# complex variables ii essentials v 2

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## Complex Variables Ii Essentials

**Author :**Alan D. Solomon

**ISBN :**0738672173

**Genre :**Mathematics

**File Size :**20. 98 MB

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Includes elementary mappings and mobius transformation, mappings by general functions, conformal mappings and harmonic functions, applying complex functions to applied mathematics, analytic continuation, and analytic function properties.

## Complex Analysis In One Variable

**Author :**NARASIMHAN

**ISBN :**9781475711066

**Genre :**Mathematics

**File Size :**73. 26 MB

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This book is based on a first-year graduate course I gave three times at the University of Chicago. As it was addressed to graduate students who intended to specialize in mathematics, I tried to put the classical theory of functions of a complex variable in context, presenting proofs and points of view which relate the subject to other branches of mathematics. Complex analysis in one variable is ideally suited to this attempt. Of course, the branches of mathema tics one chooses, and the connections one makes, must depend on personal taste and knowledge. My own leaning towards several complex variables will be apparent, especially in the notes at the end of the different chapters. The first three chapters deal largely with classical material which is avai lable in the many books on the subject. I have tried to present this material as efficiently as I could, and, even here, to show the relationship with other branches of mathematics. Chapter 4 contains a proof of Picard's theorem; the method of proof I have chosen has far-reaching generalizations in several complex variables and in differential geometry. The next two chapters deal with the Runge approximation theorem and its many applications. The presentation here has been strongly influenced by work on several complex variables.

## Complex Variables I Essentials

**Author :**Alan D. Solomon

**ISBN :**0738672432

**Genre :**Mathematics

**File Size :**35. 92 MB

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Includes functions of a complex variable, elementary complex functions, integrals of complex functions in the complex plane, sequences and series, and poles and residues.

## Essentials Of Math Methods For Physicists

**Author :**Hans J. Weber

**ISBN :**9781483225623

**Genre :**Science

**File Size :**75. 32 MB

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Essentials of Math Methods for Physicists aims to guide the student in learning the mathematical language used by physicists by leading them through worked examples and then practicing problems. The pedagogy is that of introducing concepts, designing and refining methods and practice them repeatedly in physics examples and problems. Geometric and algebraic approaches and methods are included and are more or less emphasized in a variety of settings to accommodate different learning styles of students. Comprised of 19 chapters, this book begins with an introduction to the basic concepts of vector algebra and vector analysis and their application to classical mechanics and electrodynamics. The next chapter deals with the extension of vector algebra and analysis to curved orthogonal coordinates, again with applications from classical mechanics and electrodynamics. These chapters lay the foundations for differential equations, variational calculus, and nonlinear analysisin later discussions. High school algebra of one or two linear equations is also extended to determinants and matrix solutions of general systems of linear equations, eigenvalues and eigenvectors, and linear transformations in real and complex vector spaces. The book also considers probability and statistics as well as special functions and Fourier series. Historical remarks are included that describe some physicists and mathematicians who introduced the ideas and methods that were perfected by later generations to the tools routinely used today. This monograph is intended to help undergraduate students prepare for the level of mathematics expected in more advanced undergraduate physics and engineering courses.

## An Introduction To Complex Analysis In Several Variables

**Author :**L. Hormander

**ISBN :**9780444105233

**Genre :**Mathematics

**File Size :**37. 46 MB

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An Introduction to Complex Analysis in Several Variables

## Introduction To Complex Analysis

**Author :**Boris Vladimirovich Shabat

**ISBN :**9780821819753

**Genre :**Functions of complex variables

**File Size :**42. 55 MB

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Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space.

## Introduction To Complex Analysis In Several Variables

**Author :**Volker Scheidemann

**ISBN :**3764374918

**Genre :**Mathematics

**File Size :**52. 69 MB

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This book provides a comprehensive introduction to complex analysis in several variables. One major focus of the book is extension phenomena alien to the one-dimensional theory (Hartog's Kugelsatz, theorem of Cartan-Thullen, Bochner's theorem). The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a university lecture. Therefore, the book contains more than 50 examples and more than 100 supporting exercises.

## Complex Analysis

**Author :**D.H. Luecking

**ISBN :**9781461382959

**Genre :**Mathematics

**File Size :**62. 97 MB

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The main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely identifies the dual of H(G) with the space of germs of holomorphic functions on the complement of G. From this result, for example, Runge's approximation theorem and the global Cauchy integral theorem follow in a few short steps. Other consequences of this duality theorem are the Germay interpolation theorem and the Mittag-Leffler Theorem. The approach via duality is entirely consistent with Cauchy's approach to complex variables, since curvilinear integrals are typical examples of linear functionals. The prerequisite for the book is a one-semester course in com plex variables at the undergraduate-graduate level, so that the elements of the local theory are supposed known. In particular, the Cauchy Theorem for the square and the circle are assumed, but not the global Cauchy Theorem in any of its forms. The second author has three times taught a graduate course based on this material at the University of Illinois, with good results.

## Essentials Of Mathematica

**Author :**Nino Boccara

**ISBN :**9780387495149

**Genre :**Science

**File Size :**76. 90 MB

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This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.

## Advanced Calculus Ii Essentials

**Author :**

**ISBN :**0738670111

**Genre :**

**File Size :**40. 49 MB

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