COMPLEX VARIABLES AND APPLICATIONS

"Complex Variables and Applications, 5E" is a revision of the fourth edition, published in 1984. That edition has served, just as the first three editions did, as a textbook for a one-term introductory course in the theory and application of functions of a complex variable. This revision preserves the basic content and style of the earlier editions, the first two of which were written by the late Ruel V. Churchill alone.

In this edition, the second author has concentrated on revising the first eight chapters. To mention some of the major improvements, the treatment of antiderivatives now precedes and motivates the presentation on the Cauchy-Goursat theorem, the appears much earlier in the text, the mappings in the mapping chapter have been rearranged so that the more difficult ones now appear toward the endo for the chapter.

As for certain other improvements, the point at infinity is now introduced more naturally with the definition of limit, several, several additional mapping exampled have been the logarithmic function has been strengthened. Also, the derivation of various trigonometric identifies has been simplified, the derivation of the maximum modulus principle is now more self-contained, and Laurent’s theorem is presented in a way that is more convenient to use Finally, the exposition has been improved throughout, and a substantial number of figures and exercises have been recast and added.