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An Introduction to Analysis
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Robert C. Gunning

An Introduction to Analysis

Robert C. Gunning

$135

Hardback

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English
Princeton University Press
29 May 2018
Calculus & mathematical analysis
An essential undergraduate textbook on algebra, topology, and calculusAn Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.

With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning-differentiation, the Riemann integral, series, and differential forms and Stokes's theorem-enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.

Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.

Provides a rigorous introduction to calculus in one and several variablesIntroduces students to basic topologyCovers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappingsDiscusses differential forms and Stokes's theorem in n dimensionsAlso covers the Riemann integral, integrability, improper integrals, and series expansions
By:  
Imprint:   Princeton University Press
Country of Publication:   United States
Dimensions:   Height: 254mm,  Width: 178mm, 
Weight:   907g
ISBN:   9780691178790
ISBN 10:   0691178798
Pages:   384
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Preface ix 1 Algebraic Fundamentals 1 1.1 Sets and Numbers 1 1.2 Groups, Rings, and Fields 13 1.3 Vector Spaces 30 2 Topological Fundamentals 62 2.1 Normed Spaces 62 2.2 Metric Spaces 72 2.3 Topological Spaces 87 2.4 Compact Sets 98 3 Mappings 110 3.1 Continuous Mappings 110 3.2 Differentiable Mappings 129 3.3 AnalyticMappings 149 4 Linear Mappings 189 4.1 Endomorphisms 189 4.2 Inner Product Spaces 211 5 Geometry of Mappings 231 5.1 Inverse Mapping Theorem 231 5.2 Implicit Function Theorem 246 5.3 Rank Theorem 255 6 Integration 266 6.1 Riemann Integral 266 6.2 Calculation of Integrals 284 7 Differential Forms 304 7.1 Line Integrals 304 7.2 Differential Forms 318 7.3 Integrals of Differential Forms 338 Index 363 Index of Notation 369

Robert C. Gunning is professor of mathematics at Princeton University. His books include Lectures on Riemann Surfaces and Lectures on ComplexAnalytic Varieties (both Princeton).

Reviews for An Introduction to Analysis

One would expect that this book offers a demanding, sophisticated look at this material, done rapidly and concisely. One would be correct. . . . [F]or very sophisticated honors courses with exceptionally well-prepared students who are prepared to work hard, it would certainly offer a vivid, exciting and informative introduction to this material.---Mark Hunacek, MAA Reviews An excellent and unusual book by an esteemed mathematician and teacher. An Introduction to Analysis is a uniquely valuable sourcebook for much of undergraduate mathematics. --John B. Garnett, University of California, Los Angeles A valuable, wonderful book. --Camil Muscalu, Cornell University Gunning's book is a great introduction to analysis that presents precisely what an honors analysis course should include. The writing is rigorous but lively, and much interesting mathematics is packed in it. --Wilhelm Schlag, University of Chicago


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