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by Ron Larson, Robert P. Hostetler and Bruce H. Edwards

Edition: 7TH 02Copyright: 2002

Publisher: Houghton Mifflin Harcourt

Published: 2002

International: No

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Ideal for the single-variable, one-, or two-semester calculus course, Calculus of a Single Variable, 7/e, contains the first 9 chapers of Calculus with Analytic Geometry, 7/e.

**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.

**Hostetler, Robert P. : The Pennsylvania State University**

Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.

**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.

**P. Preparation for Calculus**

P.1 Graphs and Models

P.2 Linear Models and Rates of Change

P.3 Functions and Their Graphs

P.4 Fitting Models to Data

**1. Limits and Their Properties**

1.1 A Preview of Calculus

1.2 Finding Limits Graphically and Numerically

1.3 Evaluating Limits Analytically

1.4 Continuity and One-Sided Limits

1.5 Infinite Limits

Section Project: Graphs and Limits of Trigonometric Functions

**2. Differentiation**

2.1 The Derivative and the Tangent Line Problem

2.2 Basic Differentiation Rules and Rates of Change

2.3 The Product and Quotient Rules and Higher-Order Derivatives

2.4 The Chain Rule

2.5 Implicit Differentiation

Section Project: Optical Illusions

2.6 Related Rates

**3. Applications of Differentiation**

3.1 Extrema on an Interval

3.2 Rolle's Theorem and the Mean Value Theorem

3.3 Increasing and Decreasing Functions and the First Derivative Test

Section Project: Rainbows

3.4 Concavity and the Second Derivative Test

3.5 Limits at Infinity

3.6 A Summary of Curve Sketching

3.7 Optimization Problems

Section Project: Connecticut River

3.8 Newton's Method

3.9 Differentials

**4. Integration**

4.1 Antiderivatives and Indefinite Integration

4.2 Area

4.3 Reimann Sums and Definite Integrals

4.4 The Fundamental Theorem of Calculus

Section Project: Demonstrating the Fundamental Theorem

4.5 Integration by Substitution

4.6 Numerical Integration

**5. Logarithmic, Exponential, and Other Transcendental Functions**

5.1 The Natural Logarithmic Function: Differentiation

5.2 The Natural Logarithmic Function: Integration

5.3 Inverse Functions

5.4 Exponential Functions: Differentiation and Integration

5.5 Bases Other Than e and Applications

Section Project: Using Graphing Utilities to Estimate Slope

5.6 Differential Equations: Growth and Decay

5.7 Differential Equations: Separation of Variables

5.8 Inverse Trigonometric Functions: Differentiation

5.9 Inverse Trigonometric Functions: Integration

5.10 Hyperbolic Functions

Section Project: St. Louis Arch

**6. Applications of Integration**

6.1 Area of a Region Between Two Curves

6.2 Volume: The Disk Method

6.3 Volume: The Shell Method

Section Project: Saturn

6.4 Arc Length and Surfaces of Revolution

6.5 Work

Section Project: Tidal Energy

6.6 Moments, Centers of Mass, and Centroids

6.7 Fluid Pressure and Fluid Force

**7. Integration Techniques, L'Hôpital's Rule, and Improper Integrals**

7.1 Basic Integration Rules

7.2 Integration by Parts

7.3 Trigonometric Integrals

Section Project: Power Lines

7.4 Trigonometric Substitution

7.5 Partial Fractions

7.6 Integration by Tables and Other Integration Techniques

7.7 Indeterminant Forms and L'Hôpital's Rule

7.8 Improper Integrals

**8. Infinite Series**

8.1 Sequences

8.2 Series and Convergence

Section Project: Cantor's Disappearing Table

8.3 The Integral Test and p-Series

Section Project: The Harmonic Series

8.4 Comparisons of Series

Section Project: Solera Method

8.5 Alternating Series

8.6 The Ratio and Root Tests

8.7 Taylor Polynomials and Approximations

8.8 Power Series

8.9 Representation of Functions by Power Series

8.10 Taylor and Maclaurin Series

**9. Conics, Parametric Equations, and Polar Coordinates**

9.1 Conics and Calculus

9.2 Plane Curves and Parametric Equations

Section Project: Cycloids

9.3 Parametric Equations and Calculus

9.4 Polar Coordinates and Polar Graphs

Section Project: Anamorphic Art

9.5 Area and Arc Length in Polar Coordinates

9.6 Polar Equations of Conics and Kepler's Laws

**Appendices**

A. Additional Topics in Differential Equations

B. Proofs of Selected Theorems

C. Integration Tables

D. Precalculus Review

E. Rotation and the General Second-Degree Equation

F. Complex Numbers

G. Business and Economic Applications

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Summary

Ideal for the single-variable, one-, or two-semester calculus course, Calculus of a Single Variable, 7/e, contains the first 9 chapers of Calculus with Analytic Geometry, 7/e.

