<電子ブック>
A Concise Introduction to Analysis / by Daniel W. Stroock
版 | 1st ed. 2015. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2015 |
大きさ | XII, 218 p : online resource |
著者標目 | *Stroock, Daniel W author SpringerLink (Online service) |
件 名 | LCSH:Functional analysis LCSH:Functions of real variables LCSH:Functions of complex variables LCSH:Sequences (Mathematics) LCSH:Integral equations FREE:Functional Analysis FREE:Real Functions FREE:Functions of a Complex Variable FREE:Sequences, Series, Summability FREE:Integral Equations |
一般注記 | Analysis on The Real Line -- Elements of Complex Analysis -- Integration -- Higher Dimensions -- Integration in Higher Dimensions -- A Little Bit of Analytic Function Theory This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them HTTP:URL=https://doi.org/10.1007/978-3-319-24469-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319244693 |
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EB00208417 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA319-329.9 DC23:515.7 |
書誌ID | 4000120473 |
ISBN | 9783319244693 |
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※2017年9月4日以降