# Theory of the algebraic functions of a complex variable

• 186 Pages
• 3.14 MB
• English
by
Mayer & Müller , Berlin
Algebraic func
Classifications The Physical Object Statement by John Charles Fields. LC Classifications QA341 .F46 Pagination vii, 186 p. Open Library OL6995842M LC Control Number 08011507 OCLC/WorldCa 6502291

Theory of the algebraic functions of a complex variable [Fields, John Charles] on *FREE* shipping on qualifying offers. Theory of the algebraic functions of a complex variablePrice: \$ Complex function theory is a classic subject of mathematics that has found its definite form a long time ago.

It is still an extremely important tool in many applied fields. Markushevich's book is a unique masterpiece that presents the theory in a comprehensive and clear way, perfectly suited for students who seek to acquire the powerful Cited by:   Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

### Details Theory of the algebraic functions of a complex variable EPUB

Theory of the algebraic functions of a complex variable Item Preview remove-circle Theory of the algebraic functions of a complex variable by Fields, John Charles, Publication date   An illustration of an open book.

Books. An illustration of two cells of a film strip. Video An illustration of an audio speaker. Theory of the algebraic functions of a complex variable Theory of the algebraic functions of a complex variable by. Functions of a Complex Variable Complex Algebra Formally, the set of complex numbers can be deﬂned as the set of two-dimensional real vectors, f(x;y)g, with one extra operation, complex multi.

Introduction to complex numbers 2. Theory of functions of complex variables The real and imaginary parts of a complex number Complex number as vectors Algebraic and Transcendental Functions of complex numbers Definition of Limit of complex functions Continuity of complex functions 4.

Conformal Mapping Author: Mohamed F. El-Hewie. The level of the text assumes that the reader is acquainted with elementary real analysis. Beginning with the revision of the algebra of complex variables, the book moves on to deal with analytic functions, elementary functions, complex integration, sequences, series and infinite products, series expansions, singularities and s: 2.

function theory can omit, the reader will find here - RITT's theorem on asymptotic power series expansions, which pro-vides a function-theoretic interpretation of the famous theorem of E.

BOREL to the effect that any sequence of complex numbers is the sequence of derivatives at 0 of some infinitely differentiable function on the line.

### Download Theory of the algebraic functions of a complex variable EPUB

Functions of One Complex Variable Third Edition Lars V. Ahlfors Professor of Mathematics, Emeritus Definition and Properties of Algebraic Functions Behavior at the Critical Points 3 Picard's Theorem no more than an introduction to the basic methods and results of complex function theory.

\$\begingroup\$ Well,the objects of functions of several complex variables are manifolds with a complex topological vector space ore,they are the centerpieces of the bulk of postth century analysis and geometry and the tools of sheaf theory via commutative algebra are deeply interwoven in a result of all this,any "pure" approach-say,emphasizing analysis-only tells part.

1 Complex Numbers 1 De•nitions 1 Algebraic Properties 1 Polar Coordinates and Euler Formula 2 Roots of Complex Numbers 3 Regions in Complex Plane 3 2 Functions of Complex Variables 5 Functions of a Complex Variable 5 Elementary Functions 5 Mappings 7 Mappings by Elementary Functions.

8 3 Analytic Functions 11 Limits 11 Continuity 12 Derivative Topics covered includes: Number system, Algebra of Complex Numbers, Inequalities and complex exponents, Functions of a Complex Variable, Sequences and Series, Complex Integration, Consequences of complex integration, Residue calculus, Conformal Mapping, Mapping of Elementary transformation, Applications of conformal mapping, Further theory of.

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. ( views). Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics.

At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations.

Topics in the Theory of Functions of Several Complex Variables - The Madison Colloquium,Part II - Dover Books on Intermediate and Advanced Mathematics Osgood (William Fogg) Published by Dover, Dover Books on Intermediate and Advanced Mathematics (). About the Book Find at your local library Description Theorems are presented in a logical way and are carefully proved, making this a most useful book for students.

--Choice This magnificent textbook, translated from the Russian, was first published in The book covers all aspects of the theory of functions of one complex variable. Theory of the algebraic functions of a complex variable.

Berlin, Mayer & Müller, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: John Charles Fields.

No background in complex variables is assumed, thus making the text suitable for those encountering the subject for the first time. The Elementary Theory, General Cauchy Theorem, Applications of the Cauchy Theory, Families of Analytic Functions, Factorization of Analytic Functions and The Prime Number Theorem.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory.

The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory.

This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory Cited by: ‎The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory.

This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of.

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable).

This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in The translation has been enriched by a Translator's Introduction that includes historical background, and also by extensive commentary embedded in the translation itself.

Complex Analysis by NPTEL. The note deals with the Basic ideas of functions of one complex variable. Topics covered includes: Number system, Algebra of Complex Numbers, Inequalities and complex exponents, Functions of a Complex Variable, Sequences and Series, Complex Integration, Consequences of complex integration, Residue calculus, Conformal Mapping, Mapping of.

Functions of a complex variable. 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 us examples have been given throughout the book, and there is also a set of.

Theory of Functions of a Complex Variable by Heinrich Burkhardt. Publisher: D. Heath Number of pages: Description: Contents: Complex numbers and their geometrical representation; Rational functions of a complex variable and the conformal representations determined by them; Definitions and theorems on the theory of real variables and their functions; Single-valued analytic.

Theory of functions of a complex variable by A. Markushevich,Prentice-Hall edition, in English - Rev. English ed. translated and edited by Richard A.

Silverman. The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions (, ,)on the space C n of n-tuples of complex numbers. As in complex analysis, which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power series in.

This text presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups.

It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and.

Theory of functions of a real variable. Shlomo Sternberg course assumes that the student has seen the basics of real variable theory and point set topology.

The elements of the topology of metrics spaces are presented Lorch’s proof of the spectral theorem from his book Spectral Theory.

### Description Theory of the algebraic functions of a complex variable FB2

This has the ﬂavor of complex analysis. The.Functions of a complex variable. 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 us examples have been given throughout the book, and there is also a set of Miscellaneous Examples, arranged to .Therefore, many examples of algebraic curves are presented in the first chapters.

In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category.