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  • Textbook
  • © 2002

Real Mathematical Analysis

Authors:

  1. Charles Chapman Pugh

    1. Mathematics Department, University of California at Berkeley, Berkeley, USA

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  • The exposition is informal and relaxed, with many helpful asides, and examples
  • Contains an excellent selection of more than 500 exercises
  • Ideal for self-study

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
    PDF

  2. Real Numbers

    • Charles Chapman Pugh
    Pages 1-50

  3. A Taste of Topology

    • Charles Chapman Pugh
    Pages 51-137

  4. Functions of a Real Variable

    • Charles Chapman Pugh
    Pages 139-200

  5. Function Spaces

    • Charles Chapman Pugh
    Pages 201-266

  6. Multivariable Calculus

    • Charles Chapman Pugh
    Pages 267-361

  7. Lebesgue Theory

    • Charles Chapman Pugh
    Pages 363-429

  8. Back Matter

    Pages 431-440
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About this book

Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE's . . . . . . . . 228 5 6* Analytic Functions . . . . . . . . . . . 235 7* Nowhere Differentiable Continuous Functions . 240 8* Spaces of Unbounded Functions 248 Exercises . . . . . 251 267 5 Multivariable Calculus 1 Linear Algebra . . 267 2 Derivatives. . . . 271 3 Higher derivatives . 279 4 Smoothness Classes . 284 5 Implicit and Inverse Functions 286 290 6* The Rank Theorem 296 7* Lagrange Multipliers 8 Multiple Integrals . .
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Keywords

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Authors and Affiliations

  • Mathematics Department, University of California at Berkeley, Berkeley, USA

    Charles Chapman Pugh

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About the author



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Bibliographic Information

  • Book Title: Real Mathematical Analysis

  • Authors: Charles Chapman Pugh

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-0-387-21684-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2002

  • Softcover ISBN: 978-1-4419-2941-9Published: 01 December 2010

  • eBook ISBN: 978-0-387-21684-3Published: 19 March 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XII, 440

  • Topics: Real Functions

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Buy it now

eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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