Complex analysis / Joseph Bak, Donald J. Newman

Includes bibliographical references (page 290) and index

"This unusual and lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications, and shows the reader how to harness its powerful techniques. Complex Analysis offers new and interesting motivations for classical results and introduces related topics which have not appeared in this form in the past. Stressing motivation and technique, and complete with exercise sets, this volume may be used both as a basic text and as a reference."--Jacket

1. The Complex Numbers -- 2. Functions of the Complex Variable z -- 3. Analytic Functions -- 4. Line Integrals and Entire Functions -- 5. Properties of Entire Functions -- 6. Properties of Analytic Functions -- 7. Further Properties of Analytic Functions -- 8. Simply Connected Domains -- 9. Isolated Singularities of an Analytic Function -- 10. The Residue Theorem -- 11. Applications of The Residue Theorem to the Evaluation of Integrals Sums -- 12. Further Contour Integral Techniques -- 13. Introduction to Conformal Mapping -- 14. The Riemann Mapping Theorem -- 15. Maximum-Modulus Theorems for Unbounded Domains -- 16. Harmonic Functions -- 17. Different Forms of Analytic Functions -- 18. Analytic Continuation; The Gamma and Zeta Functions -- 19. Applications to Other Areas of Mathematics -- App. I.A Note on Simply Connected Regions -- App. II. Circulation and Flux as Contour Integrals -- App. III. Steady-State Temperatures; The Heat Equation -- App. IV. Tchebychev Estimates