Essential Real Analysis

By: Michael Field

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Paperback | 15 November 2017

At a Glance

Paperback
470 Pages

Dimensions(cm)
23.5 x 15.5 x 2.54

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This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses.

Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author's extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals.

Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

Industry Reviews

"This is a well written text on Real Analysis that may be used for a course in Advanced Calculus. It can also serve as a reference for advanced topics in Real Analysis." (Charles Traina, MAA Reviews, January 4, 2020)
"This book contains a reasonably complete exposition of real analysis which is needed for beginning undergraduate-level students. ... This is a well-written textbook with an abundance of worked examples and exercises that are intended for a first course in analysis. This book offers a sound grounding in analysis. In particular, it gives a solid base in real analysis from which progress to more advanced topics may be made." (Teodora-Liliana RÄdulescu, zbMATH 1379.26001, 2018)

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