Introduction to Analysis, Global Edition

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William Wade, William R. Wade

Introduction to Analysis, Global Edition

Paperback Engels 2021 9781292357874

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This title is a Pearson Global Edition. The Editorial team at Pearson has workedclosely with educators around the world to include content which is especiallyrelevant to students outside the United States.

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 and ordinarydifferential equations, numerical analysis, fluid mechanics, and differentialgeometry. This book is designed to challenge advanced students whileencouraging and helping weaker students. Offering readability, practicality andflexibility, Wade presents fundamental theorems and ideas from a practicalviewpoint, showing students the motivation behind the mathematics and enablingthem to construct their own proofs.

Pearson MyLab Math is not included. Students, if MyLab Math is arecommended/mandatory component of the course, please ask your instructor forthe correct ISBN. MyLab Math should only be purchased when required by aninstructor. Instructors, contact your Pearson representative for moreinformation.

Specificaties

ISBN13:9781292357874

Taal:Engels

Bindwijze:Paperback

Uitgever:Pearson Education

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Inhoudsopgave

Part I. ONE-DIMENSIONALTHEORY <o:p></o:p> 1. The Real Number System 1.1 Introduction <o:p></o:p> 1.2 Ordered field axioms <o:p></o:p> 1.3 Completeness Axiom <o:p></o:p> 1.4 Mathematical Induction <o:p></o:p> 1.5 Inverse functions and images <o:p></o:p> 1.6 Countable and uncountable sets <o:p></o:p>   <o:p></o:p> 2. Sequences in R <o:p></o:p> 2.1 Limits of sequences <o:p></o:p> 2.2 Limit theorems <o:p></o:p> 2.3 Bolzano-Weierstrass Theorem <o:p></o:p> 2.4 Cauchy sequences <o:p></o:p> *2.5 Limits supremum and infimum  3. Functions on R <o:p></o:p> 3.1 Two-sided limits <o:p></o:p> 3.2 One-sided limits and limits atinfinity <o:p></o:p> 3.3 Continuity <o:p></o:p> 3.4 Uniform continuity <o:p></o:p>   <o:p></o:p> 4. Differentiability on R <o:p></o:p> 4.1 The derivative <o:p></o:p> 4.2 Differentiability theorems <o:p></o:p> 4.3 The Mean Value Theorem <o:p></o:p> 4.4 Taylor's Theorem and l'Hôpital'sRule <o:p></o:p> 4.5 Inverse function theorems  5 Integrability on R <o:p></o:p> 5.1 The Riemann integral <o:p></o:p> 5.2 Riemann sums <o:p></o:p> 5.3 The Fundamental Theorem ofCalculus <o:p></o:p> 5.4 Improper Riemann integration <o:p></o:p> *5.5 Functions of boundedvariation <o:p></o:p> *5.6 Convex functions  6. Infinite Series of Real Numbers <o:p></o:p> 6.1 Introduction <o:p></o:p> 6.2 Series with nonnegative terms <o:p></o:p> 6.3 Absolute convergence <o:p></o:p> 6.4 Alternating series <o:p></o:p> *6.5 Estimation of series <o:p></o:p> *6.6 Additional tests  7. Infinite Series of Functions <o:p></o:p> 7.1 Uniform convergence ofsequences <o:p></o:p> 7.2 Uniform convergence of series <o:p></o:p> 7.3 Power series <o:p></o:p> 7.4 Analytic functions <o:p></o:p> *7.5 Applications  Part II. MULTIDIMENSIONAL THEORY  8. Euclidean Spaces <o:p></o:p> 8.1 Algebraic structure <o:p></o:p> 8.2 Planes and lineartransformations <o:p></o:p> 8.3 Topology of Rn <o:p></o:p> 8.4 Interior, closure, and boundary  9. Convergence in Rn <o:p></o:p> 9.1 Limits of sequences <o:p></o:p> 9.2 Heine-Borel Theorem <o:p></o:p> 9.3 Limits of functions <o:p></o:p> 9.4 Continuous functions <o:p></o:p> *9.5 Compact sets <o:p></o:p> *9.6 Applications  10. Metric Spaces <o:p></o:p> 10.1 Introduction <o:p></o:p> 10.2 Limits of functions <o:p></o:p> 10.3 Interior, closure, boundary <o:p></o:p> 10.4 Compact sets <o:p></o:p> 10.5 Connected sets <o:p></o:p> 10.6 Continuous functions <o:p></o:p> 10.7 Stone-Weierstrass Theorem  11. Differentiability on Rn <o:p></o:p> 11.1 Partial derivatives andpartial integrals <o:p></o:p> 11.2 The definition ofdifferentiability <o:p></o:p> 11.3 Derivatives, differentials, andtangent planes <o:p></o:p> 11.4 The Chain Rule <o:p></o:p> 11.5 The Mean Value Theorem andTaylor's Formula <o:p></o:p> 11.6 The Inverse Function Theorem <o:p></o:p> *11.7 Optimization  12. Integration on Rn <o:p></o:p> 12.1 Jordan regions <o:p></o:p> 12.2 Riemann integration on Jordanregions <o:p></o:p> 12.3 Iterated integrals <o:p></o:p> 12.4 Change of variables <o:p></o:p> *12.5 Partitions of unity <o:p></o:p> *12.6 The gamma function andvolume  13. Fundamental Theorems of VectorCalculus <o:p></o:p> 13.1 Curves <o:p></o:p> 13.2 Oriented curves <o:p></o:p> 13.3 Surfaces <o:p></o:p> 13.4 Oriented surfaces <o:p></o:p> 13.5 Theorems of Green and Gauss <o:p></o:p> 13.6 Stokes's Theorem  *14. Fourier Series <o:p></o:p> *14.1 Introduction <o:p></o:p> *14.2 Summability of Fourierseries <o:p></o:p> *14.3 Growth of Fouriercoefficients <o:p></o:p> *14.4 Convergence of Fourierseries <o:p></o:p> *14.5 Uniqueness  Appendices <o:p></o:p> A. Algebraic laws <o:p></o:p> B. Trigonometry <o:p></o:p> C. Matrices and determinants <o:p></o:p> D. Quadric surfaces <o:p></o:p> E. Vector calculus and physics <o:p></o:p> F. Equivalence relations  References <o:p></o:p> Answers and Hints to Selected Exercises <o:p></o:p> Subject Index <o:p></o:p> Notation Index  *Enrichment section <o:p></o:p> <o:p>   </o:p>

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