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Edition: 2ND 97

Copyright: 1997

Publisher: Houghton Mifflin Harcourt

Published: 1997

International: No

Copyright: 1997

Publisher: Houghton Mifflin Harcourt

Published: 1997

International: No

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Building on the proven success of its previous edition, *Calculus and Its Applications,* Second Edition helps students across the curriculum discover the excitement and relevance of applied calculus. Retaining his integrated problem-solving approach, the author engages students in the learning process by carefully discussing key questions, determining equations, and demonstrating the relation between the final solution and the original problem.

- Throughout the text, technology exercises reinforce concepts and understanding while adding an exciting visual dimension to the study of calculus.
- In keeping with AMATYC and MAA standards, a wealth of writing exercises encourage students to reason and understand the concepts they are studying.
- Equations and functions fit mathematical models to real data to show students how calculus applies to real-life situations.

Note: Each chapter contains Key Terms and Ideas, Review Exercises, and Projects and Essays. *Brief Calculus and Its Applications* contains Chapters 1-9.

**1. Functions**

1.1. Real Numbers

1.2. Some Algebra Review

1.3. Introduction to Functions

1.4. Linear Functions

1.5. Graphs of Functions

1.6. Translations and Reflections (optional)

1.7. Functions in Economics.

**2. An Introduction to Limits**

2.1. Introduction to Limits

2.2. Continuity

2.3. One-Sided Limits

2.4. Limits at Infinity

2.5. Infinite Limits.

**3. Derivatives**

3.1 Introduction to the Derivative

3.2. Basic Rules for Differentiation

3.3. Rates of Change

3.4. Marginal Analysis

3.5. The Product and Quotient Rules

3.6. The Chain Rule

3.7. Higher-Order Derivatives

3.8. Implicit Differentiation

3.9. Related Rates

3.10. Differentials.

**4. Additional Applications of the Derivative**

4.1. Increasing and Decreasing, Graphs, and Critical Numbers

4.2. Relative Extrema and Curve Stretching

4.3. Concavity, the Second Derivative Test, and Curve Sketching

4.4. Absolute Extrema

4.5 Additional Applications, Applied Maximum/Minimum

4.6 Elasticity of Demand .

**5. Exponential and Logarithmic Functions**

5.1 Exponential Functions

5.2 Logarithmic Functions

5.3 Differentiation of Exponential Functions

5.4 Differentiation of Logarithmic Functions

5.5 Some Additional Business Applications.

**6. Integration**

6.1. Antidifferentiation

6.2. Some Applications of Antidifferentiation

6.3 The Definite Integral as the Area Under a Curve

6.4 The Fundamental Theorem of Calculus

6.5 Some Applications of the Definite Integral

6.6. Surplus

6.7. Area in the Plane.

**7. Techniques of Integration**

7.1. Integration by Substitution

7.2. Integration by Parts

7.3. Integration by Tables

7.4. Numerical Methods of Approximation

7.5. Improper Integrals.

**8. Probability and Calculus**

8.1. Probability and Calculus

8.2. Random Variables, Expected Value, and Variance

8.3. Uniform and Exponential Random Variables

8.4. The Normal Distribution.

**9. Differential Equations**

9.1. Introduction to Differential Equations

9.2. Separation of Variables

9.3. Additional Applications

9.4 A Numerical Method.

**10. Multivariable Calculus**

10.1. Functions of Several Variables

10.2. Partial Derivatives

10.3. Maximum and Minimum

10.4. Lagrange Multipliers

10.5. The Method of Least Squares

10.6. Total Differentials

10.7. Double Integrals.

**11. Trigonometric Functions**

11.1. Right Angles

11.2. Radians and the Trigonometry for Calculus

11.3. Differentiation of Trigonometric Functions

11.4. Integration of Trigonometric Functions

11.5. Integration by Parts Revisited.

**12. Infinite Series and Other Advanced Topics**

12.1. Some Introductory Concepts

12.2. Geometric Series

12.3. Geometric Power Series

12.4. Taylor Series

12.5. Integration of Series

12.6. Newton's Method

12.7. Indeterminate Forms: L'H"pital's Rule.

- Tables; Answers to Odd-Numbered Exercises; Index.

