Complex Integration and Cauchy's Theorem
by G. N. Watson
Publisher: Cambridge University Press 1914
Number of pages: 100
This brief monograph by one of the great mathematicians of the early 20th century 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 of the theorem to the evaluation of definite integrals.
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by George Cain
The textbook for an introductory course in complex analysis. It covers complex numbers and functions, integration, Cauchy's theorem, harmonic functions, Taylor and Laurent series, poles and residues, argument principle, and more.
by Piotr Jakobczak, Marek Jarnicki - Jagiellonian University
The text contains the background theory of several complex variables. We discuss the extension of holomorphic functions, automorphisms, domains of holomorphy, pseudoconvexity, etc. Prerequisites are real analysis and complex analysis of one variable.
by Thomas S. Fiske - John Wiley & sons
This book is a brief introductory account of some of the more fundamental portions of the theory of functions of a complex variable. It will give the uninitiated some idea of the nature of one of the most important branches of modem mathematics.
by B. Ya. Levin - American Mathematical Society
This monograph aims to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis. The general theory starts with the fundamental results on the growth of entire functions of finite order.