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A Course in Mathematical Analysis

Volume 2. Metric and Topological Spaces, Functions of a Vector Variable

$57.99 (P)

  • Date Published: March 2014
  • availability: In stock
  • format: Paperback
  • isbn: 9781107675322

$ 57.99 (P)
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  • The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume I focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume III covers complex analysis and the theory of measure and integration.

    • Developed from the author's own undergraduate courses taught at the University of Cambridge
    • Over 250 exercises challenge the reader to learn through practice
    • Useful background reading for a wide range of courses in mathematics
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    Product details

    • Date Published: March 2014
    • format: Paperback
    • isbn: 9781107675322
    • length: 336 pages
    • dimensions: 247 x 174 x 18 mm
    • weight: 0.6kg
    • contains: 15 b/w illus. 280 exercises
    • availability: In stock
  • Table of Contents

    Introduction
    Part I. Metric and Topological Spaces:
    1. Metric spaces and normed spaces
    2. Convergence, continuity and topology
    3. Topological spaces
    4. Completeness
    5. Compactness
    6. Connectedness
    Part II. Functions of a Vector Variable:
    7. Differentiating functions of a vector variable
    8. Integrating functions of several variables
    9. Differential manifolds in Euclidean space
    Appendix A. Linear algebra
    Appendix B. Quaternions
    Appendix C. Tychonoff's theorem
    Index.

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    A Course in Mathematical Analysis

    D. J. H. Garling

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  • Author

    D. J. H. Garling, University of Cambridge
    D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge. He has 50 years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.

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