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Essential real analysis

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Essential real analysis/ by Michael Field.
Author:	Field, Michael.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xvii, 450 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Mathematical analysis. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-67546-6
ISBN:	9783319675466

Essential real analysis
Field, Michael.

Essential real analysis[electronic resource] /by Michael Field. - Cham :Springer International Publishing :2017. - xvii, 450 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

1 Sets, functions and the real numbers -- 2 Basic properties of real numbers, sequences and continuous functions -- 3 Infinite series -- 4 Uniform convergence -- 5 Functions -- 6. Topics from classical analysis: The Gamma-function and the Euler-Maclaurin formula -- 7 Metric spaces -- 8 Fractals and iterated function systems -- 9 Differential calculus on Rm -- Bibliography. Index.

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.

ISBN: 9783319675466

Standard No.: 10.1007/978-3-319-67546-6doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Essential real analysis
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505 0 $a 1 Sets, functions and the real numbers -- 2 Basic properties of real numbers, sequences and continuous functions -- 3 Infinite series -- 4 Uniform convergence -- 5 Functions -- 6. Topics from classical analysis: The Gamma-function and the Euler-Maclaurin formula -- 7 Metric spaces -- 8 Fractals and iterated function systems -- 9 Differential calculus on Rm -- Bibliography. Index.
520 $a 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.
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