Vector Calculus

Vector Calculus

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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.show more

Product details

  • Hardback | 558 pages
  • 208.28 x 256.54 x 27.94mm | 816.46g
  • Pearson Education Limited
  • Prentice-Hall
  • Harlow, United Kingdom
  • English
  • Revised
  • 2nd Revised edition
  • index
  • 0130415316
  • 9780130415318

About Susan Jane Coney

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.show more

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.show more

Rating details

37 ratings
3.97 out of 5 stars
5 38% (14)
4 30% (11)
3 27% (10)
2 3% (1)
1 3% (1)
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