{"product_id":"fundamental-ideas-of-analysis-paperback-softback-9780471159964","title":"Fundamental Ideas of Analysis (Paperback \/ softback) 9780471159964","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFundamental Ideas of Analysis\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\"\u003eMichael C. Reed (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780471159964, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 24 November 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e432 pages\u003cbr\u003e25.8 x 18.4 x 2.4 cm, 0.88 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Preliminaries 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Real Numbers 1\u003c\/p\u003e \u003cp\u003eSets and Functions 6\u003c\/p\u003e \u003cp\u003eCardinality 15\u003c\/p\u003e \u003cp\u003eMethods of Proof 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Sequences 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eConvergence 27\u003c\/p\u003e \u003cp\u003eLimit Theorems 35\u003c\/p\u003e \u003cp\u003eTwo-state Markov Chains 40\u003c\/p\u003e \u003cp\u003eCauchy Sequences 44\u003c\/p\u003e \u003cp\u003eSupremum and Infimum 52\u003c\/p\u003e \u003cp\u003eThe Bolzano-Weierstrass Theorem 55\u003c\/p\u003e \u003cp\u003eThe Quadratic Map 60\u003c\/p\u003e \u003cp\u003eProjects 68\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 The Riemann Integral 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eContinuity 73\u003c\/p\u003e \u003cp\u003eContinuous Functions on Closed Intervals 80\u003c\/p\u003e \u003cp\u003eThe Riemann Integral 87\u003c\/p\u003e \u003cp\u003eNumerical Methods 95\u003c\/p\u003e \u003cp\u003eDiscontinuities 103\u003c\/p\u003e \u003cp\u003eImproper Integrals 113\u003c\/p\u003e \u003cp\u003eProjects 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Differentiation 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDifferentiable Functions 121\u003c\/p\u003e \u003cp\u003eThe Fundamental Theorem of Calculus  129\u003c\/p\u003e \u003cp\u003eTaylor’s Theorem 134\u003c\/p\u003e \u003cp\u003eNewton’s Method 140\u003c\/p\u003e \u003cp\u003eInverse Functions 147\u003c\/p\u003e \u003cp\u003eFunctions of Two Variables 151\u003c\/p\u003e \u003cp\u003eProjects 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Sequences of Functions 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePointwise and Uniform Convergence 163\u003c\/p\u003e \u003cp\u003eLimit Theorems 169\u003c\/p\u003e \u003cp\u003eThe Supremum Norm 175\u003c\/p\u003e \u003cp\u003eIntegral Equations 183\u003c\/p\u003e \u003cp\u003eThe Calculus of Variations 188\u003c\/p\u003e \u003cp\u003eMetric Spaces 196\u003c\/p\u003e \u003cp\u003eThe Contraction Mapping Principle 203\u003c\/p\u003e \u003cp\u003eNormed Linear Spaces  210\u003c\/p\u003e \u003cp\u003eProjects 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Series of Functions 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLim sup and Lim inf 223\u003c\/p\u003e \u003cp\u003eSeries of Real Constants 228\u003c\/p\u003e \u003cp\u003eThe Weierstrass M-test 238\u003c\/p\u003e \u003cp\u003ePower Series 245\u003c\/p\u003e \u003cp\u003eComplex Numbers 252\u003c\/p\u003e \u003cp\u003eInfinite Products and Prime Numbers 260\u003c\/p\u003e \u003cp\u003eProjects 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Differential Equations 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLocal Existence 273\u003c\/p\u003e \u003cp\u003eGlobal Existence 283\u003c\/p\u003e \u003cp\u003eThe Error Estimate for Euler’s Method 289\u003c\/p\u003e \u003cp\u003eProjects 296\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Complex Analysis 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAnalytic Functions 299\u003c\/p\u003e \u003cp\u003eIntegration on Paths 305\u003c\/p\u003e \u003cp\u003eCauchy's Theorem 312\u003c\/p\u003e \u003cp\u003eProjects 320\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Fourier Series 323\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Heat Equation 323\u003c\/p\u003e \u003cp\u003eDefinitions and Examples 331\u003c\/p\u003e \u003cp\u003ePointwise Convergence 337\u003c\/p\u003e \u003cp\u003eMean-square Convergence 345\u003c\/p\u003e \u003cp\u003eProjects 355\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 Probability Theory 359\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDiscrete Random Variables 359\u003c\/p\u003e \u003cp\u003eCoding Theory 368\u003c\/p\u003e \u003cp\u003eContinuous Random Variables 376\u003c\/p\u003e \u003cp\u003eThe Variation Metric 386\u003c\/p\u003e \u003cp\u003eProjects 398\u003c\/p\u003e \u003cp\u003eBibliography 403\u003c\/p\u003e \u003cp\u003eSymbol Index 406\u003c\/p\u003e \u003cp\u003eIndex 409\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","offers":[{"title":"Brand 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