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Complex Analysis

e-books in Complex Analysis category

Book cover: Complex AnalysisComplex Analysis
by - Kobenhavns Universitet ,
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.
(437 views)
Book cover: Lectures On The General Theory Of Integral FunctionsLectures On The General Theory Of Integral Functions
by - Chelsea Pub. Co. ,
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.
(266 views)
Book cover: The Gamma FunctionThe Gamma Function
by - viXra ,
This book is dedicated to the subject of the Gamma function and related topics. The Gamma Function is primarily intended for advanced undergraduates in science and mathematics. The book covers each of the most important aspects of the Gamma function.
(368 views)

Book cover: Functions of a Complex VariableFunctions of a Complex Variable
by - 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.
(1544 views)
Book cover: Functions Of A Complex Variable with ApplicationsFunctions Of A Complex Variable with Applications
by - Oliver And Boyd ,
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 ...
(1413 views)
Book cover: Elements of the Theory of Functions of a Complex VariableElements of the Theory of Functions of a Complex Variable
by - Philadelphia G.E. Fisher ,
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.
(1917 views)
Book cover: The Elementary Properties of the Elliptic FunctionsThe Elementary Properties of the Elliptic Functions
by - Macmillan ,
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.
(2451 views)
Book cover: Complex Integration and Cauchy's TheoremComplex Integration and Cauchy's Theorem
by - Cambridge University Press ,
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 ...
(3516 views)
Book cover: Lectures on Holomorphic Functions of Several Complex VariablesLectures on Holomorphic Functions of Several Complex Variables
by - 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.
(1843 views)
Book cover: Complex AnalysisComplex Analysis
by - Harvard University ,
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.
(6516 views)
Book cover: Computing of the Complex Variable FunctionsComputing of the Complex Variable Functions
by - MiC ,
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.
(4190 views)
Book cover: Elliptic Functions and Elliptic CurvesElliptic Functions and Elliptic Curves
by - Institut de Mathematiques de Jussieu ,
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.
(2633 views)
Book cover: Functions of a Complex VariableFunctions of a Complex Variable
by - The Macmillan Company ,
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...
(4075 views)
Book cover: Lectures on the Mean-Value and Omega Theorems for the Riemann Zeta-FunctionLectures on the Mean-Value and Omega Theorems for the Riemann Zeta-Function
by - Tata Institute of Fundamental Research ,
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.
(3974 views)
Book cover: Methods for Finding Zeros in PolynomialsMethods for Finding Zeros in Polynomials
by - BookBoon ,
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.
(4339 views)
Book cover: Lectures on Stratification of Complex Analytic SetsLectures on Stratification of Complex Analytic Sets
by - Tata Institute of Fundamental Research ,
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.).
(3964 views)
Book cover: Lectures on Modular Functions of One Complex VariableLectures on Modular Functions of One Complex Variable
by - Tata institute of Fundamental Research ,
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.
(4001 views)
Book cover: Lectures on Riemann MatricesLectures on Riemann Matrices
by - Tata Institute of Fundamental Research ,
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.
(4154 views)
Book cover: Lectures on the Theory of Algebraic Functions of One VariableLectures on the Theory of Algebraic Functions of One Variable
by - Tata Institute of Fundamental Research ,
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.
(4251 views)
Book cover: Lectures on Meromorphic FunctionsLectures on Meromorphic Functions
by - Tata Institue of Fundamental Research ,
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).
(4287 views)
Book cover: On Riemann's Theory of Algebraic Functions and their IntegralsOn Riemann's Theory of Algebraic Functions and their Integrals
by - Macmillan and Bowes ,
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.
(6405 views)
Book cover: Lectures on The Theory of Functions of Several Complex VariablesLectures on The Theory of Functions of Several Complex Variables
by - Tata Institute of Fundamental Research ,
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.
(4897 views)
Book cover: Lectures on The Riemann Zeta-FunctionLectures on The Riemann Zeta-Function
by - Tata Institute of Fundamental Research ,
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.
(6436 views)
Book cover: Calculus of Residua: Complex Functions Theory a-2Calculus of Residua: Complex Functions Theory a-2
by - BookBoon ,
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.
(5704 views)
Book cover: Elementary Analytic Functions: Complex Functions Theory a-1Elementary Analytic Functions: Complex Functions Theory a-1
by - BookBoon ,
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.
(5974 views)
Book cover: Notes on Automorphic FunctionsNotes on Automorphic Functions
by - Kobenhavns Universitet ,
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.
(6863 views)
Book cover: Hyperbolic FunctionsHyperbolic Functions
by - John Wiley & Sons ,
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.
(6959 views)
Book cover: Holomorphic SpacesHolomorphic Spaces
by - Cambridge University Press ,
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.
(5951 views)
Book cover: Complex Analysis on Riemann SurfacesComplex Analysis on Riemann Surfaces
by - Harvard University ,
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.
(8300 views)
Book cover: Several Complex VariablesSeveral Complex Variables
by - Cambridge University Press ,
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.
(7774 views)
Book cover: Dynamics in One Complex VariableDynamics in One Complex Variable
by - Princeton University Press ,
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.
(8692 views)
Book cover: Lectures on Entire FunctionsLectures on Entire Functions
by - 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.
(8910 views)
Book cover: Complex Analysis for Mathematics and EngineeringComplex Analysis for Mathematics and Engineering
by - Jones & Bartlett Learning ,
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.
(9361 views)
Book cover: Introduction to Complex AnalysisIntroduction to Complex Analysis
by - Macquarie University ,
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.
(9347 views)
Book cover: Complex Variables: Second EditionComplex Variables: Second Edition
by - Dover Publications ,
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.
(9569 views)
Book cover: Complex AnalysisComplex Analysis
by ,
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.
(9717 views)
Book cover: A First Course in Complex AnalysisA First Course in Complex Analysis
by - San Francisco State University ,
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.
(32480 views)