A Quick Introduction To Complex Analysis

Author : Kalyan Chakraborty,Shigeru Kanemitsu,Takako Kuzumaki
Publisher : World Scientific Publishing Company
Page : 208 pages
File Size : 40,6 Mb
Release : 2016-08-08
Category : Mathematics
ISBN : 9789813108530

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A Quick Introduction to Complex Analysis by Kalyan Chakraborty,Shigeru Kanemitsu,Takako Kuzumaki Pdf

The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels. If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples. This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.

Author : H. A. Priestley
Publisher : OUP Oxford
Page : 344 pages
File Size : 53,8 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 9780191037207

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Introduction to Complex Analysis by H. A. Priestley Pdf

Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 398 pages
File Size : 53,9 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9781400831159

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Complex Analysis by Elias M. Stein,Rami Shakarchi Pdf

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author : Kalyan Chakraborty
Publisher : Unknown
Page : 206 pages
File Size : 48,9 Mb
Release : 2016
Category : Electronic books
ISBN : 9813108525

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A Quick Introduction To Complex Analysis by Kalyan Chakraborty Pdf

Author : Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 50,9 Mb
Release : 2011-07-01
Category : Mathematics
ISBN : 9781461401957

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An Introduction to Complex Analysis by Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas Pdf

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

Author : Rolf Nevanlinna,Veikko Paatero
Publisher : American Mathematical Society
Page : 366 pages
File Size : 41,7 Mb
Release : 2007-10-09
Category : Mathematics
ISBN : 9780821843994

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Introduction to Complex Analysis by Rolf Nevanlinna,Veikko Paatero Pdf

This textbook, based on lectures given by the authors, presents the elements of the theory of functions in a precise fashion. This introduction is ideal for the third or fourth year of undergraduate study and for graduate students learning complex analysis. Over 300 exercises offer important insight into the subject.

Author : Sanford L. Segal
Publisher : Elsevier
Page : 714 pages
File Size : 45,8 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 008087164X

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Nine Introductions in Complex Analysis by Sanford L. Segal Pdf

Nine Introductions in Complex Analysis

Author : Zeev Nehari
Publisher : Unknown
Page : 296 pages
File Size : 42,8 Mb
Release : 1968
Category : Functions of complex variables
ISBN : UOM:39015017132104

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Introduction to Complex Analysis by Zeev Nehari Pdf

Author : Kunihiko Kodaira
Publisher : Cambridge University Press
Page : 256 pages
File Size : 45,9 Mb
Release : 1984-12-28
Category : Mathematics
ISBN : 052128659X

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Introduction to Complex Analysis by Kunihiko Kodaira Pdf

This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy-to-understand and careful way. He emphasizes geometrical considerations and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The general versions of Cauchy's Theorem and integral formula are proved in Chapter 2. The remainder of the book deals with conformal mappings, analytic continuation, and Riemann's Mapping Theorem. The presentation here is very full and detailed. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for first courses in complex analysis.

Author : Jerry R. Muir, Jr.
Publisher : John Wiley & Sons
Page : 280 pages
File Size : 41,7 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781118705278

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Complex Analysis by Jerry R. Muir, Jr. Pdf

A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.

Author : Volker Scheidemann
Publisher : Springer Nature
Page : 239 pages
File Size : 45,8 Mb
Release : 2023
Category : Functions of complex variables
ISBN : 9783031264283

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Introduction to Complex Analysis in Several Variables by Volker Scheidemann Pdf

This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.

Author : Vladimir Eiderman
Publisher : CRC Press
Page : 383 pages
File Size : 53,9 Mb
Release : 2021-12-20
Category : Mathematics
ISBN : 9781000511123

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An Introduction to Complex Analysis and the Laplace Transform by Vladimir Eiderman Pdf

The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book. This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses. In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well. A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms. Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering.

Author : Lars Ahlfors
Publisher : Unknown
Page : 352 pages
File Size : 48,8 Mb
Release : 1979
Category : Education
ISBN : MINN:31951P010088754

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Complex Analysis by Lars Ahlfors Pdf

A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.

Author : E. Pap
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 44,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401711067

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Complex Analysis through Examples and Exercises by E. Pap Pdf

The book Complex Analysis through Examples and Exercises has come out from the lectures and exercises that the author held mostly for mathematician and physists . The book is an attempt to present the rat her involved subject of complex analysis through an active approach by the reader. Thus this book is a complex combination of theory and examples. Complex analysis is involved in all branches of mathematics. It often happens that the complex analysis is the shortest path for solving a problem in real circum stances. We are using the (Cauchy) integral approach and the (Weierstrass) power se ries approach . In the theory of complex analysis, on the hand one has an interplay of several mathematical disciplines, while on the other various methods, tools, and approaches. In view of that, the exposition of new notions and methods in our book is taken step by step. A minimal amount of expository theory is included at the beinning of each section, the Preliminaries, with maximum effort placed on weil selected examples and exercises capturing the essence of the material. Actually, I have divided the problems into two classes called Examples and Exercises (some of them often also contain proofs of the statements from the Preliminaries). The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercisesj the answers, and, occasionally, some hints, are still given.

Author : B. Choudhary
Publisher : New Age International
Page : 352 pages
File Size : 43,5 Mb
Release : 1993
Category : Mathematics
ISBN : 8122403999

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The Elements of Complex Analysis by B. Choudhary Pdf

This Book Is Intended To Be A Simple And Easy Introduction To The Subject. It Is Meant As A Textbook For A Course In Complex Analysis At Postgraduate Level Of Indian Universities.Some Of The Welcome Features Of The Book Are: Proofs And Motivation For The Theory: Examples Are Provided To Illustrate The Concepts; Exercises Of Various Levels Of Difficulty Are Given At The End Of Every Chapter: Keeping In View The Applied Nature Of The Subject, Ordinary Linear Homogeneous Differential Equations Of The Second Order And Conformal Mapping And Its Applications Are Given More Attention Than Most Other Books: Uniform Approximation And Elliptic Functions Are Treated In Great Detail; There Is Also A Detailed Treatment Of Harmonic Functions, Weierstrass Approximation Theorem, Analytic Continuation, Riemann Mapping Theorem, Homological Version OfCauchys Theorem And Its Applications; Diagrams Are Provided Whenever Feasible To Help The Reader Develop Skill In Using Imagination To Visualise Abstract Ideas; Solutions To Some Selected Exercises Which Involve Lot Of New Ideas And Theoretical Considerations Have Been Provided At The End.