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Vector Calculus, 2/E
Susan Jane Colley, Oberlin College

ISBN-10: 0130415316
ISBN-13: 9780130415318

Publisher: Pearson
Copyright: 2002
Format: Cloth; 558 pp
Published: 06/08/2001

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Description

Appropriate for sophomore-level courses in Multivariable Calculus.

A traditional and accessible calculus text with a strong conceptual and geometric slant that assumes a background in single-variable calculus. The text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. It is designed to provide a greater challenge than the multivariable material typically found in the last four or five chapters of a three-semester calculus text. This challenge is balanced by clear and expansive writing and an interesting selection of material.

Features

NEW - Expanded discussion of key topics—Includes the implicit function and inverse function theorems and the role of quadratic forms in determining extrema of functions.
- Gives students a more thorough explanation of these complex concepts. Ex.___

NEW - New Chapter 8—Covers differential forms, parametrized manifolds, and the generalized Stokes's theorem.
- Replaces and expands section 7.5 of the first edition. Ex.___

NEW - Many new and varied exercises—Provides over 1200 exercises ranging from routine reinforcement of basic definitions, computations, and results, to more challenging conceptual questions.
- Reinforces concepts that are crucial to student progression in calculus. Ex.___

NEW - Computer-based exercises—Clearly marked throughout.
- Helps students connect theory to the use of computers. Ex.___

NEW - New Student Solutions Manual.
- Provides detailed solutions to selected odd-numbered exercises. Ex.___

Vector and matrix notation is used, particularly for differential topics.
- Fosters a more general discussion and clarifies the analogy between concepts in single- and multivariable calculus. Ex.___

Over 600 diagrams and figures.
- Connects analytic work to geometry and assists with visualization. Ex.___

A large variety of topics not usually found in a text at this level.
- Offers flexibility for students and instructors. Ex.___

Proofs are placed throughout the text for reference.
- Positioned so as not to interfere with the main flow of ideas. Ex.___

Many fully worked examples that are integral to the text.
- Motivates and explicates the main ideas and techniques for students. Ex.___

New To This Edition

Expanded discussion of key topics—Includes the implicit function and inverse function theorems and the role of quadratic forms in determining extrema of functions.
- Gives students a more thorough explanation of these complex concepts. Ex.___

New Chapter 8—Covers differential forms, parametrized manifolds, and the generalized Stokes's theorem.
- Replaces and expands section 7.5 of the first edition. Ex.___

Many new and varied exercises—Provides over 1200 exercises ranging from routine reinforcement of basic definitions, computations, and results, to more challenging conceptual questions.
- Reinforces concepts that are crucial to student progression in calculus. Ex.___

Computer-based exercises—Clearly marked throughout.
- Helps students connect theory to the use of computers. Ex.___

New Student Solutions Manual.
- Provides detailed solutions to selected odd-numbered exercises. Ex.___

Table of Contents

Preface.

1. Vectors.

Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Some n-Dimensional Geometry. New Coordinate Systems. Miscellaneous Exercises for Chapter 1.

2. Differentiation in Several Variables.

Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives. The Chain Rule. Directional Derivatives and the Gradient. Miscellaneous Exercises for Chapter 2.

3. Vector-Valued Functions.

Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient, Divergence, Curl, and the Del Operator. Miscellaneous Exercises for Chapter 3.

4. Maxima and Minima in Several Variables.

Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema. Miscellaneous Exercises for Chapter 4.

5. Multiple Integration.

Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration. Miscellaneous Exercises for Chapter 5.

6. Line Integrals.

Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields. Miscellaneous Exercises for Chapter 6.

7. Surface Integrals and Vector Analysis.

Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations. Miscellaneous Exercises for Chapter 7.

8. Vector Analysis in Higher Dimensions.

An Introduction to Differential Forms. Manifolds and Integrals of k-forms. The Generalized Stokes's Theorem. Miscellaneous Exercises for Chapter 8.

Suggestions for Further Reading.

Answers to Selected Exercises.

Index.

Courses

Vector Calculus (Mathematics)
Multivariable Calculus (Mathematics)

Next Edition(s)

Vector Calculus, 3/E
Colley
©2006 | Pearson | Cloth; 576 pp | Instock
ISBN-10: 0131858742 | ISBN-13: 9780131858749
Net price: $119.00 (What's this?)Brief Description |
For sophomore-level courses in Multivariable Calculus.

This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. Accessible to anyone with a good background in single-variable calculus, it presents more linear algebra than usually found in a multivariable calculus book. Colley balances this with very clear and expansive exposition, many figures, and numerous, wide-ranging exercises. Instructors will appreciate Colley’s writing style, mathematical precision, level of rigor, and full selection of topics treated.

More Info
Vector Calculus, 4/E
Colley
©2012 | Pearson | Cloth; 624 pp | Instock
ISBN-10: 0321780655 | ISBN-13: 9780321780652
Net price: $119.00 (What's this?)Brief Description |

For undergraduate courses in Multivariable Calculus.

Vector Calculus, Fourth Edition, uses the language and notation of vectors and matrices to teach multivariable calculus. It is ideal for students with a solid background in single-variable calculus who are capable of thinking in more general terms about the topics in the course. This text is distinguished from others by its readable narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets. Colley includes not only basic and advanced exercises, but also mid-level exercises that form a necessary bridge between the two. Instructors will appreciate the mathematical precision, level of rigor, and full selection of topics.
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Author Bios

Author Bios

Susan Coney is currently the Andrew and Pauline Delaney Professor of Mathematics at Oberlin College, having previously served as Chair of the Department.

She received S.B. and Ph.D. degrees in mathematics from the Massachusetts Institute of Technology prior to joining the faculty at Oberlin in 1983.

Her research focuses on enumerative problems in algebraic geometry, particularly concerning multiple-point singularities and higher-order contact of plane curves.

Professor Coney has published papers on algebraic geometry as well as articles on other mathematical subjects. She has lectured internationally on her research and has taught a wide range of subjects in undergraduate mathematics.

Professor Coney is a member of several professional and honorary societies, including the American Mathematical Society, the Mathematical Association of America, Phi Beta Kappa, and Sigma Xi.

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Vector Calculus, 2/E