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Publisher:

McGraw-Hill

Publication Date:

2006

Number of Pages:

1104

Format:

Hardcover

Price:

132.81

ISBN:

0-07-282623-1

Category:

Textbook

[Reviewed by , on ]

William Satzer

06/11/2005

*Calculus: Concepts and Connections* is a readable introduction to the basic topics of single and multivariable calculus from the basic idea of limits up through Stokes' Theorem. It is a textbook clearly aimed at the "average" student. The main difference between this and other comparable textbooks such as Stewart's *Calculus* is that explanations of concepts and examples are more extensive and more explicit attempts are made to establish the connections between concepts. The standard topics are treated in more or less the usual order.

The authors have obviously taken pains to develop good exercise sets. Typically, each chapter has writing exercises, a collection of fairly routine problems, exercises designed to use a graphing calculator or computer algebra system, and exploratory problems. The latter are intended to be more challenging and to provoke a deeper level of understanding. A nice feature in the text is the use of an icon to identify pitfalls arising from injudicious use of calculators or computer algebra systems.

There are well over two hundred explicit examples of applications in the text or in exercises; these fall into the general categories of biology, chemistry, economics, physiology, engineering, physics and sports. While these are not especially deep applications, they generally have enough meat on them to be interesting.

Intuitive explanations and arguments of plausibility are usually favored over proofs, though there are a variety of proofs of varying levels of generality and rigor. In addition, there is an appendix with more rigorous proofs of some results.

This would be an appealing self-study text as well as a good choice for a class of average ability. It would probably seem too slow moving for strong students.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

