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by Geoffrey C. Berresford and Andrew M. Rockett

Cover type: HardbackEdition: 4TH 07

Copyright: 2007

Publisher: Houghton Mifflin Harcourt

Published: 2007

International: No

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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. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources.

The Fourth Edition maintains the hallmark features that have made Applied Calculus so popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays.

- Contemporary and Interesting Applications often use real, sourced data from a wide range of fields including: athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. Real-world examples are identified by a globe icon.
- Optional Graphing Calculator Explorations and Exercises explore new topics, carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed and exercises that require a graphing calculator are identified by icon.
- Spreadsheet Explorations are included in the first seven chapters of the text for those who prefer Excel or other spreadsheet technology. The spreadsheets referenced in the text can also be downloaded from the text's web site.
- Unique Section Summaries briefly state essential formulas and key concepts and help students prepare for tests and quizzes.
- Chapter Summary with Hints and Suggestions review key concepts of a chapter with references to specific review exercises. This feature is included at the end of each chapter. The Hints and Suggestions features unify the concepts of the chapter, give specific reminders, and reference problems in the review exercises suitable for a practice test.
- Extra Practice Problems are provided after selected worked-out examples, where students can use a little extra practice. Students are given the full solution to these problems at the end of the section.
- Exercise sets provide numerous assignment options for instructors, allowing them to customize homework to their course and student population. The exercise set begins with basic practice and increases in difficulty. Application exercises are clearly labeled with general and specific titles to make it easier for instructors to select relevant exercises for assignments.
- New! Conceptual Exercises and Explorations and Excursions have been added at reviewers' requests, to offer a more rounded view into the student's understanding of a topic. The Conceptual Exercises will encourage students to think 'outside the box,' expanding on and examining, their grasp of the mathematics behind the drill and application exercises. The underlying concepts of calculus become the focus.
- Projects and Essays are now included on the textbook website and CD-ROM to provide opportunities for collaborative work, as well as critical thinking and writing exercises.
- Cumulative Review Exercises at the end of selected chapters give students an easy way to review and reinforce previously learned concepts and skills.

**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 the Generalized Power Rule

2.7 Nondifferentiable Functions

**3. Further Applications of Derivatives**

3.1 Graphing Using the First Derivative

3.2 Graphing Using the and Second Derivatives

3.3 Oprtimization

3.4 Further Applications of Optimization

3.5 Optimizing Lot Size and Harvest Size

3.6 Implicit Differentiation and Related Rules

**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: Relative 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

**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

**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

Index

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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. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources.

The Fourth Edition maintains the hallmark features that have made Applied Calculus so popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays.

- Contemporary and Interesting Applications often use real, sourced data from a wide range of fields including: athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. Real-world examples are identified by a globe icon.
- Optional Graphing Calculator Explorations and Exercises explore new topics, carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed and exercises that require a graphing calculator are identified by icon.
- Spreadsheet Explorations are included in the first seven chapters of the text for those who prefer Excel or other spreadsheet technology. The spreadsheets referenced in the text can also be downloaded from the text's web site.
- Unique Section Summaries briefly state essential formulas and key concepts and help students prepare for tests and quizzes.
- Chapter Summary with Hints and Suggestions review key concepts of a chapter with references to specific review exercises. This feature is included at the end of each chapter. The Hints and Suggestions features unify the concepts of the chapter, give specific reminders, and reference problems in the review exercises suitable for a practice test.
- Extra Practice Problems are provided after selected worked-out examples, where students can use a little extra practice. Students are given the full solution to these problems at the end of the section.
- Exercise sets provide numerous assignment options for instructors, allowing them to customize homework to their course and student population. The exercise set begins with basic practice and increases in difficulty. Application exercises are clearly labeled with general and specific titles to make it easier for instructors to select relevant exercises for assignments.
- New! Conceptual Exercises and Explorations and Excursions have been added at reviewers' requests, to offer a more rounded view into the student's understanding of a topic. The Conceptual Exercises will encourage students to think 'outside the box,' expanding on and examining, their grasp of the mathematics behind the drill and application exercises. The underlying concepts of calculus become the focus.
- Projects and Essays are now included on the textbook website and CD-ROM to provide opportunities for collaborative work, as well as critical thinking and writing exercises.
- Cumulative Review Exercises at the end of selected chapters give students an easy way to review and reinforce previously learned concepts and skills.

Table of Contents

**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 the Generalized Power Rule

2.7 Nondifferentiable Functions

**3. Further Applications of Derivatives**

3.1 Graphing Using the First Derivative

3.2 Graphing Using the and Second Derivatives

3.3 Oprtimization

3.4 Further Applications of Optimization

3.5 Optimizing Lot Size and Harvest Size

3.6 Implicit Differentiation and Related Rules

**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: Relative 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

**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

**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

Index

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2007

International: No

Published: 2007

International: No

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. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources.

The Fourth Edition maintains the hallmark features that have made Applied Calculus so popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays.

- Contemporary and Interesting Applications often use real, sourced data from a wide range of fields including: athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. Real-world examples are identified by a globe icon.
- Optional Graphing Calculator Explorations and Exercises explore new topics, carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed and exercises that require a graphing calculator are identified by icon.
- Spreadsheet Explorations are included in the first seven chapters of the text for those who prefer Excel or other spreadsheet technology. The spreadsheets referenced in the text can also be downloaded from the text's web site.
- Unique Section Summaries briefly state essential formulas and key concepts and help students prepare for tests and quizzes.
- Chapter Summary with Hints and Suggestions review key concepts of a chapter with references to specific review exercises. This feature is included at the end of each chapter. The Hints and Suggestions features unify the concepts of the chapter, give specific reminders, and reference problems in the review exercises suitable for a practice test.
- Extra Practice Problems are provided after selected worked-out examples, where students can use a little extra practice. Students are given the full solution to these problems at the end of the section.
- Exercise sets provide numerous assignment options for instructors, allowing them to customize homework to their course and student population. The exercise set begins with basic practice and increases in difficulty. Application exercises are clearly labeled with general and specific titles to make it easier for instructors to select relevant exercises for assignments.
- New! Conceptual Exercises and Explorations and Excursions have been added at reviewers' requests, to offer a more rounded view into the student's understanding of a topic. The Conceptual Exercises will encourage students to think 'outside the box,' expanding on and examining, their grasp of the mathematics behind the drill and application exercises. The underlying concepts of calculus become the focus.
- Projects and Essays are now included on the textbook website and CD-ROM to provide opportunities for collaborative work, as well as critical thinking and writing exercises.
- Cumulative Review Exercises at the end of selected chapters give students an easy way to review and reinforce previously learned concepts and skills.

**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 the Generalized Power Rule

2.7 Nondifferentiable Functions

**3. Further Applications of Derivatives**

3.1 Graphing Using the First Derivative

3.2 Graphing Using the and Second Derivatives

3.3 Oprtimization

3.4 Further Applications of Optimization

3.5 Optimizing Lot Size and Harvest Size

3.6 Implicit Differentiation and Related Rules

**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: Relative 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

**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

**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

Index