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A Course in Mathematical Analysis

A Course in Mathematical Analysis
3 Volume Set

$360.00 (P)

  • Date Published: June 2016
  • availability: In stock
  • format: Multiple copy pack
  • isbn: 9781107625341

$ 360.00 (P)
Multiple copy pack

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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 the 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 instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. Volume 2 goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. Volume 3 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 850 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: June 2016
    • format: Multiple copy pack
    • isbn: 9781107625341
    • length: 986 pages
    • dimensions: 252 x 177 x 68 mm
    • weight: 2.22kg
    • contains: 55 b/w illus. 890 exercises
    • availability: In stock
  • Table of Contents

    Volume 1: Introduction
    Part I. Prologue: The Foundations of Analysis:
    1. The axioms of set theory
    2. Number systems
    Part II. Functions of a Real Variable:
    3. Convergent sequences
    4. Infinite series
    5. The topology of R
    6. Continuity
    7. Differentiation
    8. Integration
    9. Introduction to Fourier series
    10. Some applications
    Appendix: Zorn's lemma and the well-ordering principle
    Index. Volume 2: 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. Volume 3: Introduction
    Part I. Complex Analysis:
    1. Holomorphic functions and analytic functions
    2. The topology of the complex plane
    3. Complex integration
    4. Zeros and singularities
    5. The calculus of residues
    6. Conformal transformations
    7. Applications
    Part II. Measure and Integration:
    8. Lebesgue measure on R
    9. Measurable spaces and measurable functions
    10. Integration
    11. Constructing measures
    12. Signed measures and complex measures
    13. Measures on metric spaces
    14. Differentiation
    15. Applications
    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 and Fellow of St John's College, Cambridge. He has fifty years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.

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