Order Derivatives

2.6 The Chain Rule and Generalized Power Rule

2.7 Nondifferentiable Functions

**3. Further Applications of Derivatives**

3.1 Graphing Using the First Derivative

3.2 Graphing Using the First and Second Derivatives

3.3 Optimization

3.4 Further Applications of Optimization

3.5 Optimizing Lot Size and Harvest Size

3.6 Implicit Differentiation and Related Rates

Cumulative Review for Chapters 1-3

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Differentiation of Logarithmic and Exponential Functions

4.4 Two Applications to Economics: Related Rates and Elasticity of Demand

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 Integration Using Logarithmic and Exponential Functions

5.3 Definite Integrals and Areas

5.4 Further Applications of Definite Integrals: Average Value and Area Between Curves

5.5 Two Applications to Economics: Consumers' Surplus and Income Distribution

5.6 Integration by Substitution

**6. Integration Techniques and Differential Equations**

6.1 Integration by Parts

6.2 Integration Using Tables

6.3 Improper Integrals

6.4 Numerical Integration

6.5 Differential Equations

6.6 Further Applications of Differential Equations: Three Models of Growth

**7. Calculus of Several Variables**

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Several Variables

7.4 Least Squares

7.5 Lagrange Multipliers and Constrained Optimization

7.6 Total Differentials and Approximate Changes

7.7 Multiple Integrals

Cumulative Review for Chapters 1-7

Answers to Selected Exercises

Definitions, Formulas, and Properties