Complex Analysis

e-books in Complex Analysis category

Complex Variables with Applications
by Jeremy Orloff - LibreTexts , 2021
Complex analysis is a basic tool in many mathematical theories. There are a small number of far-reaching theorems that we'll explore in the first part of the class. We'll touch on some mathematical and engineering applications of these theorems.
(4462 views)

Theory of Functions of a Complex Variable
by Andrew Russell Forsyth - Cambridge University Press , 1918
The present treatise is an attempt to give a consecutive account of what may fairly be deemed the principal branches of the whole subject. The book may assist mathematicians, by lessening the labour of acquiring a proper knowledge of the subject.
(5937 views)

Theory of Functions of a Complex Variable
by Heinrich Burkhardt - D. C. Heath , 1913
Contents: Complex numbers and their geometrical representation; Rational functions of a complex variable; Theory of real variables and their functions; Single-valued analytic functions of a complex variable; General theory of functions; etc.
(5107 views)

Complex Analysis
by Christian Berg - Kobenhavns Universitet , 2012
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.
(7956 views)

Lectures On The General Theory Of Integral Functions
by Georges Valiron - Chelsea Pub. Co. , 1949
These lectures give us, in the form of a number of elegant and illuminating theorems, the latest word of mathematical science on the subject of Integral Functions. They descend to details, they take us into the workshop of the working mathematician.
(7207 views)

Functions of a Complex Variable
by Thomas S. Fiske - John Wiley & sons , 1907
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.
(8378 views)

Functions Of A Complex Variable with Applications
by E. G. Phillips - Oliver And Boyd , 1961
This book is concerned essentially with the application of the methods of the differential and integral calculus to complex numbers. Limitations of space made it necessary for me to confine myself to the more essential aspects of the theory ...
(8687 views)

Elements of the Theory of Functions of a Complex Variable
by G.E. Fisher, I.J. Schwatt - Philadelphia G.E. Fisher , 1896
Contents: Geometric representation of imaginary quantities; Functions of a complex variable in general; Multiform functions; Integrals with complex variables; General properties of functions; Infinite and infinitesimal values of functions; etc.
(8288 views)

The Elementary Properties of the Elliptic Functions
by Alfred Cardew Dixon - Macmillan , 1894
This textbook will supply the wants of those students who, for reasons connected with examinations or otherwise, wish to have a knowledge of the elements of Elliptic Functions, not including the Theory of Transformations and the Theta Functions.
(9102 views)

Complex Integration and Cauchy's Theorem
by G. N. Watson - Cambridge University Press , 1914
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 ...
(9499 views)

Lectures on Holomorphic Functions of Several Complex Variables
by Piotr Jakobczak, Marek Jarnicki - Jagiellonian University , 2001
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.
(7538 views)

Complex Analysis
by C. McMullen - Harvard University , 2010
This course covers some basic material on both the geometric and analytic aspects of complex analysis in one variable. Prerequisites: Background in real analysis and basic differential topology, and a first course in complex analysis.
(13756 views)

Computing of the Complex Variable Functions
by Solomon I. Khmelnik, Inna S. Doubson - MiC , 2011
Hardware algorithms for computing of all elementary complex variable functions are proposed. Contents: A method 'digit-by-digit'; Decomposition; Compositions; Two-step-by-step operations; Taking the logarithm; Potentiation; and more.
(9955 views)

Elliptic Functions and Elliptic Curves
by Jan Nekovar - Institut de Mathematiques de Jussieu , 2004
Contents: Introduction; Abel's Method; A Crash Course on Riemann Surfaces; Cubic curves; Elliptic functions; Theta functions; Construction of elliptic functions; Lemniscatology or Complex Multiplication by Z[i]; Group law on smooth cubic curves.
(8779 views)

Functions of a Complex Variable
by Thomas Murray MacRobert - The Macmillan Company , 1917
This book is designed for students who, having acquired a good working knowledge of the calculus, desire to become acquainted with the theory of functions of a complex variable, and with the principal applications of that theory...
(9994 views)

Lectures on the Mean-Value and Omega Theorems for the Riemann Zeta-Function
by K. Ramachandra - Tata Institute of Fundamental Research , 1995
This short book is a text on the mean-value and omega theorems for the Riemann Zeta-function. The author includes discussion of some fundamental theorems on Titchmarsh series and applications, and Titchmarsh's Phenomenon.
(9725 views)

Methods for Finding Zeros in Polynomials
by Leif Mejlbro - BookBoon , 2011
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.
(10643 views)

Lectures on Stratification of Complex Analytic Sets
by M.-H. Schwartz - Tata Institute of Fundamental Research , 1966
Contents: Preliminaries; Some theorems on stratification; Whitney's Theorems (Tangent Cones, Wings, The singular set Sa); Whitney Stratifications and pseudofibre bundles (Pseudo fibre spaces, Obstructions in pseudo-fibrations, etc.).
(8909 views)

Lectures on Modular Functions of One Complex Variable
by H. Maass - Tata institute of Fundamental Research , 1983
This is an elementary introduction to the theory of modular functions and modular forms. Basic facts from the theory of functions of a complex variable and some properties of the elementary transcendental functions are the only prerequisites.
(9946 views)

Lectures on Riemann Matrices
by C.L. Siegel - Tata Institute of Fundamental Research , 1963
A systematic study of Riemann matrices which arise in a natural way from the theory of abelian functions. Contents: Abelian Functions; Commutator-algebra of a R-matrix; Division algebras over Q with a positive involution; Cyclic algebras; etc.
(10238 views)

