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A Passage to Modern Analysis By William J. Terrell

A Passage to Modern Analysis by William J. Terrell

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Summary

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.

A Passage to Modern Analysis Summary

A Passage to Modern Analysis by William J. Terrell

A Passage to Modern Analysis is an extremely 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. The examples, problems, and exposition open up a student's intuition but still provide coverage of deep areas of real analysis. A yearlong course from this text provides a solid foundation for further study or application of real analysis at the graduate level.

A Passage to Modern Analysis is grounded solidly in the analysis of $\\mathbf{R}$ and $\\mathbf{R}^{n}$, but at appropriate points it introduces and discusses the more general settings of inner product spaces, normed spaces, and metric spaces. The last five chapters offer a bridge to fundamental topics in advanced areas such as ordinary differential equations, Fourier series and partial differential equations, Lebesgue measure and the Lebesgue integral, and Hilbert space. Thus, the book introduces interesting and useful developments beyond Euclidean space where the concepts of analysis play important roles, and it prepares readers for further study of those developments.

About William J. Terrell

William J. Terrell, Virginia Commonwealth University, Richmond, VA.

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.

    Additional information

    NGR9781470451356
    9781470451356
    1470451352
    A Passage to Modern Analysis by William J. Terrell
    New
    Hardback
    American Mathematical Society
    20200630
    607
    null null null null null null null null null null
    Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
    This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

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