COMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown, Ruel V. Churchill

 COMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown, Ruel V. Churchill

    The firrst nine chapters of this book have for many years formed the basis of a three-hour course given each term at The University of Michigan. The classes have consisted mainly of seniors and graduate students concentrating in mathematics, engineering, or one of the physical sciences. Before taking the course, the students have completed at least a three-term calculus sequence and a rst course in ordinary differential equations. Much of the material in the book need not be covered in the lectures and can be left for self-study or used for reference. If mapping by elementary functions is desired earlier in the course, one can skip to Chap. 8 immediately after Chap. 3 on elementary functions. In order to accommodate as wide a range of readers as possible, there are footnotes referring to other texts that give proofs and discussions of the more delicate results from calculus and advanced calculus that are occasionally needed. A bibliography of other books on complex variables, many of which are more advanced, is provided in Appendix 1. A table of conformal transformations that are useful in applications appears in Appendix 2.

The main changes in this edition appear in the rst nine chapters. Many of those changes have been suggested by users of the last edition. Some readers have urged that sections which can be skipped or postponed without disruption be more clearly identied. The statements of Taylor’s theorem and Laurent’s theorem, for example, now appear in sections that are separate from the sections containing their proofs. Another signicant change involves the extended form of the Cauchy integral formula for derivatives. The treatment of that extension has been completely rewritten, and its immediate consequences are now more focused and appear together in a single section. 

Topics are discussed in this book as per following chapters :

 1 Complex Numbers 

 2 Analytic Functions

 3 Elementary Functions 

 4 Integrals

 5 Series 

 6 Residues and Poles

 7 Applications of Residue 

 8 Mapping by Elementary Functions

 9 Conformal Mapping 

10 Applications of Conformal Mapping 

11 The Schwarz–Christoffel Transformation

12 . Integral Formulas of the Poisson Type 

To Get this book, Download page here.