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

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https://doi.org/10.1007/978-3-319-67546-6use of euler maclaurin formula; Euler-Maclaurin formula; metric space theory; metric space in real anal

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978-3-319-67545-9Springer International Publishing AG 2017

哄骗

Essential Real Analysis978-3-319-67546-6Series ISSN 1615-2085 Series E-ISSN 2197-4144

骄傲

,Extensions to Containment Control,This chapter provides a systematic account of infinite series and infinite products and includes Abel’s and Dirichlet’s tests (used later in work on Fourier series), double series, Tannery’s theorem, and the infinite product formula for . .. Results proved include versions of Riemann’s rearrangement theorem for conditionally convergent series.

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https://doi.org/10.1007/978-981-10-2492-4This chapter focuses on uniform convergence and provides the building blocks and basic results needed for the construction of continuous, smooth and analytic functions using infinite series-the subject of chapter “Functions”. The chapter concludes with van der Waerden’s example of a continuous nowhere differentiable function.

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Fractals and Iterated Function Systems,This short chapter discusses fractals and iterated function systems in terms of the Hausdorff metric and gives a vivid illustration of the power of the abstract methods developed in the previous chapter.

宽容

Michael FieldContains 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