Description

Book Synopsis
A well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an especially good balance between depth of coverage and accessible exposition.

Table of Contents
  • Sets and functions
  • The complete ordered field of real numbers
  • Basic theory of series
  • Basic topology, limits, and continuity
  • The derivative
  • The Riemann integral
  • Sequences and series of functions
  • The metric space ${\bf R}^n$
  • Metric spaces and completeness
  • Differentiation in ${\bf R}^n$
  • The inverse and implicit function theorems
  • The Riemann integral in Euclidean space
  • Transformation of integrals
  • Ordinary differential equations
  • The Dirichlet problem and Fourier series
  • Measure theory and Lebesgue measure
  • The Lebesgue integral
  • Inner product spaces and Fourier series
  • The Schroeder-Bernstein theorem
  • Symbols and notations
  • Bibliography
  • Index.

    A Passage to Modern Analysis

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      A Hardback by William J. Terrell

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        Book details

        Publisher American Mathematical Society
        Published 6/30/2020 12:00:00 AM
        ISBN-13 9781470451356
        978-1470451356
        ISBN-10 1470451352

        Description

        Book Synopsis
        A well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an especially good balance between depth of coverage and accessible exposition.

        Table of Contents
        • Sets and functions
        • The complete ordered field of real numbers
        • Basic theory of series
        • Basic topology, limits, and continuity
        • The derivative
        • The Riemann integral
        • Sequences and series of functions
        • The metric space ${\bf R}^n$
        • Metric spaces and completeness
        • Differentiation in ${\bf R}^n$
        • The inverse and implicit function theorems
        • The Riemann integral in Euclidean space
        • Transformation of integrals
        • Ordinary differential equations
        • The Dirichlet problem and Fourier series
        • Measure theory and Lebesgue measure
        • The Lebesgue integral
        • Inner product spaces and Fourier series
        • The Schroeder-Bernstein theorem
        • Symbols and notations
        • Bibliography
        • Index.

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