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Titlebook: Essential Real Analysis; Michael Field Textbook 2017 Springer International Publishing AG 2017 use of euler maclaurin formula.Euler-Maclau

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發(fā)表于 2025-3-21 16:21:27 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Essential Real Analysis
編輯Michael Field
視頻videohttp://file.papertrans.cn/316/315528/315528.mp4
概述Contains more than 570 exercises of varying difficulty.Provides proofs of basic results on existence and regularity of solutions of ordinary differential equations.Includes a full treatment of the inv
叢書名稱Springer Undergraduate Mathematics Series
圖書封面Titlebook: Essential Real Analysis;  Michael Field Textbook 2017 Springer International Publishing AG 2017 use of euler maclaurin formula.Euler-Maclau
描述.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 andfractals.. .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
出版日期Textbook 2017
關(guān)鍵詞use of euler maclaurin formula; Euler-Maclaurin formula; metric space theory; metric space in real anal
版次1
doihttps://doi.org/10.1007/978-3-319-67546-6
isbn_softcover978-3-319-67545-9
isbn_ebook978-3-319-67546-6Series ISSN 1615-2085 Series E-ISSN 2197-4144
issn_series 1615-2085
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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沙發(fā)
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Functions,at occurs when convergence of the Fourier series is not uniform (piecewise smooth functions with jumps). The chapter concludes with a second proof of the infinite product formula for .?., this time using methods based on Fourier series.
地板
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1615-2085 differential equations.Includes a full treatment of the inv.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 comp
6#
發(fā)表于 2025-3-22 16:02:19 | 只看該作者
Jianquan Lu,Jun Shen,Jinde Cao,Jürgen Kurthsonvexity. After defining Bernoulli numbers and polynomials and computing their Fourier series, a proof is given of the Euler–Maclaurin formula and a number of applications are given including Stirling’s formula, estimates of Euler’s constant and the sums of infinite series (such as the infinite sum of ..).
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發(fā)表于 2025-3-22 20:16:08 | 只看該作者
,Topics from Classical Analysis: The Gamma-Function and the Euler–Maclaurin Formula,onvexity. After defining Bernoulli numbers and polynomials and computing their Fourier series, a proof is given of the Euler–Maclaurin formula and a number of applications are given including Stirling’s formula, estimates of Euler’s constant and the sums of infinite series (such as the infinite sum of ..).
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On Habit: Peirce’s Story and Historyroofs are given of both the Leibniz rule and Faá di Bruno’s formula for the derivatives of products and composites of maps. In an appendix, there is a proof of the theorem of Frigyes Riesz on the equivalence of norms on a finite dimensional vector space.
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Textbook 2017or 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 formu
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