## 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.

(

**2101**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.

(

**4022**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.

(

**3354**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.

(

**5557**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.

(

**5209**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.

(

**6409**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 ...

(

**6638**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.

(

**6529**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.

(

**7127**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 ...

(

**7695**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.

(

**5895**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.

(

**11512**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.

(

**8295**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.

(

**6984**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...

(

**8271**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.

(

**8191**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.

(

**8848**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.).

(

**7472**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.

(

**8101**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.

(

**8279**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.

(

**7995**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).

(

**8063**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.

(

**10266**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.

(

**9804**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.

(

**10967**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.

(

**9916**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.

(

**10049**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.

(

**8913**views)

**Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators**

by

**Nicolas Lerner**-

**BirkhĂ¤user**,

**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.

(

**8612**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.

(

**10976**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.

(

**11745**views)

**Holomorphic Spaces**

by

**S. Axler, J. McCarthy, D. Sarason**-

**Cambridge University Press**,

**1998**

This volume consists of expository articles on holomorphic spaces. Topics covered are Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.

(

**9808**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.

(

**12640**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.

(

**12637**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.

(

**13957**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.

(

**14680**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.

(

**21250**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.

(

**14901**views)

**Complex Variables: Second Edition**

by

**R. B. Ash, W. P. Novinger**-

**Dover Publications**,

**2007**

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.

(

**16766**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.

(

**14862**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.

(

**38196**views)