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

Edition: 3RD 03Copyright: 2003

Publisher: Houghton Mifflin Harcourt

Published: 2003

International: No

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Designed for the three-semester engineering calculus sequence, Calculus: Early Transcendental Functions offers fully integrated coverage of exponential, logarithmic, and trigonometric functions throughout the first semester, within the hallmark balanced approach of the Larson team. A rich variety of applications encountered earlier in the course prepares students for concurrent physics, chemistry, and engineering courses. This edition features nearly 10,000 diverse and flexible exercises, carefully graded in sets progressing from skill-development problems to more rigorous application and proof problems.

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

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.

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.

Note: Each chapter concludes with Review Exercises and P.S. Problem Solving.

**P. Preparation for Calculus**

Eruptions of Old Faithful

P.1 Graphs and Models

P.2 Linear Models and Rates of Changes

P.3 Functions and Their Graphs

P.4 Fitting Models to Data

P.5 Inverse Functions

P.6 Exponential and Logarithmic Functions

**1. Limits and Their Properties**

Swimming Speed: Taking it to the Limit

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

Review Exercises

P.S. Problem Solving

**2. Differentiation**

Gravity: Finding it Experimentally

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 Derivatives of Inverse Functions

2.7 Related Rates

2.8 Newton's Method

**3. Applications of Differentiation**

Packaging: The Optimal Form

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 Differentials

**4. Integration**

The Wankel Rotary Engine and Area

4.1 Antiderivatives and Indefinite Integration

4.2 Area

4.3 Riemann 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

4.7 The Natural Logarithmic Functions: Integration

4.8 Inverse Trigonometric Functions: Integration

4.9 Hyperbolic Functions

Section Project:St. Louis Arch

**5. Differential Equations**

Plastics and Cooling

5.1 Differential Equations: Growth and Decay

5.2 Differential Equations: Separation of Variables

5.3 First-Order Linear Differential Equations

Section Project: Weight Loss

**6. Applications of Integration**

Constructing an Arch Dam

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, LHopital;s Rule, and Improper Integrals**

Making a Mercator Map

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 Indeterminate Forms and L

7.8 Improper Integrals

**8. Infinite Series**

The Koch Snowflake: Infinite Perimeter?

