Analysis in Euclidean Space

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Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions.… Celý popis ↓

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Popis Analysis in Euclidean Space

Analysis in Euclidean Space

Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory.Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions.

They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change

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