G. N. Watson

Complex Integration and Cauchy's Theorem (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

Produktdetails

• Verlag: Dover Publications
• Erscheinungstermin: 13. Mai 2013
• Englisch
• ISBN-13: 9780486283562
• Artikelnr.: 39550071

Inhaltsangabe

Introduction
1. Analysis situs
2. Complex integration
3. Cauchy's theorem
4. Miscellaneous theorems
5. The calculus of residues
6. The evaluation of definite integrals
7. Expansions in series
8. Historical summary.