Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 1470411008

Category: Mathematical analysis

Page: 641

View: 5777

A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.
Posted in Mathematical analysis

Krylov Subspace Methods

Principles and Analysis

Author: Jörg Liesen,Zdenek Strakos

Publisher: Oxford University Press

ISBN: 0199655413

Category: Mathematics

Page: 391

View: 8978

Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.
Posted in Mathematics

Orthogonal Polynomials and Continued Fractions

From Euler's Point of View

Author: S. V. Khrushchev

Publisher: Cambridge University Press

ISBN: 0521854199

Category: Mathematics

Page: 478

View: 3632

Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.
Posted in Mathematics

Dictionary of Mathematical Geosciences

With Historical Notes

Author: Richard J. Howarth

Publisher: Springer

ISBN: 3319573152

Category: Science

Page: 899

View: 8312

This dictionary includes a number of mathematical, statistical and computing terms and their definitions to assist geoscientists and provide guidance on the methods and terminology encountered in the literature. Each technical term used in the explanations can be found in the dictionary which also includes explanations of basics, such as trigonometric functions and logarithms. There are also citations from the relevant literature to show the term’s first use in mathematics, statistics, etc. and its subsequent usage in geosciences.
Posted in Science

Farey Sequences

Duality and Maps Between Subsequences

Author: Andrey O. Matveev

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 311054766X

Category: Mathematics

Page: 182

View: 9077

As a first comprehensive overview on Farey sequences and subsequences, this monograph is intended as a reference for anyone looking for specific material or formulas related to the subject. Duality of subsequences and maps between them are discussed and explicit proofs are shown in detail. From the Content Basic structural and enumerative properties of Farey sequences, Collective decision making, Committee methods in pattern recognition, Farey duality, Farey sequence, Fundamental Farey subsequences, Monotone bijections between Farey subsequences
Posted in Mathematics

The Encyclopaedia Britannica

A Dictionary of Arts, Sciences, Literature and General Information

Author: N.A

Publisher: N.A



Page: N.A

View: 981

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The Encyclopædia Britannica

A Dictionary of Arts, Sciences, Literature and General Information

Author: Hugh Chisholm

Publisher: N.A


Category: Encyclopedias and dictionaries

Page: N.A

View: 4179

Posted in Encyclopedias and dictionaries

Encyclopedia Britannica

A Dictionary of Arts, Sciences, Literature and General Information

Author: Hugh Chisholm

Publisher: N.A



Page: N.A

View: 773

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Die Lehre von den Kettenbrüchen (Classic Reprint)

Author: Oskar Perron

Publisher: Forgotten Books

ISBN: 9781390988550

Category: Mathematics

Page: 542

View: 8174

Excerpt from Die Lehre von den Kettenbrüchen Darstellung doch viel mehr auf bereits Gefundenes zu stützen in der Lage bin. Sehr oft tritt aber auch eine Formel ziemlich unerwartet in einem bisher nicht bemerkten Zusammenhang auf. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Posted in Mathematics

Die Rudolphinischen Tafeln

Author: Johannes Kepler

Publisher: N.A

ISBN: 9783826053528


Page: 620

View: 5221

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Untersuchungen über höhere Arithmetik

Author: Carl Friedrich Gauss

Publisher: American Mathematical Soc.

ISBN: 0821842137

Category: Mathematics

Page: 695

View: 3434

In this volume are included all of Gauss's number-theoretic works: his masterpiece, Disquisitiones Arithmeticae, published when Gauss was only 25 years old; several papers published during the ensuing 31 years; and papers taken from material found in Gauss's handwriting after his death. These papers include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. This reprint of the German translation from Latin of the second edition published in 1889 includes an extensive appendix and concludes with a commentary on the papers (with references, where appropriate, to the relevant pages of the Disquisitiones).
Posted in Mathematics

Anschauliche Funktionentheorie

Author: Tristan Needham

Publisher: De Gruyter Oldenbourg

ISBN: 9783486245783

Category: Functions of complex variables

Page: 685

View: 6791

Needhams neuartiger Zugang zur Funktionentheorie wurde von der angelsächsischen Fachpresse begeistert aufgenommen. Mit über 500 zum großen Teil perspektivischen Grafiken vermittelt er im wahrsten Sinne des Wortes eine Anschauung von der ansonsten oft als trocken empfundenen Funktionentheorie. Weitere Informationenen zu Buch und Autor finden Sie auf der Web-Site des Autors.
Posted in Functions of complex variables

Endliche Gruppen

Eine Einführung in die Theorie der endlichen Gruppen

Author: H. Kurzweil

Publisher: Springer-Verlag

ISBN: 3642953131

Category: Mathematics

Page: 190

View: 9140

Posted in Mathematics

Vorlesungen über die Hypergeometrische Funktion

Gehalten an der Universität Göttingen im Wintersemester 1893/94

Author: Felix Klein,Ernst Ritter,Otto Haupt

Publisher: Springer-Verlag

ISBN: 3662247364

Category: Mathematics

Page: 346

View: 6609

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

Einführung in die Variationsrechnung

Author: Ursula Brechtken-Manderscheid

Publisher: N.A


Category: Algebraiese varieteite

Page: 207

View: 8277

Posted in Algebraiese varieteite