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A Course in Mathematical Analysis (3 Volume Set)

D.J.H. Garling

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Description:Three volumes that provide a full and detailed account of all those elements of real and complex analysis an undergraduate mathematics student can expect to encounter in the first two or three years of study. Numerous exercises, examples and applications are included.D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge and Fellow of St John's College, Cambridge. He has fifty years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.ContentsIntroductionPart One - Prologue: The foundations of analysis1 - The axioms of set theory2 - Number systemsPart Two - Functions of a real variable3 - Convergent sequences4 - Infinite series5 - The topology of R6 - Continuity7 - Differentiation8 - Integration9 - Introduction to Fourier series10 - Some applicationsAppendix A - Zorn's lemma and the well-ordering principleIndexIntroductionPart Three - Metric and topological spaces11 - Metric spaces and normed spaces12 - Convergence, continuity and topology13 - Topological spaces14 - Completeness15 - Compactness16 - ConnectednessPart Four - Functions of a vector variable17 - Differentiating functions of a vector variable18 - Integrating functions of several variables19 - Differential manifolds in Euclidean spaceAppendix B - Linear AlgebraAppendix C - Exterior algebras and the cross productAppendix D - Tychonoff's theoremIndexIntroductionPart Five - Complex Analysis20 - Holomorphic functions and analytic functions21 - The topology of the complex plane22 - Complex integration23 - Zeros and singularities24 - The calculus of residues25 - Conformal transformations26 - ApplicationsPart Six - Measure and Integration27 - Lebesgue measure on R28 - Measurable spaces and measurable functions29 - Integration30 - Constructing measures31 - Signed measures and complex measures32 - Measures on metric spaces33 - Differentiation34 - ApplicationsIndexWe have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with A Course in Mathematical Analysis (3 Volume Set). To get started finding A Course in Mathematical Analysis (3 Volume Set), you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 986

Format: PDF, EPUB & Kindle Edition

Publisher: Cambridge University Press

Release: 2014

ISBN

Description: Three volumes that provide a full and detailed account of all those elements of real and complex analysis an undergraduate mathematics student can expect to encounter in the first two or three years of study. Numerous exercises, examples and applications are included.D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge and Fellow of St John's College, Cambridge. He has fifty years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.ContentsIntroductionPart One - Prologue: The foundations of analysis1 - The axioms of set theory2 - Number systemsPart Two - Functions of a real variable3 - Convergent sequences4 - Infinite series5 - The topology of R6 - Continuity7 - Differentiation8 - Integration9 - Introduction to Fourier series10 - Some applicationsAppendix A - Zorn's lemma and the well-ordering principleIndexIntroductionPart Three - Metric and topological spaces11 - Metric spaces and normed spaces12 - Convergence, continuity and topology13 - Topological spaces14 - Completeness15 - Compactness16 - ConnectednessPart Four - Functions of a vector variable17 - Differentiating functions of a vector variable18 - Integrating functions of several variables19 - Differential manifolds in Euclidean spaceAppendix B - Linear AlgebraAppendix C - Exterior algebras and the cross productAppendix D - Tychonoff's theoremIndexIntroductionPart Five - Complex Analysis20 - Holomorphic functions and analytic functions21 - The topology of the complex plane22 - Complex integration23 - Zeros and singularities24 - The calculus of residues25 - Conformal transformations26 - ApplicationsPart Six - Measure and Integration27 - Lebesgue measure on R28 - Measurable spaces and measurable functions29 - Integration30 - Constructing measures31 - Signed measures and complex measures32 - Measures on metric spaces33 - Differentiation34 - ApplicationsIndexWe have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with A Course in Mathematical Analysis (3 Volume Set). To get started finding A Course in Mathematical Analysis (3 Volume Set), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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A Course in Mathematical Analysis (3 Volume Set)

A Course in Mathematical Analysis (3 Volume Set)

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