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

ISBN-10: 0130415316
ISBN-13: 9780130415318

Publisher: Prentice Hall
Copyright: 2002
Format: Cloth; 558 pp
Status: Out of Print

Suggested retail price: $107.00
This item is out of print and is no longer available for purchase.

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.

  • 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.___

  • 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.___



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.

    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.

     

  • 0131858742Vector Calculus, 3/E
    Colley
    © 2006 | Prentice Hall | Cloth; 576 pages | Instock
    ISBN-10: 0131858742 | ISBN-13: 9780131858749
    Brief Description | Buy from myPearsonStore

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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