A Course of Modern Analysis

A Course of Modern Analysis
Author E. T. Whittaker and G. N. Watson
Language English
Subject Mathematics
Publisher Cambridge University Press
Publication date
 1902

A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions (colloquially known as Whittaker and Watson) is a landmark textbook on mathematical analysis written by E. T. Whittaker and G. N. Watson, first published by Cambridge University Press in 1902.[1] (The first edition was Whittaker's alone; it was in later editions with Watson that this book is best known.)

Its first, second, third, and the fourth, last edition were published in 1902, 1915, 1920, and 1927, respectively. Since then, it has continuously been reprinted and still in print today.

The book is notable for being the standard reference and textbook for a generation of Cambridge mathematicians including Littlewood and G. H. Hardy. Mary Cartwright studied it as preparation for her final honours on the advice of fellow student V.C. Morton, later Professor of Mathematics at Aberystwyth University.[2] But its reach was much further than just the Cambridge school; André Weil in his obituary of the French mathematician Jean Delsarte noted that Delsarte always had a copy on his desk.[3]

Today, the book retains much of its original appeal.[4] Some idiosyncratic but interesting problems from the salad days of the Cambridge Mathematical Tripos are to be found in the exercises. It is terse, yet readable by the motivated student. It conforms to high standards of mathematical rigour, while compressing much actual formulaic information also.[4]

The book was one of the earliest to use decimal numbering for its sections, an innovation the authors attribute to Giuseppe Peano.[5]

Contents

Below is the contens 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. Linear Differential Equations
  10. 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

See also

References

  1. ↑ Bôcher, Maxime (1904). "Review: A Course of Modern Analysis, by E. T. Whittaker". Bull. Amer. Math. Soc. 10 (7): 351–354. doi:10.1090/s0002-9904-1904-01123-4.
  2. ↑ "Dame Mary Lucy Cartwright". www-history.mcs.st-and.ac.uk. St. Andrews University.
  3. ↑ "Jean Frédéric Auguste Delsarte". www-history.mcs.st-and.ac.uk. St. Andrews University.
  4. 1 2 "A Course of Modern Analysis". cambridge.org. Cambridge University Press.
  5. ↑ Kowalski, E. "Peano paragraphing". blogs.ethz.ch.
  • E. T. Whittaker and G. N. Watson. A Course of Modern Analysis. Cambridge University Press; 4th edition (January 2, 1927). ISBN 0-521-09189-6
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