Analysis in Vector Spaces 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024


Analysis in Vector Spaces

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Mustafa A. Akcoglu 作者
Wiley-Blackwell
译者
2009-3-10 出版日期
480 页数
GBP 88.95 价格
Hardcover
丛书系列
9780470148242 图书编码

Analysis in Vector Spaces 在线电子书 图书标签: 高等微积分  线性代数  数学  向量分析   


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Analysis in Vector Spaces 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Analysis in Vector Spaces 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Analysis in Vector Spaces 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024



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A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology, and notation and also provide a basic introduction to set theory, the properties of real numbers, and a review of linear algebra. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts.

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