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Guide to Analysis by F. Mary Hart


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Guide to Analysis written by F. Mary Hart, Department of Pure Mathematics, University of Sheffield . This is an other book of mathematics cover the following topics.


  • Editor's foreword
    Preface
    Glossary of symbols and notation

  • 1. NUMBERS AND NUMBER SYSTEMS
    1.1 Natural numbers
    1.2 Integers
    1.3 Rational numbers
    1.4 The real number system
    Appendix: Mathematical induction

  • 2. SEQUENCES
    2.1 Introduction
    2.2 Sequences
    2.3 Standard limits
    2.4 Some general results for sequences
    2.5 Subsequences
    Appendix: Triangle inequal

  • 3. INFINITE SERIES
    3.1 Introduction
    3.2 Series and notation
    3.3 Tests for convergence
    3.4 Absolute convergence, rearrangement of series, multiplication of series
    Appendix
    Tests for convergence-summary

  • 4. FUNCTIONS Limits of functions, continuous functions
    4.1 Limits offunctions
    4.2 Continuity
    4.3 Some properties of continuous functions on closed intervals

  • 5. DIFFERENTIABLE FUNCTIONS Dilferentiable functions, Rolle's theorem, mean value theorem, Taylor's theorem, I'Hopital's rule, maxima and minima, Taylor series
    5.1 Differentiation
    5.2 Rolle's theorem and the mean value theorem
    5.3 Taylor's theorem
    5.4 L'Hopital's rule
    5.5 Maxima and minima

  • Index

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