Complex Integration and Cauchy's Theorem

This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.
Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the evaluation of definite integrals, and expansions in series. A historical summary concludes the text, which is supplemented by numerous challenging exercises.

English mathematician George Neville Watson (1886–1965) was a Fellow of Trinity College, Cambridge, and a Professor at the University of Birmingham from 1918 to 1951.

Preface Introduction I. Analysis Situs II. Complex Integration III. Cauchy's Theorem IV. Miscellaneous Theorems V. The Calculus of Residues VI. The Evaluation of Definite Integrals VII. Expansions in Series VIII. Historical Summary