Complex Integration and Cauchy's Theorem

Complex Integration and Cauchy's Theorem
Author: G. N. Watson
Publisher:
Total Pages: 100
Release: 1914
Genre: Mathematics
ISBN:

Originally published in 1914, this book provides a concise proof of Cauchy's Theorem, with applications of the theorem to the evaluation of definite integrals.

Complex Integration and Cauchy's Theorem

Complex Integration and Cauchy's Theorem
Author: G. N. Watson
Publisher: Courier Corporation
Total Pages: 98
Release: 2012-01-01
Genre: Mathematics
ISBN: 0486488144

Brief monograph by a distinguished mathematician offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Includes applications to the calculus of residues. 1914 edition.

Complex Integration and Cauchy's Theorem

Complex Integration and Cauchy's Theorem
Author: G. N. Watson
Publisher: Cambridge University Press
Total Pages: 89
Release: 1914
Genre: Mathematics
ISBN: 1107493951

Originally published in 1914, this book provides a concise proof of Cauchy's Theorem, with applications of the theorem to the evaluation of definite integrals.

Complex Variables with Applications

Complex Variables with Applications
Author: Saminathan Ponnusamy
Publisher: Springer Science & Business Media
Total Pages: 521
Release: 2007-05-26
Genre: Mathematics
ISBN: 0817645136

Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students

Cauchy and the Creation of Complex Function Theory

Cauchy and the Creation of Complex Function Theory
Author: Frank Smithies
Publisher: Cambridge University Press
Total Pages: 242
Release: 1997-11-20
Genre: Mathematics
ISBN: 9780521592789

Dr Smithies' analysis of the process whereby Cauchy created the basic structure of complex analysis, begins by describing the 18th century background. He then proceeds to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem. Controversies associated with the the birth of the subject are also considered in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This authoritative book is the first to make use of the whole spectrum of available original sources.

Complex Analysis

Complex Analysis
Author: Elias M. Stein
Publisher: Princeton University Press
Total Pages: 398
Release: 2010-04-22
Genre: Mathematics
ISBN: 1400831156

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

The Cauchy Transform, Potential Theory and Conformal Mapping

The Cauchy Transform, Potential Theory and Conformal Mapping
Author: Steven R. Bell
Publisher: CRC Press
Total Pages: 221
Release: 2015-11-04
Genre: Mathematics
ISBN: 1498727212

The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f

Visual Complex Analysis

Visual Complex Analysis
Author: Tristan Needham
Publisher: Oxford University Press
Total Pages: 620
Release: 1997
Genre: Mathematics
ISBN: 9780198534464

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Complex Function Theory

Complex Function Theory
Author: Donald Sarason
Publisher: American Mathematical Society
Total Pages: 177
Release: 2021-02-16
Genre: Mathematics
ISBN: 1470463237

Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.