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Summary

Building on the proven success of its previous edition, *Calculus and Its Applications,* Second Edition helps students across the curriculum discover the excitement and relevance of applied calculus. Retaining his integrated problem-solving approach, the author engages students in the learning process by carefully discussing key questions, determining equations, and demonstrating the relation between the final solution and the original problem.

- Throughout the text, technology exercises reinforce concepts and understanding while adding an exciting visual dimension to the study of calculus.
- In keeping with AMATYC and MAA standards, a wealth of writing exercises encourage students to reason and understand the concepts they are studying.
- Equations and functions fit mathematical models to real data to show students how calculus applies to real-life situations.

Table of Contents

Note: Each chapter contains Key Terms and Ideas, Review Exercises, and Projects and Essays. *Brief Calculus and Its Applications* contains Chapters 1-9.

**1. Functions**

1.1. Real Numbers

1.2. Some Algebra Review

1.3. Introduction to Functions

1.4. Linear Functions

1.5. Graphs of Functions

1.6. Translations and Reflections (optional)

1.7. Functions in Economics.

**2. An Introduction to Limits**

2.1. Introduction to Limits

2.2. Continuity

2.3. One-Sided Limits

2.4. Limits at Infinity

2.5. Infinite Limits.

**3. Derivatives**

3.1 Introduction to the Derivative

3.2. Basic Rules for Differentiation

3.3. Rates of Change

3.4. Marginal Analysis

3.5. The Product and Quotient Rules

3.6. The Chain Rule

3.7. Higher-Order Derivatives

3.8. Implicit Differentiation

3.9. Related Rates

3.10. Differentials.

**4. Additional Applications of the Derivative**

4.1. Increasing and Decreasing, Graphs, and Critical Numbers

4.2. Relative Extrema and Curve Stretching

4.3. Concavity, the Second Derivative Test, and Curve Sketching

4.4. Absolute Extrema

4.5 Additional Applications, Applied Maximum/Minimum

4.6 Elasticity of Demand .

**5. Exponential and Logarithmic Functions**

5.1 Exponential Functions

5.2 Logarithmic Functions

5.3 Differentiation of Exponential Functions

5.4 Differentiation of Logarithmic Functions

5.5 Some Additional Business Applications.

**6. Integration**

6.1. Antidifferentiation

6.2. Some Applications of Antidifferentiation

6.3 The Definite Integral as the Area Under a Curve

6.4 The Fundamental Theorem of Calculus

6.5 Some Applications of the Definite Integral

6.6. Surplus

6.7. Area in the Plane.

**7. Techniques of Integration**

7.1. Integration by Substitution

7.2. Integration by Parts

7.3. Integration by Tables

7.4. Numerical Methods of Approximation

7.5. Improper Integrals.

**8. Probability and Calculus**

8.1. Probability and Calculus

8.2. Random Variables, Expected Value, and Variance

8.3. Uniform and Exponential Random Variables

8.4. The Normal Distribution.

**9. Differential Equations**

9.1. Introduction to Differential Equations

9.2. Separation of Variables

9.3. Additional Applications

9.4 A Numerical Method.

**10. Multivariable Calculus**

10.1. Functions of Several Variables

10.2. Partial Derivatives

10.3. Maximum and Minimum

10.4. Lagrange Multipliers

10.5. The Method of Least Squares

10.6. Total Differentials

10.7. Double Integrals.

**11. Trigonometric Functions**

11.1. Right Angles

11.2. Radians and the Trigonometry for Calculus

11.3. Differentiation of Trigonometric Functions

11.4. Integration of Trigonometric Functions

11.5. Integration by Parts Revisited.

**12. Infinite Series and Other Advanced Topics**

12.1. Some Introductory Concepts

12.2. Geometric Series

12.3. Geometric Power Series

12.4. Taylor Series

12.5. Integration of Series

12.6. Newton's Method

12.7. Indeterminate Forms: L'H"pital's Rule.

- Tables; Answers to Odd-Numbered Exercises; Index.