2 pp. -- Endpaper

Add 3 pp. -- Index of Applications

Add 5 pp. -- Preface

Add 6 pp. -- Guided Tour

Add 1 pg. -- To the Student

0. Preliminaries

Add 2 pp. -- Introduction

Add 14 pp. -- 0.1 Polynomials and Rational Functions

Add 3 pp. -- Exercises 0.1

Add 8 pp. -- 0.2 Graphing Calculators and Computer Algebra Systems

Add 2 pp. -- Exercises 0.2

Add 5 pp. -- 0.3 Inverse Functions

Add 2 pp. -- Exercises 0.3

Add 10 pp. -- 0.4 Trigonometric and Inverse Trigonometric Functions

Add 4 pp. -- Exercises 0.4

Add 11 pp. -- 0.5 Exponential and Logarithmic Functions

Add 3 pp. -- Exercises 0.5

Add 7 pp. -- 0.6 Transformations of Functions

Add 2 pp. -- Exercises 0.6

Add 13 pp. -- 0.7 Parametric Equations and Polar Coordinates

Add 4 pp. -- Exercises 0.7

Add 5 pp. -- Review Exercises

1. Limits and Continuity

Add 2 pp. -- Introduction

Add 5 pp. -- 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve

Add 2 pp. -- Exercises 1.1

Add 7 pp. -- 1.2 The Concept of Limit

Add 3 pp. -- Exercise 1.2

Add 10 pp. -- 1.3 Computation of Limits

Add 3 pp. -- Exercises 1.3

Add 9 pp. -- 1.4 Continuity and Its Consequences

Add 5 pp. -- Exercises 1.4

Add 9 pp. -- 1.5 Limits Involving Infinity

Add 4 pp. -- Exercises 1.5

Add 7 pp. -- 1.6 Limits and Loss-Of-Significance Errors

Add 2 pp. -- Exercises 1.6

Add 4 pp. -- Review Exercises

2. Differentiation

Add 2 pp. -- Introduction

Add 9 pp. -- 2.1 Tangent Lines and Velocity

Add 4 pp. -- Exercises 2.1

Add 8 pp. -- 2.2 The Derivative

Add 5 pp. -- Exercises 2.2

Add 7 pp. -- 2.3 Computation of Derivatives: The Power Rule

Add 4 pp. -- Exercises 2.3

Add 6 pp. -- 2.4 The Product and Quotient Rules

Add 4 pp. -- Exercises 2.4

Add 7 pp. -- 2.5 The Chain Rule

Add 3 pp. -- Exercises 2.5

Add 7 pp. -- 2.6 Derivatives of Trigonometric Functions

Add 3 pp. -- Exercises 2.6

Add 8 pp. -- 2.7 Derivatives of Exponential and Logarithmic Functions

Add 3 pp. -- Exercises 2.7

Add 8 pp. -- 2.8 Implicit Differentiation and Inverse Trigonometric Functions

Add 3 pp. -- Exercises 2.8

Add 6 pp. -- 2.9 The Mean Value Theorem

Add 3 pp. -- Exercises 2.9

Add 5 pp. -- Review Exercise

3. Applications of Differentiation

Add 2 pp. -- Introduction

Add 9 pp. -- 3.1 Linear Approximations and Newton?s Method

Add 5 pp. -- Exercises 3.1

Add 9 pp. -- 3.2 Indeterminate Forms and L?HÂ¢pital?s Rule

Add 3 pp. -- Exercises 3.2

Add 9 pp. -- 3.3 Maximum and Minimum Values

Add 4 pp. -- Exercises 3.3

Add 9 pp. -- 3.4 Increasing and Decreasing Functions

Add 3 pp. -- Exercises 3.4

Add 12 pp. -- 3.5 Concavity and Overview of Curve Sketching

Add 5 pp. -- Exercises 3.5

Add 8 pp. -- 3.6 Optimization

Add 5 pp. -- Exercises 3.6

Add 8 pp. -- 3.7 Rates of Change in Economics and the Sciences

Add 4 pp. -- Exercises 3.7

Add 6 pp. -- 3.8 Related Rates and Parametric Equations

Add 4 pp. -- Exercises 3.8

Add 3 pp. -- Review Exercises

4. Integration

Add 2 pp. -- Introduction

Add 10 pp. -- 4.1 Area Under a Curve

Add 3 pp. -- Exercises 4.1

Add 11 pp. -- 4.2 The Definite Integral

Add 4 pp. -- Exercises 4.2

