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OverviewFor one- or two-semester junior orsenior level courses in Advanced Calculus, Analysis I, or Real Analysis. This title is part of the Pearson Modern Classicsseries. This text prepares students for future coursesthat use analytic ideas, such as real and complex analysis, partial andordinary differential equations, numerical analysis, fluid mechanics, anddifferential geometry. This book is designed to challenge advanced studentswhile encouraging and helping weaker students. Offering readability,practicality and flexibility, Wade presents fundamental theorems and ideas froma practical viewpoint, showing students the motivation behind the mathematicsand enabling them to construct their own proofs. Full Product DetailsAuthor: William WadePublisher: Pearson Education Limited Imprint: Pearson Education Limited Edition: 4th edition Dimensions: Width: 17.80cm , Height: 4.00cm , Length: 23.60cm Weight: 1.200kg ISBN: 9781292357874ISBN 10: 1292357878 Pages: 696 Publication Date: 10 December 2021 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Not yet available  This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release. Table of ContentsPart I. ONE-DIMENSIONALTHEORY 1. The Real Number System 1.1 Introduction 1.2 Ordered field axioms 1.3 Completeness Axiom 1.4 Mathematical Induction 1.5 Inverse functions and images 1.6 Countable and uncountable sets 2. Sequences in R 2.1 Limits of sequences 2.2 Limit theorems 2.3 Bolzano-Weierstrass Theorem 2.4 Cauchy sequences *2.5 Limits supremum and infimum 3. Functions on R 3.1 Two-sided limits 3.2 One-sided limits and limits atinfinity 3.3 Continuity 3.4 Uniform continuity 4. Differentiability on R 4.1 The derivative 4.2 Differentiability theorems 4.3 The Mean Value Theorem 4.4 Taylor's Theorem and l'Hôpital'sRule 4.5 Inverse function theorems 5 Integrability on R 5.1 The Riemann integral 5.2 Riemann sums 5.3 The Fundamental Theorem ofCalculus 5.4 Improper Riemann integration *5.5 Functions of boundedvariation *5.6 Convex functions 6. Infinite Series of Real Numbers 6.1 Introduction 6.2 Series with nonnegative terms 6.3 Absolute convergence 6.4 Alternating series *6.5 Estimation of series *6.6 Additional tests 7. Infinite Series of Functions 7.1 Uniform convergence ofsequences 7.2 Uniform convergence of series 7.3 Power series 7.4 Analytic functions *7.5 Applications Part II. MULTIDIMENSIONAL THEORY 8. Euclidean Spaces 8.1 Algebraic structure 8.2 Planes and lineartransformations 8.3 Topology of Rn 8.4 Interior, closure, and boundary 9. Convergence in Rn 9.1 Limits of sequences 9.2 Heine-Borel Theorem 9.3 Limits of functions 9.4 Continuous functions *9.5 Compact sets *9.6 Applications 10. Metric Spaces 10.1 Introduction 10.2 Limits of functions 10.3 Interior, closure, boundary 10.4 Compact sets 10.5 Connected sets 10.6 Continuous functions 10.7 Stone-Weierstrass Theorem 11. Differentiability on Rn 11.1 Partial derivatives andpartial integrals 11.2 The definition ofdifferentiability 11.3 Derivatives, differentials, andtangent planes 11.4 The Chain Rule 11.5 The Mean Value Theorem andTaylor's Formula 11.6 The Inverse Function Theorem *11.7 Optimization 12. Integration on Rn 12.1 Jordan regions 12.2 Riemann integration on Jordanregions 12.3 Iterated integrals 12.4 Change of variables *12.5 Partitions of unity *12.6 The gamma function andvolume 13. Fundamental Theorems of VectorCalculus 13.1 Curves 13.2 Oriented curves 13.3 Surfaces 13.4 Oriented surfaces 13.5 Theorems of Green and Gauss 13.6 Stokes's Theorem *14. Fourier Series *14.1 Introduction *14.2 Summability of Fourierseries *14.3 Growth of Fouriercoefficients *14.4 Convergence of Fourierseries *14.5 Uniqueness Appendices A. Algebraic laws B. Trigonometry C. Matrices and determinants D. Quadric surfaces E. Vector calculus and physics F. Equivalence relations References Answers and Hints to Selected Exercises Subject Index Notation Index *Enrichment sectionReviewsAuthor InformationWilliam Wade received his PhD in harmonic analysis from the University of California—Riverside. He has been a professor of the Department of Mathematics at the University of Tennessee for more than forty years. During that time, he has received multiple awards including two Fulbright Scholarships, the Chancellor's Award for Research and Creative Achievements, the Dean's Award for Extraordinary Service, and the National Alumni Association Outstanding Teaching Award. Wade’s research interests include problems of uniqueness, growth and dyadic harmonic analysis, on which he has published numerous papers, two books and given multiple presentations on three continents. His current publication, An Introduction to Analysis,is now in its fourth edition. In his spare time, Wade loves to travel and take photographs to document his trips. He is also musically inclined, and enjoys playing classical music, mainly baroque on the trumpet, recorder, and piano. Tab Content 6Author Website:Countries AvailableAll regions |
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