Essential Real Analysis. 1st ed. 2017

種類:

電子ブック

責任表示:

by Michael Field

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Field, Michael.
• SpringerLink (Online service)

シリーズ名:

Springer Undergraduate Mathematics Series ;

ISBN:

9783319675466 [331967546X]    

注記:

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 stu

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