Add 9 pp. -- 4.3 Antiderivatives

Add 3 pp. -- Exercises 4.3

Add 8 pp. -- 4.4 The Fundamental Theorem of Calculus

Add 3 pp. -- Exercises 4.4

Add 6 pp. -- 4.5 Integration by Substitution

Add 3 pp. -- Exercises 4.5

Add 6 pp. -- 4.6 Integration by Parts

Add 2 pp. -- Exercises 4.6

Add 11 pp. -- 4.7 Other Techniques of Integration

Add 3 pp. -- Exercises 4.7

Add 8 pp. -- 4.8 Integration Tables and Computer Algebra Systems

Add 2 pp. -- Exercises 4.8

Add 11 pp. -- 4.9 Numerical Integration

Add 4 pp. -- Exercises 4.9

Add 12 pp. -- 4.10 Improper Integrals

Add 3 pp. -- Exercises 4.10

Add 4 pp. -- Review Exercises

5. Applications of the Definite Integral

Add 1 pg. -- Introduction

Add 7 pp. -- 5.1 Area of a Plane Region

Add 4 pp. -- Exercises 5.1

Add 16 pp. -- 5.2 Volume

Add 4 pp. -- Exercises 5.2

Add 7 pp. -- 5.3 Arc Length and Surface Area

Add 3 pp. -- Exercises 5.3

Add 7 pp. -- 5.4 Projectile Motion

Add 5 pp. -- Exercises 5.4

Add 10 pp. -- 5.5 Applications of Integration to Physics and Engineering

Add 4 pp. -- Exercises 5.5

Add 8 pp. -- 5.6 Probability

Add 4 pp. -- Exercises 5.6

Add 5 pp. -- Review Exercises

6. Differential Equations

Add 2 pp. -- Introduction

Add 8 pp. -- 6.1 Growth and Decay Problems

Add 5 pp. -- Exercises 6.1

Add 8 pp. -- 6.2 Separable Differential Equations

Add 4 pp. -- Exercises 6.2

Add 10 pp. -- 6.3 Direction Fields and Euler?s Method

Add 4 pp. -- Exercises 6.3

Add 8 pp. -- 6.4 Second-Order Equations with Constant Coefficients

Add 3 pp. -- Exercises 6.4

Add 8 pp. -- 6.5 Nonhomogeneous Equations: Undetermined Coefficients

Add 4 pp. -- Exercises 6.5

Add 3 pp. -- Review Exercises

7. Infinite Series

Add 2 pp. -- Introduction

Add 10 pp. -- 7.1 Sequences of Real Numbers

Add 3 pp. -- Exercises 7.1

Add 8 pp. -- 7.2 Infinite Series

Add 3 pp. -- Exercises 7.2

Add 9 pp. -- 7.3 The Integral Test and Comparison Tests

Add 3 pp. -- Exercises 7.3

Add 6 pp. -- 7.4 Alternating Series

Add 3 pp. -- Exercises 7.4

Add 6 pp. -- 7.5 Absolute Convergence and the Ratio Test

Add 2 pp. -- Exercises 7.5

Add 7 pp. -- 7.6 Power Series

Add 3 pp. -- Exercises 7.6

Add 12 pp. -- 7.7 Taylor Series

Add 3 pp. -- Exercises 7.7

Add 7 pp. -- 7.8 Applications of Taylor Series

Add 2 pp. -- Exercises 7.8

Add 13 pp. -- 7.9 Fourier Series

Add 4 pp. -- Exercises 7.9

Add 10 pp. -- 7.10 Using Series to Solve Differential Equations

Add 2 pp. -- Exercises 7.10

Add 4 pp. -- Review Exercises

8. Vectors and the Geometry of Space

Add 2 pp. -- Introduction

Add 9 pp. -- 8.1 Vectors in the Plane

Add 3 pp. -- Exercises 8.1

Add 7 pp. -- 8.2 Vectors in Space

Add 3 pp. -- Exercises 8.2

Add 7 pp. -- 8.3 The Dot Product

Add 5 pp. -- Exercises 8.3

Add 10 pp. -- 8.4 The Cross Product

Add 3 pp. -- Exercises 8.4

Add 8 pp. -- 8.5 Lines and Planes in Space

Add 3 pp. -- Exercises 8.5

Add 11 pp. -- 8.6 Surfaces in Space

Add 3 pp. -- Exercises 8.6

Add 3 pp. -- Review Exercises

9. Vector-Valued Functions

Add 1 pg. -- Introduction

Add 8 pp. -- 9.1 Vector-Valued Functions