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**

Exploring New Planets

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

**10. Vectors and the Geometry of Space**

Suspension Bridges

10.1 Vectors in the Plane

10.2 Space Coordinates and Vectors in Space

10.3 The Dot Product of Two Vectors

10.4 The Cross Product of Two Vectors in Space

10.5 Lines and Planes in Space

Section Project: Distances in Space

10.6 Surfaces in Space

10.7 Cylindrical and Spherical Coordinates

**11. Vector-Valued Functions**

Race Car Cornering

11.1 Vector-Valued Functions

Section Project: Witch of Agnesi

11.2 Differentiation and Integration of Vector-Valued Functions

11.3 Velocity and Acceleration

11.4 Tangent Vectors and Normal Vectors

11.5 Arc Length and Curvature

**12. Functions of Several Variables**

Satellite Receiving Dish

12.1 Introduction to Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

Section Project: Moire Fringes

12.4 Differentials

12.5 Chain Rules for Functions of Several Variables

12.6 Directional Derivatives and Gradients

12.7 Tangent Planes and Normal Lines

Section Project: Wildflowers

12.8 Extrema of Functions of Two Variables

12.9 Applications of Extrema of Functions of Two Variables

Section Project: Building a Pipeline

12.10 Lagrange Multipliers

**13. Multiple Integration**

Hyperthermia Treatments for Tumors

13.1 Iterated Integrals and Area in the Plane

13.2 Double Integrals and Volume

13.3 Change of Variables: Polar Coordinates

13.4 Center of Mass and Moments of Inertia

Section Project: Center of Pressure on a Sail

13.5 Surface Area

Section Project: Capillary Action

13.6 Triple Integrals and Applications

13.7 Triple Integrals in Cylindrical and Spherical Coordinates

Section Project: Wrinkled and Bumpy Spheres

13.8 Change of Variables: Jacobians

**14. Vector Analysis**

Mathematical Sculpture

14.1 Vector Fields

14.2 Line Integrals

14.3 Conservative Vector Fields and Independence of Path

14.4 Green's Theorem

Section Project: Hyperbolic and Trigonometric Functions

14.5 Parametric Surfaces

14.6 Surface Integrals

Section Project: Hyperboloid of One Sheet

14.7 Divergence Theorem

14.8 Stoke's Theorem

Section Project: The Planimeter

**Appendices**

A. Business and Economic Applications

B. Proofs of Selected Theorems

C. Integration Tables

D. Precalculus Review

E. Rotation and the General Second-Degree Equation

F. Complex

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Summary

Designed for the three-semester engineering calculus sequence, Calculus: Early Transcendental Functions offers fully integrated coverage of exponential, logarithmic, and trigonometric functions throughout the first semester, within the hallmark balanced approach of the Larson team. A rich variety of applications encountered earlier in the course prepares students for concurrent physics, chemistry, and engineering courses. This edition features nearly 10,000 diverse and flexible exercises, carefully graded in sets progressing from skill-development problems to more rigorous application and proof problems.

Author Bio

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

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.

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.

Table of Contents

Note: Each chapter concludes with Review Exercises and P.S. Problem Solving.

**P. Preparation for Calculus**

Eruptions of Old Faithful

P.1 Graphs and Models

P.2 Linear Models and Rates of Changes

P.3 Functions and Their Graphs

P.4 Fitting Models to Data

P.5 Inverse Functions

P.6 Exponential and Logarithmic Functions

**1. Limits and Their Properties**

Swimming Speed: Taking it to the Limit

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

Review Exercises

P.S. Problem Solving

**2. Differentiation**

Gravity: Finding it Experimentally

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 Derivatives of Inverse Functions

2.7 Related Rates

2.8 Newton's Method

**3. Applications of Differentiation**

Packaging: The Optimal Form

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 Differentials

**4. Integration**

The Wankel Rotary Engine and Area

4.1 Antiderivatives and Indefinite Integration

4.2 Area

4.3 Riemann 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

4.7 The Natural Logarithmic Functions: Integration

4.8 Inverse Trigonometric Functions: Integration

4.9 Hyperbolic Functions

Section Project:St. Louis Arch

**5. Differential Equations**

Plastics and Cooling

5.1 Differential Equations: Growth and Decay

5.2 Differential Equations: Separation of Variables

5.3 First-Order Linear Differential Equations

Section Project: Weight Loss

**6. Applications of Integration**

Constructing an Arch Dam

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, LHopital;s Rule, and Improper Integrals**

Making a Mercator Map

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 Indeterminate Forms and L

7.8 Improper Integrals

**8. Infinite Series**

The Koch Snowflake: Infinite Perimeter?

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**

Exploring New Planets

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

**10. Vectors and the Geometry of Space**

Suspension Bridges

10.1 Vectors in the Plane

10.2 Space Coordinates and Vectors in Space

10.3 The Dot Product of Two Vectors

10.4 The Cross Product of Two Vectors in Space

10.5 Lines and Planes in Space

Section Project: Distances in Space

10.6 Surfaces in Space

10.7 Cylindrical and Spherical Coordinates

**11. Vector-Valued Functions**

Race Car Cornering

11.1 Vector-Valued Functions

Section Project: Witch of Agnesi

11.2 Differentiation and Integration of Vector-Valued Functions

11.3 Velocity and Acceleration

11.4 Tangent Vectors and Normal Vectors

11.5 Arc Length and Curvature

**12. Functions of Several Variables**

Satellite Receiving Dish

12.1 Introduction to Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

Section Project: Moire Fringes

12.4 Differentials

12.5 Chain Rules for Functions of Several Variables

12.6 Directional Derivatives and Gradients

12.7 Tangent Planes and Normal Lines

Section Project: Wildflowers

12.8 Extrema of Functions of Two Variables

12.9 Applications of Extrema of Functions of Two Variables

Section Project: Building a Pipeline

12.10 Lagrange Multipliers

**13. Multiple Integration**

Hyperthermia Treatments for Tumors

13.1 Iterated Integrals and Area in the Plane

13.2 Double Integrals and Volume

13.3 Change of Variables: Polar Coordinates

13.4 Center of Mass and Moments of Inertia

Section Project: Center of Pressure on a Sail

13.5 Surface Area

Section Project: Capillary Action

13.6 Triple Integrals and Applications

13.7 Triple Integrals in Cylindrical and Spherical Coordinates

Section Project: Wrinkled and Bumpy Spheres

13.8 Change of Variables: Jacobians

**14. Vector Analysis**

Mathematical Sculpture

14.1 Vector Fields

14.2 Line Integrals

14.3 Conservative Vector Fields and Independence of Path

14.4 Green's Theorem

Section Project: Hyperbolic and Trigonometric Functions

14.5 Parametric Surfaces

14.6 Surface Integrals

Section Project: Hyperboloid of One Sheet

14.7 Divergence Theorem

14.8 Stoke's Theorem

Section Project: The Planimeter

**Appendices**

A. Business and Economic Applications

B. Proofs of Selected Theorems

C. Integration Tables

D. Precalculus Review

E. Rotation and the General Second-Degree Equation

F. Complex

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2003

International: No

Published: 2003

International: No

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

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.

