Complex variables / Stephen D. Fisher

From the preface: "The greatest changes from the first edition [1986; MR0831931 (88b:30001)] occur in Chapter 2, principally in the presentation of the all-important Cauchy's theorem. In Section 3, I give only the Green's theorem proof of Cauchy's theorem (which assumes the continuity of the derivative); the Goursat version of Cauchy's theorem is now in the special starred Subsection 2.3.1. In the remainder of Section 3, I discuss simple connectivity (but not star-shaped domains) and derive some of the consequences of Cauchy's theorem. These parallel developments, one assuming continuity of the derivative and the other not, are brought together in the first theorem of Section 4, where I derive the power-series representation of an analytic function. In Sections 5 and 6 of Chapter 2, I have made other rearrangements and clarifications in the presentation of residues, Laurent series, and the use of the residue theorem to evaluate definite integrals.
"In Chapter 4, I have made a number of alterations in the discussion of flows. Moreover, I have modified the text and many of the exercises, throughout—adding here and deleting or rearranging there—all for added clarity. Otherwise, I have done my best to correct typographical errors that were brought to my attention by readers and teachers of the first edition.''

Index