A Course of Modern Analysis

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A Course of Modern Analysis
George N. Watson
LanguageEnglish
SubjectMathematics
PublisherCambridge University Press
Publication date
1902
Title page for the third edition of the book.

A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal

George N. Watson, first published by Cambridge University Press in 1902.[1]
The first edition was Whittaker's alone, but later editions were co-authored with Watson.

History

Its first, second, third, and the fourth edition were published in 1902,

Victor H. Moll, was published in 2021.[7]

The book is notable for being the standard reference and textbook for a generation of Cambridge mathematicians including

American Mathematical Monthly.[10]

Notable features

Some idiosyncratic but interesting problems from an older era of the

Cambridge Mathematical Tripos
are in the exercises.

The book was one of the earliest to use

decimal numbering for its sections, an innovation the authors attribute to Giuseppe Peano.[11]

Contents

Below are the contents of the fourth edition:

Part I. The Process of Analysis
  1. Complex Numbers
  2. The Theory of Convergence
  3. Continuous Functions and Uniform Convergence
  4. The Theory of Riemann Integration
  5. The fundamental properties of Analytic Functions; Taylor's, Laurent's, and Liouville's Theorems
  6. The Theory of Residues; application to the evaluation of Definite Integrals
  7. The expansion of functions in Infinite Series
  8. Asymptotic Expansions and Summable Series
  9. Fourier Series and Trigonometrical Series
  10. Linear Differential Equations
  11. Integral Equations
Part II. The Transcendental Functions
  1. The Gamma Function
  2. The Zeta Function of Riemann
  3. The Hypergeometric Function
  4. Legendre Functions
  5. The Confluent Hypergeometric Function
  6. Bessel Functions
  7. The Equations of Mathematical Physics
  8. Mathieu Functions
  9. Elliptic Functions. General theorems and the Weierstrassian Functions
  10. The Theta Functions
  11. The Jacobian Elliptic Functions
  12. Ellipsoidal Harmonics and Lamé's Equation

Reception

Reviews of the first edition

Bessel functions, elliptic functions, and mathematical physics
.

infinite series are "considered in all their phases" along with "all those important series and functions" developed by mathematicians such as Joseph Fourier, Friedrich Bessel, Joseph-Louis Lagrange, Adrien-Marie Legendre, Pierre-Simon Laplace, Carl Friedrich Gauss, Niels Henrik Abel, and others in their respective studies of "practice problems".[13] He goes on to say it "is a useful book for those who wish to make use of the most advanced developments of mathematical analysis in theoretical investigations of physical and chemical questions."[13]

In a third review of the first edition, Maxime Bôcher, in a 1904 review published in the Bulletin of the American Mathematical Society notes that while the book falls short of the "rigor" of French, German, and Italian writers, it is a "gratifying sign of progress to find in an English book such an attempt at rigorous treatment as is here made".[1] He notes that important parts of the book were otherwise non-existent in the English language.

See also

References

  1. ^
    doi:10.1090/s0002-9904-1904-01123-4
    . (4 pages)
  2. OCLC 1072208628
    . (xvi+378 pages)
  3. OCLC 474155529
    . (viii+560 pages)
  4. OCLC 1170617940
    .
  5. ^
    ISBN 978-0-521-06794-2
    . (vi+608 pages) (reprinted: 1935, 1940, 1946, 1950, 1952, 1958, 1962, 1963, 1992)
  6. ISBN 0-521-58807-3. (reprinted: 1999, 2000, 2002, 2010) [1]
  7. ISBN 1-31651893-0. Archived
    from the original on 2021-08-10. Retrieved 2021-12-26. (700 pages)
  8. St. Andrews University. Archived
    from the original on 2021-03-21. Retrieved 2021-03-21.
  9. St. Andrews University. Archived
    from the original on 2021-03-21. Retrieved 2021-03-21.
  10. JSTOR 2303868
    . (10 pages)
  11. ^ Kowalski, Emmanuel [in German] (2008-06-03). "Peano paragraphing". E. Kowalski's blog - Comments on mathematics, mostly. Archived from the original on 2021-02-25. Retrieved 2021-03-21.
  12. S2CID 221486387
    . (3 pages)
  13. ^
    ISSN 0002-7863
    .

Further reading
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