Calculus in vector spaces
著者
書誌事項
Calculus in vector spaces
（Monographs and textbooks in pure and applied mathematics, 189）
M. Dekker, c1995
2nd ed
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注記
Includes index
内容説明・目次
内容説明
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.
目次
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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