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.

**Hostetler, Robert P. : The Pennsylvania State University**

Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.

**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

**P. Preparation for Calculus**

P.1 Graphs and Models

P.2 Linear Models and Rates of Change

P.3 Functions and Their Graphs

P.4 Fitting Models to Data

**1. Limits and Their Properties**

1.1 A Preview of Calculus

1.2 Finding Limits Graphically and Numerically

1.3 Evaluating Limits Analytically

1.4 Continuity and One-Sided Limits

1.5 Infinite Limits

Section Project: Graphs and Limits of Trigonometric Functions

**2. Differentiation**

2.1 The Derivative and the Tangent Line Problem

2.2 Basic Differentiation Rules and Rates of Change

2.3 The Product and Quotient Rules and Higher-Order Derivatives

2.4 The Chain Rule

2.5 Implicit Differentiation

Section Project: Optical Illusions

2.6 Related Rates

**3. Applications of Differentiation**

3.1 Extrema on an Interval

3.2 Rolle's Theorem and the Mean Value Theorem

3.3 Increasing and Decreasing Functions and the First Derivative Test

Section Project: Rainbows

3.4 Concavity and the Second Derivative Test

3.5 Limits at Infinity

3.6 A Summary of Curve Sketching

3.7 Optimization Problems

Section Project: Connecticut River

3.8 Newton's Method

3.9 Differentials

**4. Integration**

4.1 Antiderivatives and Indefinite Integration

4.2 Area

4.3 Reimann Sums and Definite Integrals

4.4 The Fundamental Theorem of Calculus

Section Project: Demonstrating the Fundamental Theorem

4.5 Integration by Substitution

4.6 Numerical Integration

**5. Logarithmic, Exponential, and Other Transcendental Functions**

5.1 The Natural Logarithmic Function: Differentiation

5.2 The Natural Logarithmic Function: Integration

5.3 Inverse Functions

5.4 Exponential Functions: Differentiation and Integration

5.5 Bases Other Than e and Applications

Section Project: Using Graphing Utilities to Estimate Slope

5.6 Differential Equations: Growth and Decay

5.7 Differential Equations: Separation of Variables

5.8 Inverse Trigonometric Functions: Differentiation

5.9 Inverse Trigonometric Functions: Integration

5.10 Hyperbolic Functions

Section Project: St. Louis Arch

**6. Applications of Integration**

6.1 Area of a Region Between Two Curves

6.2 Volume: The Disk Method

6.3 Volume: The Shell Method

Section Project: Saturn

6.4 Arc Length and Surfaces of Revolution

6.5 Work

Section Project: Tidal Energy

6.6 Moments, Centers of Mass, and Centroids

6.7 Fluid Pressure and Fluid Force

**7. Integration Techniques, L'Hôpital's Rule, and Improper Integrals**

7.1 Basic Integration Rules

7.2 Integration by Parts

7.3 Trigonometric Integrals

Section Project: Power Lines

7.4 Trigonometric Substitution

7.5 Partial Fractions

7.6 Integration by Tables and Other Integration Techniques

7.7 Indeterminant Forms and L'Hôpital's Rule

7.8 Improper Integrals

**8. Infinite Series**

8.1 Sequences

8.2 Series and Convergence

Section Project: Cantor's Disappearing Table

8.3 The Integral Test and p-Series

Section Project: The Harmonic Series

8.4 Comparisons of Series

Section Project: Solera Method

8.5 Alternating Series

8.6 The Ratio and Root Tests

8.7 Taylor Polynomials and Approximations

8.8 Power Series

8.9 Representation of Functions by Power Series

8.10 Taylor and Maclaurin Series

**9. Conics, Parametric Equations, and Polar Coordinates**

9.1 Conics and Calculus

9.2 Plane Curves and Parametric Equations

Section Project: Cycloids

9.3 Parametric Equations and Calculus

9.4 Polar Coordinates and Polar Graphs

Section Project: Anamorphic Art

9.5 Area and Arc Length in Polar Coordinates

9.6 Polar Equations of Conics and Kepler's Laws

**Appendices**

A. Additional Topics in Differential Equations

B. Proofs of Selected Theorems

C. Integration Tables

D. Precalculus Review

E. Rotation and the General Second-Degree Equation

F. Complex Numbers

G. Business and Economic Applications

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2002

International: No

Published: 2002

International: No

**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.

**Hostetler, Robert P. : The Pennsylvania State University**

Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.

