Principles of Mathematical Analysis by Walter Rudin (English) Hardcover Book

Description: Principles of Mathematical Analysis by Walter Rudin Part of the Student Series in Advanced Mathematics, this book provides a foundation in mathematical analysis. It begins with a discussion of the real number system as a complete ordered field. It also provides the topological background needed for the development of convergence, continuity, differentiation and integration. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekinds construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.This text is part of the Walter Rudin Student Series in Advanced Mathematics. Table of Contents Chapter 1: The Real and Complex Number SystemsIntroductionOrdered SetsFieldsThe Real FieldThe Extended Real Number SystemThe Complex FieldEuclidean SpacesAppendixExercisesChapter 2: Basic TopologyFinite, Countable, and Uncountable SetsMetric SpacesCompact SetsPerfect SetsConnected SetsExercisesChapter 3: Numerical Sequences and SeriesConvergent SequencesSubsequencesCauchy SequencesUpper and Lower LimitsSome Special SequencesSeriesSeries of Nonnegative TermsThe Number eThe Root and Ratio TestsPower SeriesSummation by PartsAbsolute ConvergenceAddition and Multiplication of SeriesRearrangementsExercisesChapter 4: ContinuityLimits of FunctionsContinuous FunctionsContinuity and CompactnessContinuity and ConnectednessDiscontinuitiesMonotonic FunctionsInfinite Limits and Limits at InfinityExercisesChapter 5: DifferentiationThe Derivative of a Real FunctionMean Value TheoremsThe Continuity of DerivativesLHospitals RuleDerivatives of Higher-OrderTaylors TheoremDifferentiation of Vector-valued FunctionsExercisesChapter 6: The Riemann-Stieltjes IntegralDefinition and Existence of the IntegralProperties of the IntegralIntegration and DifferentiationIntegration of Vector-valued FunctionsRectifiable CurvesExercisesChapter 7: Sequences and Series of FunctionsDiscussion of Main ProblemUniform ConvergenceUniform Convergence and ContinuityUniform Convergence and IntegrationUniform Convergence and DifferentiationEquicontinuous Families of FunctionsThe Stone-Weierstrass TheoremExercisesChapter 8: Some Special FunctionsPower SeriesThe Exponential and Logarithmic FunctionsThe Trigonometric FunctionsThe Algebraic Completeness of the Complex FieldFourier SeriesThe Gamma FunctionExercisesChapter 9: Functions of Several VariablesLinear TransformationsDifferentiationThe Contraction PrincipleThe Inverse Function TheoremThe Implicit Function TheoremThe Rank TheoremDeterminantsDerivatives of Higher OrderDifferentiation of IntegralsExercisesChapter 10: Integration of Differential FormsIntegrationPrimitive MappingsPartitions of UnityChange of VariablesDifferential FormsSimplexes and ChainsStokes TheoremClosed Forms and Exact FormsVector AnalysisExercisesChapter 11: The Lebesgue TheorySet FunctionsConstruction of the Lebesgue MeasureMeasure SpacesMeasurable FunctionsSimple FunctionsIntegrationComparison with the Riemann IntegralIntegration of Complex FunctionsFunctions of Class L2ExercisesBibliographyList of Special SymbolsIndex Description for Bookstore The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekinds construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. Details ISBN007054235X Author Walter Rudin Short Title PRINCIPLES OF MATHEMATICAL ANA Pages 352 Series International Series in Pure & Applied Mathematics Language English Edition 3rd ISBN-10 007054235X ISBN-13 9780070542358 Media Book Format Hardcover DEWEY 515 Year 1976 Place of Publication London Country of Publication United States Birth 1921 Affiliation Univ. of Wisconsin, Madison Death 2010 DOI 10.1604/9780070542358 UK Release Date 1976-02-16 AU Release Date 1976-02-16 NZ Release Date 1976-02-16 US Release Date 1976-02-16 Imprint McGraw Hill Higher Education Publisher McGraw-Hill Education - Europe Edition Description 3rd edition Publication Date 1976-02-16 Audience Tertiary & Higher Education We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:137451710;

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