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Advanced Mathematical Analysis

Periodic Functions and Distributions, Complex Analysis, Laplace Transform and Applications

  • Textbook
  • © 1973

Overview

Authors:
  1. Richard Beals

    1. Department of Mathematics, University of Chicago, Chicago, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 12)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
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  2. Basic Concepts

    • Richard Beals
    Pages 1-33

  3. Continuous Functions

    • Richard Beals
    Pages 34-68

  4. Periodic Functions and Periodic Distributions

    • Richard Beals
    Pages 69-102

  5. Hilbert Spaces and Fourier Series

    • Richard Beals
    Pages 103-130

  6. Applications of Fourier Series

    • Richard Beals
    Pages 131-154

  7. Complex Analysis

    • Richard Beals
    Pages 155-189

  8. The Laplace Transform

    • Richard Beals
    Pages 190-222

  9. Back Matter

    Pages 223-232
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Keywords

About this book

Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for science and engi­ neering" from what might be called "advanced mathematical analysis for mathematicians." It seems to me both useful and timely to attempt a reconciliation. The separation between kinds of courses has unhealthy effects. Mathe­ matics students reverse the historical development of analysis, learning the unifying abstractions first and the examples later (if ever). Science students learn the examples as taught generations ago, missing modern insights. A choice between encountering Fourier series as a minor instance of the repre­ sentation theory of Banach algebras, and encountering Fourier series in isolation and developed in an ad hoc manner, is no choice at all. It is easy to recognize these problems, but less easy to counter the legiti­ mate pressures which have led to a separation. Modern mathematics has broadened our perspectives by abstraction and bold generalization, while developing techniques which can treat classical theories in a definitive way. On the other hand, the applier of mathematics has continued to need a variety of definite tools and has not had the time to acquire the broadest and most definitive grasp-to learn necessary and sufficient conditions when simple sufficient conditions will serve, or to learn the general framework encompass­ ing different examples.

Authors and Affiliations

  • Department of Mathematics, University of Chicago, Chicago, USA

    Richard Beals

Bibliographic Information

  • Book Title: Advanced Mathematical Analysis

  • Book Subtitle: Periodic Functions and Distributions, Complex Analysis, Laplace Transform and Applications

  • Authors: Richard Beals

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9886-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1973

  • Hardcover ISBN: 978-0-387-90065-0Published: 26 December 1973

  • Softcover ISBN: 978-0-387-90066-7Published: 26 December 1973

  • eBook ISBN: 978-1-4684-9886-8Published: 01 December 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 234

  • Topics: Mathematics, general

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