**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.

**P. Preparation for Calculus**

P.1 Graphs and Models

P.2 Linear Models and Rates of Change

P.3 Functions and Their Graphs

P.4 Fitting Models to Data

**1. Limits and Their Properties**

1.1 A Preview of Calculus

1.2 Finding Limits Graphically and Numerically

1.3 Evaluating Limits Analytically

1.4 Continuity and One-Sided Limits

1.5 Infinite Limits

Section Project: Graphs and Limits of Trigonometric Functions

**2. Differentiation**

2.1 The Derivative and the Tangent Line Problem

2.2 Basic Differentiation Rules and Rates of Change

2.3 The Product and Quotient Rules and Higher-Order Derivatives

2.4 The Chain Rule

2.5 Implicit Differentiation

Section Project: Optical Illusions

2.6 Related Rates

**3. Applications of Differentiation**

3.1 Extrema on an Interval

3.2 Rolle's Theorem and the Mean Value Theorem

3.3 Increasing and Decreasing Functions and the First Derivative Test

Section Project: Rainbows

3.4 Concavity and the Second Derivative Test

3.5 Limits at Infinity

3.6 A Summary of Curve Sketching

3.7 Optimization Problems

Section Project: Connecticut River

3.8 Newton's Method

3.9 Differentials

**4. Integration**

4.1 Antiderivatives and Indefinite Integration

4.2 Area

4.3 Reimann Sums and Definite Integrals

4.4 The Fundamental Theorem of Calculus

Section Project: Demonstrating the Fundamental Theorem

4.5 Integration by Substitution

4.6 Numerical Integration

**5. Logarithmic, Exponential, and Other Transcendental Functions**

5.1 The Natural Logarithmic Function: Differentiation

5.2 The Natural Logarithmic Function: Integration

5.3 Inverse Functions

5.4 Exponential Functions: Differentiation and Integration

5.5 Bases Other Than e and Applications

Section Project: Using Graphing Utilities to Estimate Slope

5.6 Differential Equations: Growth and Decay

5.7 Differential Equations: Separation of Variables

5.8 Inverse Trigonometric Functions: Differentiation

5.9 Inverse Trigonometric Functions: Integration

5.10 Hyperbolic Functions

Section Project: St. Louis Arch

**6. Applications of Integration**

6.1 Area of a Region Between Two Curves

6.2 Volume: The Disk Method

6.3 Volume: The Shell Method

Section Project: Saturn

6.4 Arc Length and Surfaces of Revolution

6.5 Work

Section Project: Tidal Energy

6.6 Moments, Centers of Mass, and Centroids

6.7 Fluid Pressure and Fluid Force

**7. Integration Techniques, L'Hôpital's Rule, and Improper Integrals**

7.1 Basic Integration Rules

7.2 Integration by Parts

7.3 Trigonometric Integrals

Section Project: Power Lines

7.4 Trigonometric Substitution

7.5 Partial Fractions

7.6 Integration by Tables and Other Integration Techniques

7.7 Indeterminant Forms and L'Hôpital's Rule

7.8 Improper Integrals

**8. Infinite Series**

8.1 Sequences

8.2 Series and Convergence

Section Project: Cantor's Disappearing Table

8.3 The Integral Test and p-Series

Section Project: The Harmonic Series

8.4 Comparisons of Series

Section Project: Solera Method

8.5 Alternating Series

8.6 The Ratio and Root Tests

8.7 Taylor Polynomials and Approximations

8.8 Power Series

8.9 Representation of Functions by Power Series

8.10 Taylor and Maclaurin Series

**9. Conics, Parametric Equations, and Polar Coordinates**

9.1 Conics and Calculus

9.2 Plane Curves and Parametric Equations

Section Project: Cycloids

9.3 Parametric Equations and Calculus

9.4 Polar Coordinates and Polar Graphs

Section Project: Anamorphic Art

9.5 Area and Arc Length in Polar Coordinates

9.6 Polar Equations of Conics and Kepler's Laws

**Appendices**

A. Additional Topics in Differential Equations

B. Proofs of Selected Theorems

C. Integration Tables

D. Precalculus Review

E. Rotation and the General Second-Degree Equation

F. Complex Numbers

G. Business and Economic Applications