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题名/责任者:

Real analysis and infinity / H. Sedaghat.

出版发行项:

Oxford, United Kingdom : Oxford University Press, 2022.

ISBN:

9780192895622:

ISBN:

0192895621

载体形态项:

xiv, 547 pages : illustrations ; 24 cm

个人责任者:

Sedaghat, Hassan, author.

论题主题:

Mathematical analysis.

论题主题:

Infinite.

中图法分类号:

O17

书目附注:

Includes bibliographical references (page 541) and index.

摘要附注:

"Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions. Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge. Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills."--

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