Add 4 pp. -- Exercises 9.1

Add 10 pp. -- 9.2 The Calculus of Vector-Valued Functions

Add 2 pp. -- Exercises 9.2

Add 9 pp. -- 9.3 Motion in Space

Add 4 pp. -- Exercises 9.3

Add 7 pp. -- 9.4 Curvature

Add 2 pp. -- Exercises 9.4

Add 13 pp. -- 9.5 Tangent and Normal Vectors

Add 3 pp. -- Exercises 9.5

Add 4 pp. -- 9.6 Parametric Surfaces

Add 3 pp. -- Exercises 9.6

Add 4 pp. -- Review Exercises

10. Functions of Several Variables and Partial Differentiation

Add 1 pg. -- Introduction

Add 2 pp. -- 10.1 Functions of Several Variables

Add 8 pp. -- Exercises 10.1

Add 10 pp. -- 10.2 Limits and Continuity

Add 2 pp. -- Exercises 10.2

Add 9 pp. -- 10.3 Partial Derivatives

Add 5 pp. -- Exercises 10.3

Add 11 pp. -- 10.4 Tangent Planes and Linear Approximations

Add 4 pp. -- Exercises 10.4

Add 9 pp. -- 10.5 The Chain Rule

Add 3 pp. -- Exercises 10.5

Add 9 pp. -- 10.6 The Gradient and Directional Derivatives

Add 5 pp. -- Exercises 10.6

Add 12 pp. -- 10.7 Extrema of Functions of Several Variables

Add 4 pp. -- Exercises 10.7

Add 10 pp. -- 10.8 Constrained Optimization and Lagrange Multipliers

Add 3 pp. -- Exercises 10.8

Add 7 pp. -- Review Exercises

11. Multiple Integrals

Add 2 pp. -- Introduction

Add 14 pp. -- 11.1 Double Integrals

Add 4 pp. -- Exercises 11.1

Add 9 pp. -- 11.2 Area, Volume and Center of Mass

Add 4 pp. -- Exercises 11.2

Add 6 pp. -- 11.3 Double Integrals in Polar Coordinates

Add 3 pp. -- Exercises 11.3

Add 6 pp. -- 11.4 Surface Area

Add 2 pp. -- Exercises 11.4

Add 11 pp. -- 11.5 Triple Integrals

Add 3 pp. -- Exercises 11.5

Add 6 pp. -- 11.6 Cylindrical Coordinates

Add 2 pp. -- Exercises 11.6

Add 8 pp. -- 11.7 Spherical Coordinates

Add 3 pp. -- Exercises 11.7

Add 11 pp. -- 11.8 Change of Variables in Multiple Integrals

Add 3 pp. -- Exercises 11.8

Add 3 pp. -- Review Exercises

12. Vector Calculus

Add 1 pg. -- Introduction

Add 12 pp. -- 12.1 Vector Fields

Add 4 pp. -- Exercises 12.1

Add 7 pp. -- 12.2 Curl and Divergence

Add 3 pp. -- Exercises 12.2

Add 14 pp. -- 12.3 Line Integrals

Add 4 pp. -- Exercises 12.3

Add 7 pp. -- 12.4 Independence of Path and Conservative Vector Fields

Add 3 pp. -- Exercises 12.4

Add 9 pp. -- 12.5 Green?s Theorem

Add 2 pp. -- Exercises 12.5

Add 11 pp. -- 12.6 Surface Integrals

Add 3 pp. -- Exercises 12.6

Add 6 pp. -- 12.7 The Divergence Theorem

Add 3 pp. -- Exercises 12.7

Add 9 pp. -- 12.8 Stokes? Theorem

Add 2 pp. -- Exercises 12.8

Add 7 pp. -- 12.9 Applications of Vector Calculus

Add 2 pp. -- Exercises 12.9

Add 5 pp. -- Review Exercises

Back Matter

Add 4 pp. -- Appendix A: Additional Polar Graphs

Add 13 pp. -- Appendix B: Formal Definition of the Limit

Add 4 pp. -- Appendix C: Derivative of the Sine Function

Add 10 pp. -- Appendix D: The Natural Logarithm as an Integral

Add 7 pp. -- Appendix E: Conic Sections in Polar Coordinates

12 pp. -- Appendix F: Proofs of Selected Theorems

2 pp. -- Answers to Odd-Numbered Exercises Chapter 0

2 pp. -- Answers to Odd-Numbered Exercises Chapter 0 Review

Add 3 pp. -- Answers to Odd-Numbered Exercises chapter 1