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 1997

International: No

Published: 1997

International: No

Building on the proven success of its previous edition, *Calculus and Its Applications,* Second Edition helps students across the curriculum discover the excitement and relevance of applied calculus. Retaining his integrated problem-solving approach, the author engages students in the learning process by carefully discussing key questions, determining equations, and demonstrating the relation between the final solution and the original problem.

- Throughout the text, technology exercises reinforce concepts and understanding while adding an exciting visual dimension to the study of calculus.
- In keeping with AMATYC and MAA standards, a wealth of writing exercises encourage students to reason and understand the concepts they are studying.
- Equations and functions fit mathematical models to real data to show students how calculus applies to real-life situations.

Note: Each chapter contains Key Terms and Ideas, Review Exercises, and Projects and Essays. *Brief Calculus and Its Applications* contains Chapters 1-9.

**1. Functions**

1.1. Real Numbers

1.2. Some Algebra Review

1.3. Introduction to Functions

1.4. Linear Functions

1.5. Graphs of Functions

1.6. Translations and Reflections (optional)

1.7. Functions in Economics.

**2. An Introduction to Limits**

2.1. Introduction to Limits

2.2. Continuity

2.3. One-Sided Limits

2.4. Limits at Infinity

2.5. Infinite Limits.

**3. Derivatives**

3.1 Introduction to the Derivative

3.2. Basic Rules for Differentiation

3.3. Rates of Change

3.4. Marginal Analysis

3.5. The Product and Quotient Rules

3.6. The Chain Rule

3.7. Higher-Order Derivatives

3.8. Implicit Differentiation

3.9. Related Rates

3.10. Differentials.

**4. Additional Applications of the Derivative**

4.1. Increasing and Decreasing, Graphs, and Critical Numbers

4.2. Relative Extrema and Curve Stretching

4.3. Concavity, the Second Derivative Test, and Curve Sketching

4.4. Absolute Extrema

4.5 Additional Applications, Applied Maximum/Minimum

4.6 Elasticity of Demand .

**5. Exponential and Logarithmic Functions**

5.1 Exponential Functions

5.2 Logarithmic Functions

5.3 Differentiation of Exponential Functions

5.4 Differentiation of Logarithmic Functions

5.5 Some Additional Business Applications.

**6. Integration**

6.1. Antidifferentiation

6.2. Some Applications of Antidifferentiation

6.3 The Definite Integral as the Area Under a Curve

6.4 The Fundamental Theorem of Calculus

6.5 Some Applications of the Definite Integral

6.6. Surplus

6.7. Area in the Plane.

**7. Techniques of Integration**

7.1. Integration by Substitution

7.2. Integration by Parts

7.3. Integration by Tables

7.4. Numerical Methods of Approximation

7.5. Improper Integrals.

**8. Probability and Calculus**

8.1. Probability and Calculus

8.2. Random Variables, Expected Value, and Variance

8.3. Uniform and Exponential Random Variables

8.4. The Normal Distribution.

**9. Differential Equations**

9.1. Introduction to Differential Equations

9.2. Separation of Variables

9.3. Additional Applications

9.4 A Numerical Method.

**10. Multivariable Calculus**

10.1. Functions of Several Variables

10.2. Partial Derivatives

10.3. Maximum and Minimum

10.4. Lagrange Multipliers

10.5. The Method of Least Squares

10.6. Total Differentials

10.7. Double Integrals.

**11. Trigonometric Functions**

11.1. Right Angles

11.2. Radians and the Trigonometry for Calculus

11.3. Differentiation of Trigonometric Functions

11.4. Integration of Trigonometric Functions

11.5. Integration by Parts Revisited.

**12. Infinite Series and Other Advanced Topics**

12.1. Some Introductory Concepts

12.2. Geometric Series

12.3. Geometric Power Series

12.4. Taylor Series

12.5. Integration of Series

12.6. Newton's Method

12.7. Indeterminate Forms: L'H"pital's Rule.

- Tables; Answers to Odd-Numbered Exercises; Index.