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Calculus for K-12 Textbooks

by Ron Larson and Bruce H. Edwards

ISBN13: 978-0618218691

ISBN10: 0618218696

Edition: 6TH 03

Copyright: 2003

Publisher: Houghton Mifflin Harcourt

Published: 2003

International: No

ISBN10: 0618218696

Edition: 6TH 03

Copyright: 2003

Publisher: Houghton Mifflin Harcourt

Published: 2003

International: No

Designed specifically for the non-math major who will be using calculus in business, economics, or life and social science courses, Calculus: An Applied Approach, 6/e, offers students added structure and guidance on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter.

Author Bio

**Larson, Ron : The Pennsylvania State University**

Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about the use of computer technology as a teaching tool and motivational aid. His Interactive Calculus(a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level. It is currently the first mainstream college textbook to be offered on the Internet.

**Edwards, Bruce H. : University of Florida**

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Bruce was a mathematics major at Stanford University and graduated in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to Dartmouth in 1972 and completed his Ph.D. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. Bruce's hobbies include jogging, reading, chess, simulation baseball games, and travel.

**0. A Precalculus Review**

0.1 The Real Line and Order

0.2 Absolute Value and Distance on the Real Line

0.3 Exponents and Radicals

0.4 Factoring Polynomials

0.5 Fractions and Rationalization

**1. Functions, Graphs, and Limits**

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

1.5 Limits

1.6 Continuity

**2. Differentiation**

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Higher-Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

**3. Applications of the Derivative**

3.1 Increasing and Decreasing Functions

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second-Derivative Test

3.4 Optimization Problems

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

5.6 The Definite Integral as the Limit of a Sum

5.7 Volumes of Solids of Revolution

**6. Techniques of Integration**

6.1 Integration by Substitution

6.2 Integration by Parts and Present Value

6.3 Partial Fractions and Logistic Growth

6.4 Integration Tables and Completing the Square

6.5 Numerical Integration

6.6 Improper Integrals

**7. Functions of Several Variables**

7.1 The Three-Dimensional Coordinate System

7.2 Surfaces in Space

7.3 Functions of Several Variables

7.4 Partial Derivatives

7.5 Extrema of Functions of Two Variables

7.6 Lagrange Multipliers

7.7 Least Squares Regression Analysis

7.8 Double Integrals and Area in the Plane

7.9 Applications of Double Integrals

**8. Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Trigonometric Functions

8.3 Graphs of Trigonometric Functions

8.4 Derivatives of Trigonometric Functions

8.5 Integrals of Trigonometric Functions

8.6 L'nHôpital's Rule

**9. Probability and Calculus**

9.1 Discrete Probability

9.2 Continuous Random Variables

9.3 Expected Value and Variance

**10. Series and Taylor Polynomials**

10.1 Sequences

10.2 Series and Convergence

10.3 *p*-Series and the Ratio Test

10.4 Power Series and Taylor's Theorem

10.5 Taylor Polynomials

10.6 Newton's Method

**Appendices**

A. Alternate Introduction to the Fundamental Theorem of Calculus

B. Formulas

C. Differential Equations:

C.1 Solutions of Differential Equations.

C.2 Separation of Variables.

C.3 First-Order Linear Differential Equations.

C.4 Applications of Differential Equations

Answers to Odd-Numbered Exercises

Index

Ron Larson and Bruce H. Edwards

ISBN13: 978-0618218691ISBN10: 0618218696

Edition: 6TH 03

Copyright: 2003

Publisher: Houghton Mifflin Harcourt

Published: 2003

International: No

Designed specifically for the non-math major who will be using calculus in business, economics, or life and social science courses, Calculus: An Applied Approach, 6/e, offers students added structure and guidance on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter.

Author Bio

**Larson, Ron : The Pennsylvania State University**

Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about the use of computer technology as a teaching tool and motivational aid. His Interactive Calculus(a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level. It is currently the first mainstream college textbook to be offered on the Internet.

**Edwards, Bruce H. : University of Florida**

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Bruce was a mathematics major at Stanford University and graduated in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to Dartmouth in 1972 and completed his Ph.D. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. Bruce's hobbies include jogging, reading, chess, simulation baseball games, and travel.

Table of Contents

**0. A Precalculus Review**

0.1 The Real Line and Order

0.2 Absolute Value and Distance on the Real Line

0.3 Exponents and Radicals

0.4 Factoring Polynomials

0.5 Fractions and Rationalization

**1. Functions, Graphs, and Limits**

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

1.5 Limits

1.6 Continuity

**2. Differentiation**

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Higher-Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

**3. Applications of the Derivative**

3.1 Increasing and Decreasing Functions

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second-Derivative Test

3.4 Optimization Problems

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

**5. Integration and Its Applications**

5.1 Antiderivatives and Indefinite Integrals

5.2 The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

5.6 The Definite Integral as the Limit of a Sum

5.7 Volumes of Solids of Revolution

**6. Techniques of Integration**

6.1 Integration by Substitution

6.2 Integration by Parts and Present Value

6.3 Partial Fractions and Logistic Growth

6.4 Integration Tables and Completing the Square

6.5 Numerical Integration

6.6 Improper Integrals

**7. Functions of Several Variables**

7.1 The Three-Dimensional Coordinate System

7.2 Surfaces in Space

7.3 Functions of Several Variables

7.4 Partial Derivatives

7.5 Extrema of Functions of Two Variables

7.6 Lagrange Multipliers

7.7 Least Squares Regression Analysis

7.8 Double Integrals and Area in the Plane

7.9 Applications of Double Integrals

**8. Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Trigonometric Functions

8.3 Graphs of Trigonometric Functions

8.4 Derivatives of Trigonometric Functions

8.5 Integrals of Trigonometric Functions

8.6 L'nHôpital's Rule

**9. Probability and Calculus**

9.1 Discrete Probability

9.2 Continuous Random Variables

9.3 Expected Value and Variance

**10. Series and Taylor Polynomials**

10.1 Sequences

10.2 Series and Convergence

10.3 *p*-Series and the Ratio Test

10.4 Power Series and Taylor's Theorem

10.5 Taylor Polynomials

10.6 Newton's Method

**Appendices**

A. Alternate Introduction to the Fundamental Theorem of Calculus

B. Formulas

C. Differential Equations:

C.1 Solutions of Differential Equations.

C.2 Separation of Variables.

C.3 First-Order Linear Differential Equations.

C.4 Applications of Differential Equations

Answers to Odd-Numbered Exercises

Index

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