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 1 Review

Add 6 pp. -- Answers to Odd-Numbered Exercises chapter 2

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 2 Review

Add 5 pp. -- Answers to Odd-Numbered Exercises chapter 3

Add 1 pg. -- Answers to Odd-Numbered Exercises Chapter 3 Review

Add 3 pp. -- Answers to Odd-Numbered Exercises chapter 4

Add 1 pg. -- Answers to Odd-Numbered Exercises Chapter 4 Review

Add 4 pp. -- Answers to Odd-Numbered Exercises chapter 5

Add 2 pp. -- Answers to Odd-Numbered Exercises chapter 5 Review

Add 4 pp. -- Answers to Odd-Numbered Exercises chapter 6

Add 1 pg. -- Answers to Odd-Numbered Exercises chapter 6 Review

Add 5 pp. -- Answers to Odd-Numbered Exercises Chapter 7

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 7 Review

Add 5 pp. -- Answers to Odd-Numbered Exercises Chapter 8

Add 1 pg. -- Answers to Odd-Numbered Exercises Chapter 8 Review

Add 4 pp. -- Answers to Odd-Numbered Exercises Chapter 9

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 10

Add 4 pp. -- Answers to Odd-Numbered Exercises Chapter 10 Review

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 11

Add 3 pp. -- Answers to Odd-Numbered Exercises Chapter 11 Review

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 12

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 12 Review

Add 10 pp. -- Bibliography

Add 1 pg. -- Credits

Add 15 pp. -- Index

Add 4 pp. -- Derivative Formulas

Add 2 pp. -- Table of Integrals

Add 3 pp. -- Index of Applications

Add 5 pp. -- Preface

Add 6 pp. -- Guided Tour

Add 1 pg. -- To the Student

0. Preliminaries

Add 2 pp. -- Introduction

Add 14 pp. -- 0.1 Polynomials and Rational Functions

Add 3 pp. -- Exercises 0.1

Add 8 pp. -- 0.2 Graphing Calculators and Computer Algebra Systems

Add 2 pp. -- Exercises 0.2

Add 5 pp. -- 0.3 Inverse Functions

Add 2 pp. -- Exercises 0.3

Add 10 pp. -- 0.4 Trigonometric and Inverse Trigonometric Functions

Add 4 pp. -- Exercises 0.4

Add 11 pp. -- 0.5 Exponential and Logarithmic Functions

Add 3 pp. -- Exercises 0.5

Add 7 pp. -- 0.6 Transformations of Functions

Add 2 pp. -- Exercises 0.6

Add 13 pp. -- 0.7 Parametric Equations and Polar Coordinates

Add 4 pp. -- Exercises 0.7

Add 5 pp. -- Review Exercises

1. Limits and Continuity

Add 2 pp. -- Introduction

Add 5 pp. -- 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve

Add 2 pp. -- Exercises 1.1

Add 7 pp. -- 1.2 The Concept of Limit

Add 3 pp. -- Exercise 1.2

Add 10 pp. -- 1.3 Computation of Limits

Add 3 pp. -- Exercises 1.3

Add 9 pp. -- 1.4 Continuity and Its Consequences

Add 5 pp. -- Exercises 1.4

Add 9 pp. -- 1.5 Limits Involving Infinity

Add 4 pp. -- Exercises 1.5

Add 7 pp. -- 1.6 Limits and Loss-Of-Significance Errors

Add 2 pp. -- Exercises 1.6

Add 4 pp. -- Review Exercises

2. Differentiation

Add 2 pp. -- Introduction

Add 9 pp. -- 2.1 Tangent Lines and Velocity

Add 4 pp. -- Exercises 2.1

Add 8 pp. -- 2.2 The Derivative

Add 5 pp. -- Exercises 2.2

Add 7 pp. -- 2.3 Computation of Derivatives: The Power Rule

