複素解析の基礎と応用 Fundamentals and Applications of Complex Analysis

Cohen, Harold

Kluwer Academic / Plenum Publishers（2003/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 440 p.
• 言語 ENG
• 商品コード 9780306477485
• DDC分類 515.9

Full Description

This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts.

Contents

Introduction.- Complex Numbers.- Complex Variables.- Series, Limits and Residues.- Evaluation of Integrals.- Multivalued Functions, Branch Points and Cuts.- Conformal Mapping.- Dispersion Relations.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- Appendix 5.- References.- Index.