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.

Note: Each chapter concludes with Review Exercises and P.S. Problem Solving.

**P. Preparation for Calculus**

Eruptions of Old Faithful

P.1 Graphs and Models

P.2 Linear Models and Rates of Changes

P.3 Functions and Their Graphs

P.4 Fitting Models to Data

P.5 Inverse Functions

P.6 Exponential and Logarithmic Functions

**1. Limits and Their Properties**

Swimming Speed: Taking it to the Limit

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

Review Exercises

P.S. Problem Solving

**2. Differentiation**

Gravity: Finding it Experimentally

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 Derivatives of Inverse Functions

2.7 Related Rates

2.8 Newton's Method

**3. Applications of Differentiation**

Packaging: The Optimal Form

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 Differentials

**4. Integration**

The Wankel Rotary Engine and Area

4.1 Antiderivatives and Indefinite Integration

4.2 Area

4.3 Riemann 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

4.7 The Natural Logarithmic Functions: Integration

4.8 Inverse Trigonometric Functions: Integration

4.9 Hyperbolic Functions

Section Project:St. Louis Arch

**5. Differential Equations**

Plastics and Cooling

5.1 Differential Equations: Growth and Decay

5.2 Differential Equations: Separation of Variables

5.3 First-Order Linear Differential Equations

Section Project: Weight Loss

**6. Applications of Integration**

Constructing an Arch Dam

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, LHopital;s Rule, and Improper Integrals**

Making a Mercator Map

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 Indeterminate Forms and L

7.8 Improper Integrals

**8. Infinite Series**

The Koch Snowflake: Infinite Perimeter?

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**

Exploring New Planets

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

**10. Vectors and the Geometry of Space**

Suspension Bridges

10.1 Vectors in the Plane

10.2 Space Coordinates and Vectors in Space

10.3 The Dot Product of Two Vectors

10.4 The Cross Product of Two Vectors in Space

10.5 Lines and Planes in Space

Section Project: Distances in Space

10.6 Surfaces in Space

10.7 Cylindrical and Spherical Coordinates

**11. Vector-Valued Functions**

Race Car Cornering

11.1 Vector-Valued Functions

Section Project: Witch of Agnesi

11.2 Differentiation and Integration of Vector-Valued Functions

11.3 Velocity and Acceleration

11.4 Tangent Vectors and Normal Vectors

11.5 Arc Length and Curvature

**12. Functions of Several Variables**

Satellite Receiving Dish

12.1 Introduction to Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

Section Project: Moire Fringes

12.4 Differentials

12.5 Chain Rules for Functions of Several Variables

12.6 Directional Derivatives and Gradients

12.7 Tangent Planes and Normal Lines

Section Project: Wildflowers

12.8 Extrema of Functions of Two Variables

12.9 Applications of Extrema of Functions of Two Variables

Section Project: Building a Pipeline

12.10 Lagrange Multipliers

**13. Multiple Integration**

Hyperthermia Treatments for Tumors

13.1 Iterated Integrals and Area in the Plane

13.2 Double Integrals and Volume

13.3 Change of Variables: Polar Coordinates

13.4 Center of Mass and Moments of Inertia

Section Project: Center of Pressure on a Sail

13.5 Surface Area

Section Project: Capillary Action

13.6 Triple Integrals and Applications

13.7 Triple Integrals in Cylindrical and Spherical Coordinates

Section Project: Wrinkled and Bumpy Spheres

13.8 Change of Variables: Jacobians

**14. Vector Analysis**

Mathematical Sculpture

14.1 Vector Fields

14.2 Line Integrals

14.3 Conservative Vector Fields and Independence of Path

14.4 Green's Theorem

Section Project: Hyperbolic and Trigonometric Functions

14.5 Parametric Surfaces

14.6 Surface Integrals

Section Project: Hyperboloid of One Sheet

14.7 Divergence Theorem

14.8 Stoke's Theorem

Section Project: The Planimeter

**Appendices**

A. Business and Economic Applications

B. Proofs of Selected Theorems

C. Integration Tables

D. Precalculus Review

E. Rotation and the General Second-Degree Equation

F. Complex