Add 4 pp. -- Exercises 2.3

Add 6 pp. -- 2.4 The Product and Quotient Rules

Add 4 pp. -- Exercises 2.4

Add 7 pp. -- 2.5 The Chain Rule

Add 3 pp. -- Exercises 2.5

Add 7 pp. -- 2.6 Derivatives of Trigonometric Functions

Add 3 pp. -- Exercises 2.6

Add 8 pp. -- 2.7 Derivatives of Exponential and Logarithmic Functions

Add 3 pp. -- Exercises 2.7

Add 8 pp. -- 2.8 Implicit Differentiation and Inverse Trigonometric Functions

Add 3 pp. -- Exercises 2.8

Add 6 pp. -- 2.9 The Mean Value Theorem

Add 3 pp. -- Exercises 2.9

Add 5 pp. -- Review Exercise

3. Applications of Differentiation

Add 2 pp. -- Introduction

Add 9 pp. -- 3.1 Linear Approximations and Newton?s Method

Add 5 pp. -- Exercises 3.1

Add 9 pp. -- 3.2 Indeterminate Forms and L?HÂ¢pital?s Rule

Add 3 pp. -- Exercises 3.2

Add 9 pp. -- 3.3 Maximum and Minimum Values

Add 4 pp. -- Exercises 3.3

Add 9 pp. -- 3.4 Increasing and Decreasing Functions

Add 3 pp. -- Exercises 3.4

Add 12 pp. -- 3.5 Concavity and Overview of Curve Sketching

Add 5 pp. -- Exercises 3.5

Add 8 pp. -- 3.6 Optimization

Add 5 pp. -- Exercises 3.6

Add 8 pp. -- 3.7 Rates of Change in Economics and the Sciences

Add 4 pp. -- Exercises 3.7

Add 6 pp. -- 3.8 Related Rates and Parametric Equations

Add 4 pp. -- Exercises 3.8

Add 3 pp. -- Review Exercises

4. Integration

Add 2 pp. -- Introduction

Add 10 pp. -- 4.1 Area Under a Curve

Add 3 pp. -- Exercises 4.1

Add 11 pp. -- 4.2 The Definite Integral

Add 4 pp. -- Exercises 4.2

Add 9 pp. -- 4.3 Antiderivatives

Add 3 pp. -- Exercises 4.3

Add 8 pp. -- 4.4 The Fundamental Theorem of Calculus

Add 3 pp. -- Exercises 4.4

Add 6 pp. -- 4.5 Integration by Substitution

Add 3 pp. -- Exercises 4.5

Add 6 pp. -- 4.6 Integration by Parts

Add 2 pp. -- Exercises 4.6

Add 11 pp. -- 4.7 Other Techniques of Integration

Add 3 pp. -- Exercises 4.7

Add 8 pp. -- 4.8 Integration Tables and Computer Algebra Systems

Add 2 pp. -- Exercises 4.8

Add 11 pp. -- 4.9 Numerical Integration

Add 4 pp. -- Exercises 4.9

Add 12 pp. -- 4.10 Improper Integrals

Add 3 pp. -- Exercises 4.10

Add 4 pp. -- Review Exercises

5. Applications of the Definite Integral

Add 1 pg. -- Introduction

Add 7 pp. -- 5.1 Area of a Plane Region

Add 4 pp. -- Exercises 5.1

Add 16 pp. -- 5.2 Volume

Add 4 pp. -- Exercises 5.2

Add 7 pp. -- 5.3 Arc Length and Surface Area

Add 3 pp. -- Exercises 5.3

Add 7 pp. -- 5.4 Projectile Motion

Add 5 pp. -- Exercises 5.4

Add 10 pp. -- 5.5 Applications of Integration to Physics and Engineering

Add 4 pp. -- Exercises 5.5

Add 8 pp. -- 5.6 Probability

Add 4 pp. -- Exercises 5.6

Add 5 pp. -- Review Exercises

6. Differential Equations

Add 2 pp. -- Introduction

Add 8 pp. -- 6.1 Growth and Decay Problems

Add 5 pp. -- Exercises 6.1

Add 8 pp. -- 6.2 Separable Differential Equations

Add 4 pp. -- Exercises 6.2

Add 10 pp. -- 6.3 Direction Fields and Euler?s Method

Add 4 pp. -- Exercises 6.3

Add 8 pp. -- 6.4 Second-Order Equations with Constant Coefficients

Add 3 pp. -- Exercises 6.4

