{"product_id":"solutions-manual-to-accompany-analysis-in-vector-spaces-paperback-softback-9780470148259","title":"Solutions Manual to accompany Analysis in Vector Spaces (Paperback \/ softback) 9780470148259","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSolutions Manual to accompany Analysis in Vector Spaces\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eMustafa A. Akcoglu (Author), Paul F. A. Bartha (Author), Dzung Minh Ha (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470148259, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 29 April 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e160 pages\u003cbr\u003e23.1 x 15 x 1.3 cm, 0.272 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The authors do not shy away from doing the hard work involved in proving say, the change of variable theorem for integration, the inverse function theorem, and Stokes's theorem--work which is not generally seen in standard calculus books--and thus they are quite correct when they state that students need a firm grip on single-variable calculus and some linear algebra, and a good comfort level with the comprehension and construction of rigorous proofs. Includes many examples and an excellent selection of exercises.\" (\u003ci\u003eCHOICE,\u003c\/i\u003e November 2010)\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eA rigorous introduction to calculus in vector spaces\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. \u003ci\u003eAnalysis in Vector Spaces\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eThe 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:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eSets and functions\u003c\/li\u003e \u003cli\u003eReal numbers\u003c\/li\u003e \u003cli\u003eVector functions\u003c\/li\u003e \u003cli\u003eNormed vector spaces\u003c\/li\u003e \u003cli\u003eFirst- and higher-order derivatives\u003c\/li\u003e \u003cli\u003eDiffeomorphisms and manifolds\u003c\/li\u003e \u003cli\u003eMultiple integrals\u003c\/li\u003e \u003cli\u003eIntegration on manifolds\u003c\/li\u003e \u003cli\u003eStokes' theorem\u003c\/li\u003e \u003cli\u003eBasic point set topology\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eNumerous 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.\u003c\/p\u003e \u003cp\u003eAssuming only a fundamental understanding of linear algebra and single variable calculus, \u003ci\u003eAnalysis in Vector Spaces\u003c\/i\u003e 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.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface ix\u003cbr\u003e\u003cbr\u003e1 Sets and Functions 3\u003cbr\u003e\u003cbr\u003e2 Real Numbers 13\u003cbr\u003e\u003cbr\u003e3 Vector Functions 27\u003cbr\u003e\u003cbr\u003e4 Normed Vector Spaces 45\u003cbr\u003e\u003cbr\u003e5 Derivatives 63\u003cbr\u003e\u003cbr\u003e6 Diffeomorphisms and Manifolds 83\u003cbr\u003e\u003cbr\u003e7 High-Order Derivatives 95\u003cbr\u003e\u003cbr\u003e8 Multiple Integrals 99\u003cbr\u003e\u003cbr\u003e9 Integration of Manifolds 115\u003cbr\u003e\u003cbr\u003e10 Stokes Theorem 131\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52257119142168,"sku":"9780470148259","price":30.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470148259.jpg?v=1781277095","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/solutions-manual-to-accompany-analysis-in-vector-spaces-paperback-softback-9780470148259","provider":"Freshly Printed Books","version":"1.0","type":"link"}