Analysis in Euclidean Space
Analysis in Euclidean Space
- ISBN 13:
9780486833651
- ISBN 10:
0486833658
- Edition: Reprint
- Format: Paperback
- Copyright: 07/17/2019
- Publisher: Dover Publications
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Summary
Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.