Add 8 pp. -- 6.5 Nonhomogeneous Equations: Undetermined Coefficients

Add 4 pp. -- Exercises 6.5

Add 3 pp. -- Review Exercises

7. Infinite Series

Add 2 pp. -- Introduction

Add 10 pp. -- 7.1 Sequences of Real Numbers

Add 3 pp. -- Exercises 7.1

Add 8 pp. -- 7.2 Infinite Series

Add 3 pp. -- Exercises 7.2

Add 9 pp. -- 7.3 The Integral Test and Comparison Tests

Add 3 pp. -- Exercises 7.3

Add 6 pp. -- 7.4 Alternating Series

Add 3 pp. -- Exercises 7.4

Add 6 pp. -- 7.5 Absolute Convergence and the Ratio Test

Add 2 pp. -- Exercises 7.5

Add 7 pp. -- 7.6 Power Series

Add 3 pp. -- Exercises 7.6

Add 12 pp. -- 7.7 Taylor Series

Add 3 pp. -- Exercises 7.7

Add 7 pp. -- 7.8 Applications of Taylor Series

Add 2 pp. -- Exercises 7.8

Add 13 pp. -- 7.9 Fourier Series

Add 4 pp. -- Exercises 7.9

Add 10 pp. -- 7.10 Using Series to Solve Differential Equations

Add 2 pp. -- Exercises 7.10

Add 4 pp. -- Review Exercises

8. Vectors and the Geometry of Space

Add 2 pp. -- Introduction

Add 9 pp. -- 8.1 Vectors in the Plane

Add 3 pp. -- Exercises 8.1

Add 7 pp. -- 8.2 Vectors in Space

Add 3 pp. -- Exercises 8.2

Add 7 pp. -- 8.3 The Dot Product

Add 5 pp. -- Exercises 8.3

Add 10 pp. -- 8.4 The Cross Product

Add 3 pp. -- Exercises 8.4

Add 8 pp. -- 8.5 Lines and Planes in Space

Add 3 pp. -- Exercises 8.5

Add 11 pp. -- 8.6 Surfaces in Space

Add 3 pp. -- Exercises 8.6

Add 3 pp. -- Review Exercises

9. Vector-Valued Functions

Add 1 pg. -- Introduction

Add 8 pp. -- 9.1 Vector-Valued Functions

Add 4 pp. -- Exercises 9.1

Add 10 pp. -- 9.2 The Calculus of Vector-Valued Functions

Add 2 pp. -- Exercises 9.2

Add 9 pp. -- 9.3 Motion in Space

Add 4 pp. -- Exercises 9.3

Add 7 pp. -- 9.4 Curvature

Add 2 pp. -- Exercises 9.4

Add 13 pp. -- 9.5 Tangent and Normal Vectors

Add 3 pp. -- Exercises 9.5

Add 4 pp. -- 9.6 Parametric Surfaces

Add 3 pp. -- Exercises 9.6

Add 4 pp. -- Review Exercises

10. Functions of Several Variables and Partial Differentiation

Add 1 pg. -- Introduction

Add 2 pp. -- 10.1 Functions of Several Variables

Add 8 pp. -- Exercises 10.1

Add 10 pp. -- 10.2 Limits and Continuity

Add 2 pp. -- Exercises 10.2

Add 9 pp. -- 10.3 Partial Derivatives

Add 5 pp. -- Exercises 10.3

Add 11 pp. -- 10.4 Tangent Planes and Linear Approximations

Add 4 pp. -- Exercises 10.4

Add 9 pp. -- 10.5 The Chain Rule

Add 3 pp. -- Exercises 10.5

Add 9 pp. -- 10.6 The Gradient and Directional Derivatives

Add 5 pp. -- Exercises 10.6

Add 12 pp. -- 10.7 Extrema of Functions of Several Variables

Add 4 pp. -- Exercises 10.7

Add 10 pp. -- 10.8 Constrained Optimization and Lagrange Multipliers

Add 3 pp. -- Exercises 10.8

Add 7 pp. -- Review Exercises

11. Multiple Integrals

Add 2 pp. -- Introduction

Add 14 pp. -- 11.1 Double Integrals

Add 4 pp. -- Exercises 11.1

Add 9 pp. -- 11.2 Area, Volume and Center of Mass

Add 4 pp. -- Exercises 11.2

Add 6 pp. -- 11.3 Double Integrals in Polar Coordinates

Add 3 pp. -- Exercises 11.3

Add 6 pp. -- 11.4 Surface Area

Add 2 pp. -- Exercises 11.4

Add 11 pp. -- 11.5 Triple Integrals

Add 3 pp. -- Exercises 11.5

