For 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.
Language
Place of publication
Publishing group
Pearson Education Limited
Dimensions
Height: 235 mm
Width: 178 mm
Thickness: 38 mm
Weight
ISBN-13
978-1-292-35787-4 (9781292357874)
Schweitzer Classification
William 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.
Part I. ONE-DIMENSIONALTHEORY1. The Real Number System1.1 Introduction1.2 Ordered field axioms1.3 Completeness Axiom1.4 Mathematical Induction1.5 Inverse functions and images1.6 Countable and uncountable sets 2. Sequences in R2.1 Limits of sequences2.2 Limit theorems2.3 Bolzano-Weierstrass Theorem2.4 Cauchy sequences*2.5 Limits supremum and infimum 3. Functions on R3.1 Two-sided limits3.2 One-sided limits and limits atinfinity3.3 Continuity3.4 Uniform continuity 4. Differentiability on R4.1 The derivative4.2 Differentiability theorems4.3 The Mean Value Theorem4.4 Taylor's Theorem and l'Hôpital'sRule4.5 Inverse function theorems 5 Integrability on R5.1 The Riemann integral5.2 Riemann sums5.3 The Fundamental Theorem ofCalculus5.4 Improper Riemann integration*5.5 Functions of boundedvariation*5.6 Convex functions 6. Infinite Series of Real Numbers6.1 Introduction6.2 Series with nonnegative terms6.3 Absolute convergence6.4 Alternating series*6.5 Estimation of series*6.6 Additional tests 7. Infinite Series of Functions7.1 Uniform convergence ofsequences7.2 Uniform convergence of series7.3 Power series7.4 Analytic functions*7.5 Applications Part II. MULTIDIMENSIONAL THEORY 8. Euclidean Spaces8.1 Algebraic structure8.2 Planes and lineartransformations8.3 Topology of Rn8.4 Interior, closure, and boundary 9. Convergence in Rn9.1 Limits of sequences9.2 Heine-Borel Theorem9.3 Limits of functions9.4 Continuous functions*9.5 Compact sets*9.6 Applications 10. Metric Spaces10.1 Introduction10.2 Limits of functions10.3 Interior, closure, boundary10.4 Compact sets10.5 Connected sets10.6 Continuous functions10.7 Stone-Weierstrass Theorem 11. Differentiability on Rn11.1 Partial derivatives andpartial integrals11.2 The definition ofdifferentiability11.3 Derivatives, differentials, andtangent planes11.4 The Chain Rule11.5 The Mean Value Theorem andTaylor's Formula11.6 The Inverse Function Theorem*11.7 Optimization 12. Integration on Rn12.1 Jordan regions12.2 Riemann integration on Jordanregions12.3 Iterated integrals12.4 Change of variables*12.5 Partitions of unity*12.6 The gamma function andvolume 13. Fundamental Theorems of VectorCalculus13.1 Curves13.2 Oriented curves13.3 Surfaces13.4 Oriented surfaces13.5 Theorems of Green and Gauss13.6 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 AppendicesA. Algebraic lawsB. TrigonometryC. Matrices and determinantsD. Quadric surfacesE. Vector calculus and physicsF. Equivalence relations ReferencesAnswers and Hints to Selected ExercisesSubject IndexNotation Index *Enrichment section
