Principles of mathematical analysis

書誌事項

Principles of mathematical analysis

Walter Rudin

(International series in pure and applied mathematics)

McGraw-Hill Kogakusha, c1976

3rd ed., international student ed

  • : pbk

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注記

Bibliography: p. [335]-336

Includes index

内容説明・目次

内容説明

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. (Dedekind's 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.

目次

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 DerivativesL'Hospital's RuleDerivatives of Higher-OrderTaylor's 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

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詳細情報

  • NII書誌ID(NCID)
    BB00412042
  • ISBN
    • 007054235X
  • LCCN
    75017903
  • 出版国コード
    ja
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Tokyo
  • ページ数/冊数
    x, 342 p.
  • 大きさ
    21 cm
  • 分類
  • 件名
  • 親書誌ID
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