Lectures on the Theory of Algebraic Functions of One Variable
by M. Deuring - Tata Institute of Fundamental Research , 1959
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.
(9574 views)

Lectures on Meromorphic Functions
by W.K. Hayman - Tata Institue of Fundamental Research , 1959
We shall develop in this course Nevanlinna's theory of meromorphic functions. From the table of contents: Basic Theory; Nevanlinna's Second Fundamental Theorem; Univalent Functions (Schlicht functions, Asymptotic behaviour).
(9765 views)

On Riemann's Theory of Algebraic Functions and their Integrals
by Felix Klein - Macmillan and Bowes , 1893
In his scholarly supplement to Riemann's complex mathematical theory, rather than offer proofs in support of the theorem, Klein chose to offer this exposition and annotation, first published in 1893, in an effort to broaden and deepen understanding.
(11981 views)

Lectures on The Theory of Functions of Several Complex Variables
by B. Malgrange - Tata Institute of Fundamental Research , 1958
Contents: Cauchy's formula and elementary consequences; Reinhardt domains and circular domains; Complex analytic manifolds; Analytic Continuation; Envelopes of Holomorphy; Domains of Holomorphy - Convexity Theory; d''-cohomology on the cube; etc.
(11425 views)

Lectures on The Riemann Zeta-Function
by K. Chandrasekharan - Tata Institute of Fundamental Research , 1953
These notes provide an intorduction to the theory of the Riemann Zeta-function for students who might later want to do research on the subject. The Prime Number Theorem, Hardy's theorem, and Hamburger's theorem are the principal results proved here.
(12821 views)

Calculus of Residua: Complex Functions Theory a-2
by Leif Mejlbro - BookBoon , 2010
This is the second part in the series of books on complex functions theory. From the table of contents: Introduction; Power Series; Harmonic Functions; Laurent Series and Residua; Applications of the Calculus of Residua; Index.
(11696 views)

Elementary Analytic Functions: Complex Functions Theory a-1
by Leif Mejlbro - BookBoon , 2010
This is an introductory book on complex functions theory. From the table of contents: Introduction; The Complex Numbers; Basic Topology and Complex Functions; Analytic Functions; Some elementary analytic functions; Index.
(11829 views)

Stability, Riemann Surfaces, Conformal Mappings: Complex Functions Theory a-3
by Leif Mejlbro - BookBoon , 2010
The book on complex functions theory. From the table of contents: Introduction; The argument principle, and criteria of stability; Many-valued functions and Riemann surfaces; Conformal mappings and the Dirichlet problem; Index.
(10458 views)

Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators
by Nicolas Lerner - Birkhäuser , 2009
This is a book on pseudodifferential operators, with emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. The first part of the book is accessible to graduate students with a decent background in Analysis.
(10057 views)

Notes on Automorphic Functions
by Anders Thorup - Kobenhavns Universitet , 1995
In mathematics, the notion of factor of automorphy arises for a group acting on a complex-analytic manifold. From the contents: Moebius transformations; Discrete subgroups; Modular groups; Automorphic forms; Poincare Series and Eisenstein Series.
(12386 views)

Hyperbolic Functions
by James McMahon - John Wiley & Sons , 1906
College students who wish to know something of the hyperbolic trigonometry, will find it presented in a simple and comprehensive way in the first half of the work. Readers are then introduced to the more general trigonometry of the complex plane.
(13676 views)

Complex Analysis on Riemann Surfaces
by Curtis McMullen - Harvard University , 2005
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
(14627 views)

Several Complex Variables
by Michael Schneider, Yum-Tong Siu - Cambridge University Press , 1999
Several Complex Variables is a central area of mathematics with interactions with partial differential equations, algebraic geometry and differential geometry. This text emphasizes these interactions and concentrates on problems of current interest.
(14748 views)

Dynamics in One Complex Variable
by John Milnor - Princeton University Press , 1991
This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the case of rational maps of the Riemann sphere. The book introduces some key ideas in the field, and forms a basis for further study.
(16350 views)

Lectures on Entire Functions
by B. Ya. Levin - American Mathematical Society , 1996
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.
(17191 views)

Complex Analysis for Mathematics and Engineering
by John H. Mathews, Russell W. Howell - Jones & Bartlett Learning , 2006
This book presents a comprehensive, student-friendly introduction to Complex Analysis concepts. Its clear, concise writing style and numerous applications make the foundations of the subject matter easily accessible to students.
(26089 views)

Introduction to Complex Analysis
by W W L Chen - Macquarie University , 2003
Introduction to some of the basic ideas in complex analysis: complex numbers; foundations of complex analysis; complex differentiation; complex integrals; Cauchy's integral theorem; Cauchy's integral formula; Taylor series; Laurent series; etc.
(16751 views)

Complex Variables
by R. B. Ash, W. P. Novinger , 2004
The text for advanced undergraduates and graduates, it offers a concise treatment, explanations, problems and solutions. Topics include elementary theory, general Cauchy theorem and applications, analytic functions, and prime number theorem.
(19059 views)

Complex Analysis
by George Cain , 2001
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.
(16805 views)

A First Course in Complex Analysis
by M. Beck, G. Marchesi, D. Pixton - San Francisco State University , 2012
These are the lecture notes of a one-semester undergraduate course: complex numbers, differentiation, functions, integration, Cauchy's theorem, harmonic functions, power series, Taylor and Laurent series, isolated singularities, etc.
(40283 views)