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Titlebook: Complex Analysis; John M. Howie Textbook 2003 Springer-Verlag London 2003 Analysis.Complex analysis.Complex numbers.Functions of a complex

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发表于 2025-3-21 16:20:44 | 显示全部楼层 |阅读模式
书目名称Complex Analysis
编辑John M. Howie
视频video
概述Suitable for both pure and applied mathematicians.Takes account of readers‘ varying needs and backgrounds by presenting ideas through worked examples and informal explanations rather than through "dry
丛书名称Springer Undergraduate Mathematics Series
图书封面Titlebook: Complex Analysis;  John M. Howie Textbook 2003 Springer-Verlag London 2003 Analysis.Complex analysis.Complex numbers.Functions of a complex
描述Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy‘s theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
出版日期Textbook 2003
关键词Analysis; Complex analysis; Complex numbers; Functions of a complex variable; Residue theorem; calculus; c
版次1
doihttps://doi.org/10.1007/978-1-4471-0027-0
isbn_softcover978-1-85233-733-9
isbn_ebook978-1-4471-0027-0Series ISSN 1615-2085 Series E-ISSN 2197-4144
issn_series 1615-2085
copyrightSpringer-Verlag London 2003
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https://doi.org/10.1007/978-3-663-14309-3rcise 11.1), and are instances of a general theorem to be proved shortly. First, however, we need to develop a little more of the theory of the parametric representation of curves that was introduced in Section 5.2.
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Conformal Mappings,rcise 11.1), and are instances of a general theorem to be proved shortly. First, however, we need to develop a little more of the theory of the parametric representation of curves that was introduced in Section 5.2.
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https://doi.org/10.1007/978-3-663-14309-3njecture (there are infinitely many pairs (.) of prime numbers with . = . + 2) but it is hugely more important than either of these, for a successful proof would have many, many consequences in analysis and number theory.
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1615-2085 examples and informal explanations rather than through "dryComplex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This
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,Kognitivistische Erklärungsmodelle,rt on this book, with references to suitable texts. It is written as a reminder: if there is anything you don’t know at all, then at some point you will need to consult another book, either the suggested reference or another similar volume.
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Differentiation,tical to those in real analysis. (See [9, Chapter 4].) Since (trivially) . ↦ . is differentiable, with derivative 1, it follows that polynomials are differentiable at every point in the plane, and that a rational function .(.)/.(.) (where . and . are polynomials with no common factor) is differentiable except at the zeros of ..
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