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Catalogue Information
Field name	Details
Dewey Class	515.8
Title	Essential Real Analysis ([EBook]) / by Michael Field.
Author	Field, Michael
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2017.
Physical Details	XVII, 450 p. 30 illus., 1 illus. in color. : online resource.
Series	Springer undergraduate mathematics series 1615-2085
ISBN	9783319675466
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-67546-6
Links to Related Works	Subject References: Fourier Analysis . Functions of real variables . Mathematics . Real Functions . Sequences (Mathematics) . Sequences, Series, Summability . Topology . Authors: Field, Michael . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 515.8 . 515.8 (DDC 23) .

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Essential Real Analysis

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