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by Geoffrey C. Berresford and Andrew M. Rockett

Edition: 3RD 04Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Geoffrey C. Berresford and Andrew M. Rockett

Edition: 3RD 04
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This text for the one- or two-semester applied or business calculus course uses intriguing real-world applications to engage students' interest and show them the practical side of calculus. Integrated use of graphing calculators, combined with thought-provoking writing exercises, give students a well-rounded mathematical experience. Brief Applied Calculus has been praised by reviewers for its optional integration of technology and its strong pedagogy, which includes unique end-of-section summaries.

**Berresford, Geoffrey C. : Long Island University Rockett, Andrew M. : Long Island University**

*Note: Each chapter concludes with a Chapter Summary and Review Exercises.*

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

6.1 Integration by Parts

6.2 Integration Using Tables

6.3 Improper Integrals

6.4 Numerical Integration

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*

8. Trigonometric Functions

8.1 Triangles, Angles, and Radian Measure

8.2 Sine and Cosine Functions

8.3 Derivatives of Sine and Cosine Functions

8.4 Integrals of Sine and Cosine Functions

8.5 Other Trigonometric Functions

9. Differential Equations

9.1 Separation of Variables

9.2 Further Applications of Differential Equations: Three Models of Growth

9.3 First-Order Linear Differential Equations

9.4 Approximate Solutions of Differential Equations: Euler's Method

10. Sequences and Series

10.1 Geometric Series

10.2 Taylor Polynomials

10.3 Taylor Series

10.4 Newton's Method

11. Probability

11.1 Discrete Probability

11.2 Continuous Probability

11.3 Uniform and Exponential Random Variables

11.4 Normal Random Variables

Cumulative Review for Chapters 1-11

Appendix: Normal Probabilities from Tables

Answers to Selected Exercises

Definitions, Formulas, and Properties

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Summary

This text for the one- or two-semester applied or business calculus course uses intriguing real-world applications to engage students' interest and show them the practical side of calculus. Integrated use of graphing calculators, combined with thought-provoking writing exercises, give students a well-rounded mathematical experience. Brief Applied Calculus has been praised by reviewers for its optional integration of technology and its strong pedagogy, which includes unique end-of-section summaries.

Author Bio

**Berresford, Geoffrey C. : Long Island University Rockett, Andrew M. : Long Island University**

Table of Contents

*Note: Each chapter concludes with a Chapter Summary and Review Exercises.*

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

6.1 Integration by Parts

6.2 Integration Using Tables

6.3 Improper Integrals

6.4 Numerical Integration

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*

8. Trigonometric Functions

8.1 Triangles, Angles, and Radian Measure

8.2 Sine and Cosine Functions

8.3 Derivatives of Sine and Cosine Functions

8.4 Integrals of Sine and Cosine Functions

8.5 Other Trigonometric Functions

9. Differential Equations

9.1 Separation of Variables

9.2 Further Applications of Differential Equations: Three Models of Growth

9.3 First-Order Linear Differential Equations

9.4 Approximate Solutions of Differential Equations: Euler's Method

10. Sequences and Series

10.1 Geometric Series

10.2 Taylor Polynomials

10.3 Taylor Series

10.4 Newton's Method

11. Probability

11.1 Discrete Probability

11.2 Continuous Probability

11.3 Uniform and Exponential Random Variables

11.4 Normal Random Variables

Cumulative Review for Chapters 1-11

Appendix: Normal Probabilities from Tables

Answers to Selected Exercises

Definitions, Formulas, and Properties

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

**Berresford, Geoffrey C. : Long Island University Rockett, Andrew M. : Long Island University**

*Note: Each chapter concludes with a Chapter Summary and Review Exercises.*

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

6.1 Integration by Parts

6.2 Integration Using Tables

6.3 Improper Integrals

6.4 Numerical Integration

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*

8. Trigonometric Functions

8.1 Triangles, Angles, and Radian Measure

8.2 Sine and Cosine Functions

8.3 Derivatives of Sine and Cosine Functions

8.4 Integrals of Sine and Cosine Functions

8.5 Other Trigonometric Functions

9. Differential Equations

9.1 Separation of Variables

9.2 Further Applications of Differential Equations: Three Models of Growth

9.3 First-Order Linear Differential Equations

9.4 Approximate Solutions of Differential Equations: Euler's Method

10. Sequences and Series

10.1 Geometric Series

10.2 Taylor Polynomials

10.3 Taylor Series

10.4 Newton's Method

11. Probability

11.1 Discrete Probability

11.2 Continuous Probability

11.3 Uniform and Exponential Random Variables

11.4 Normal Random Variables

Cumulative Review for Chapters 1-11

Appendix: Normal Probabilities from Tables

Answers to Selected Exercises

Definitions, Formulas, and Properties