by George Cain
This textbook is written for an introductory undergraduate course in complex analysis. From the table of contents: Complex Numbers; Complex Functions; Elementary Functions; Integration; Cauchy's Theorem; Harmonic Functions; Series; Taylor and Laurent Series; Poles and Residues; Argument Principle.
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by G. N. Watson - Cambridge University Press
This brief monograph offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications ...
by Leif Mejlbro - BookBoon
Polynomials are the first class of functions that the student meets. Therefore, one may think that they are easy to handle. They are not in general! Topics as e.g. finding roots in a polynomial and the winding number are illustrated.
by M. Deuring - Tata Institute of Fundamental Research
We shall be dealing in these lectures with the algebraic aspects of the theory of algebraic functions of one variable. Since an algebraic function w(z) is defined by f(z,w)=0, the study of such functions should be possible by algebraic methods.
by Christian Berg - Kobenhavns Universitet
Contents: Holomorphic functions; Contour integrals and primitives; The theorems of Cauchy; Applications of Cauchy's integral formula; Zeros and isolated singularities; The calculus of residues; The maximum modulus principle; Moebius transformations.