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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.
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...
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.
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.
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.).
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Introduction to Complex Analysis
by W W L Chen - Macquarie University , 2008
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.
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.
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.
A First Course in Complex Analysis
by Matthias Beck, Gerald Marchesi, Dennis Pixton - San Francisco State University , 2007
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.