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
Edmund T. Whittaker and
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,^{
[2]} 1915,^{
[3]} 1920,^{
[4]} and 1927,^{
[5]} respectively. Since then, it has continuously been reprinted and is still in print today.^{
[5]}^{
[6]} A revised, expanded and
digitally reset fifth edition, edited by
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
Littlewood and
Godfrey H. Hardy.
Mary L. Cartwright studied it as preparation for her final honours on the advice of fellow student
Vernon C. Morton, later Professor of Mathematics at
Aberystwyth University.^{
[8]} 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.^{
[9]} In 1941 the book was included among a "selected list" of mathematical analysis books for use in universities in an article for that purpose published by
American Mathematical Monthly.^{
[10]}
Notable features
Some idiosyncratic but interesting problems from an older era of the
Cambridge Mathematical Tripos are in the exercises.
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.
Jourdain, Philip E. B. (1916-01-01). "(1) A Course of Pure Mathematics. By G. H. Hardy. Cambridge University Press, 1908. Pp. xvi, 428. Cloth, 12s. net. (2) A Course of Pure Mathematics. By G. H. Hardy. Second edition. Cambridge University Press, 1914. Pp. xii, 443. Cloth, 12s. net. (3) 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. By E. T. Whittaker. Cambridge University Press, 1902. Pp. xvi, 378. Cloth, 12s. 6d. net. (4) 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. Second edition, completely revised. By E. T. Whittaker and G. N. Watson. Cambridge University Press, 1915. Pp. viii, 560. Cloth, 18s. net". VI. Critical Notices. Mind (review). XXV (4): 525–533.
doi:
10.1093/mind/XXV.4.525.
ISSN0026-4423.
JSTOR2248860. (9 pages)
Φ (1916). "Review of 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. Second edition, completely revised". The Monist (review). 26 (4): 639–640.
ISSN0026-9662.
JSTOR27900617. (2 pages)
"Review of A Course of Modern Analysis. An Introduction to the General Theory of Infinite Processes and of Analytical Functions, with an Account of the Principal Transcendental Functions. Second Edition". Science Progress (1916–1919) (review).
Sage Publications, Inc.11 (41): 160–161. 1916.
ISSN2059-495X.
JSTOR43426733. (2 pages)
"Review of A Course of Modern Analysis: An introduction to the General Theory of Infinite Processes and of Analytical Functions; With an Account of the Principal Transcendental Functions". The Mathematical Gazette (review). 8 (124): 306–307. 1916.
doi:
10.2307/3604810.
ISSN0025-5572.
JSTOR3604810.
S2CID40238008. (2 pages)
Schubert, A. (1963). "E. T. Whittaker and G. N. Watson, 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. Fourth Edition. 608 S. Cambridge 1962. Cambridge University Press. Preis brosch. 27/6 net". ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (review). 43 (9): 435.
Bibcode:
1963ZaMM...43R.435S.
doi:
10.1002/zamm.19630430916.
ISSN1521-4001. (1 page)