{"product_id":"advanced-calculus-an-introduction-to-linear-analysis-hardback-9780470232880","title":"Advanced Calculus; An Introduction to Linear Analysis (Hardback) 9780470232880","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAdvanced Calculus\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction to Linear Analysis\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eLeonard F. Richardson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470232880, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 27 May 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e416 pages, Graphs: 33 B\u0026amp;W, 0 Color\u003cbr\u003e24.1 x 16.5 x 2.5 cm, 0.744 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\u003cp\u003e“The book is well-suited for students who have had some basic calculus and linear algebra, as an intermediate step before beginning more advanced topics as measure theory, functional analysis, and the theory of differential equations.”  (\u003ci\u003eBull Belg Math Soc\u003c\/i\u003e, 1 July 2010)\u003c\/p\u003e \u003cp\u003e\"This is an excellent book, well worth considering for a textbook for an undergraduate analysis course.\" (\u003ci\u003eMAA Reviews July, 2008)\u003c\/i\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eFeatures an introduction to advanced calculus and highlights its inherent concepts from linear algebra  \u003cp\u003e\u003ci\u003eAdvanced Calculus\u003c\/i\u003e reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis.\u003c\/p\u003e \u003cp\u003eFollowing an introduction dedicated to writing proofs, the book is divided into three parts:\u003c\/p\u003e \u003cp\u003ePart One explores foundational one-variable calculus topics from the viewpoint of linear spaces, norms, completeness, and linear functionals.\u003c\/p\u003e \u003cp\u003ePart Two covers Fourier series and Stieltjes integration, which are advanced one-variable topics.\u003c\/p\u003e \u003cp\u003ePart Three is dedicated to multivariable advanced calculus, including inverse and implicit function theorems and Jacobian theorems for multiple integrals.\u003c\/p\u003e \u003cp\u003eNumerous exercises guide readers through the creation of their own proofs, and they also put newly learned methods into practice. In addition, a \"Test Yourself\" section at the end of each chapter consists of short questions that reinforce the understanding of basic concepts and theorems. The answers to these questions and other selected exercises can be found at the end of the book along with an appendix that outlines key terms and symbols from set theory.\u003c\/p\u003e \u003cp\u003eGuiding readers from the study of the topology of the real line to the beginning theorems and concepts of graduate analysis, \u003ci\u003eAdvanced Calculus\u003c\/i\u003e is an ideal text for courses in advanced calculus and introductory analysis at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for engineers, scientists, and mathematicians.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface.  \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003eIntroduction.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I. ADVANCED CALCULUS IN ONE VARIABLE.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1. Real Numbers and Limits of Sequences.\u003c\/p\u003e \u003cp\u003e2. Continuous Functions.\u003c\/p\u003e \u003cp\u003e3. Rieman Integral.\u003c\/p\u003e \u003cp\u003e4. The Derivative.\u003c\/p\u003e \u003cp\u003e5. Infinite Series.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II. ADVANCED TOPICS IN ONE VARIABLE.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6. Fourier Series.\u003c\/p\u003e \u003cp\u003e7. The Riemann-Stieltjes Integral.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III. ADVANCED CALCULUS IN SEVERAL VARIABLES.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8. Euclidean Space.\u003c\/p\u003e \u003cp\u003e9. Continuous Functions on Euclidean Space.\u003c\/p\u003e \u003cp\u003e10. The Derivative in Euclidean Space.\u003c\/p\u003e \u003cp\u003e11. Riemann Integration in Euclidean Space.\u003c\/p\u003e \u003cp\u003eAppendix A. Set Theory.\u003c\/p\u003e \u003cp\u003eProblem Solutions.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e\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-Interscience","offers":[{"title":"Brand New","offer_id":52257218199832,"sku":"9780470232880","price":95.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470232880.jpg?v=1781278034","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/advanced-calculus-an-introduction-to-linear-analysis-hardback-9780470232880","provider":"Freshly Printed Books","version":"1.0","type":"link"}