Calculus in Vector Spaces, Revised Expanded  book cover
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2nd Edition

Calculus in Vector Spaces, Revised Expanded




ISBN 9780824792794
Published December 8, 1994 by CRC Press
600 Pages

 
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Book Description

Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.

Table of Contents

Some Preliminaries. Vector Spaces. The Derivative. The Structure of Vector Spaces. Compact and Connected Sets. The Chain Rule, Higher Derivatives, and Taylor's Theorem. Linear Transformations and Matrices. Maxima and Minima. The Inverse and Implicit Function Theorems. The Spectral Theorem. Integration. Iterated Integrals and the Fubini Theorem. Line Integrals. Surface Integrals. Differential Forms. Integration of Differential Forms. Appendices: the existence of determinants, Jordan canonical form, solutions of selected exercises.

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