Add 6 pp. -- 11.6 Cylindrical Coordinates

Add 2 pp. -- Exercises 11.6

Add 8 pp. -- 11.7 Spherical Coordinates

Add 3 pp. -- Exercises 11.7

Add 11 pp. -- 11.8 Change of Variables in Multiple Integrals

Add 3 pp. -- Exercises 11.8

Add 3 pp. -- Review Exercises

12. Vector Calculus

Add 1 pg. -- Introduction

Add 12 pp. -- 12.1 Vector Fields

Add 4 pp. -- Exercises 12.1

Add 7 pp. -- 12.2 Curl and Divergence

Add 3 pp. -- Exercises 12.2

Add 14 pp. -- 12.3 Line Integrals

Add 4 pp. -- Exercises 12.3

Add 7 pp. -- 12.4 Independence of Path and Conservative Vector Fields

Add 3 pp. -- Exercises 12.4

Add 9 pp. -- 12.5 Green?s Theorem

Add 2 pp. -- Exercises 12.5

Add 11 pp. -- 12.6 Surface Integrals

Add 3 pp. -- Exercises 12.6

Add 6 pp. -- 12.7 The Divergence Theorem

Add 3 pp. -- Exercises 12.7

Add 9 pp. -- 12.8 Stokes? Theorem

Add 2 pp. -- Exercises 12.8

Add 7 pp. -- 12.9 Applications of Vector Calculus

Add 2 pp. -- Exercises 12.9

Add 5 pp. -- Review Exercises

Back Matter

Add 4 pp. -- Appendix A: Additional Polar Graphs

Add 13 pp. -- Appendix B: Formal Definition of the Limit

Add 4 pp. -- Appendix C: Derivative of the Sine Function

Add 10 pp. -- Appendix D: The Natural Logarithm as an Integral

Add 7 pp. -- Appendix E: Conic Sections in Polar Coordinates

12 pp. -- Appendix F: Proofs of Selected Theorems

2 pp. -- Answers to Odd-Numbered Exercises Chapter 0

2 pp. -- Answers to Odd-Numbered Exercises Chapter 0 Review

Add 3 pp. -- Answers to Odd-Numbered Exercises chapter 1

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 1 Review

Add 6 pp. -- Answers to Odd-Numbered Exercises chapter 2

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 2 Review

Add 5 pp. -- Answers to Odd-Numbered Exercises chapter 3

Add 1 pg. -- Answers to Odd-Numbered Exercises Chapter 3 Review

Add 3 pp. -- Answers to Odd-Numbered Exercises chapter 4

Add 1 pg. -- Answers to Odd-Numbered Exercises Chapter 4 Review

Add 4 pp. -- Answers to Odd-Numbered Exercises chapter 5

Add 2 pp. -- Answers to Odd-Numbered Exercises chapter 5 Review

Add 4 pp. -- Answers to Odd-Numbered Exercises chapter 6

Add 1 pg. -- Answers to Odd-Numbered Exercises chapter 6 Review

Add 5 pp. -- Answers to Odd-Numbered Exercises Chapter 7

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 7 Review

Add 5 pp. -- Answers to Odd-Numbered Exercises Chapter 8

Add 1 pg. -- Answers to Odd-Numbered Exercises Chapter 8 Review

Add 4 pp. -- Answers to Odd-Numbered Exercises Chapter 9

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 10

Add 4 pp. -- Answers to Odd-Numbered Exercises Chapter 10 Review

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 11

Add 3 pp. -- Answers to Odd-Numbered Exercises Chapter 11 Review

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 12

Add 2 pp. -- Answers to Odd-Numbered Exercises Chapter 12 Review

Add 10 pp. -- Bibliography

Add 1 pg. -- Credits

Add 15 pp. -- Index

Add 4 pp. -- Derivative Formulas

Add 2 pp. -- Table of Integrals

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