An Introduction To Complex Analysis And The Laplace Transform

Author : Vladimir Eiderman
Publisher : CRC Press
Page : 383 pages
File Size : 51,8 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 : Vladimir Ya Eiderman
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 2022
Category : Functions of complex variables
ISBN : 1032162031

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

Author : William R. Derrick
Publisher : Academic Press
Page : 233 pages
File Size : 50,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260488

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Introductory Complex and Analysis Applications by William R. Derrick Pdf

Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics, including integral transforms, asymptotic expansions, harmonic functions, Fourier transformation, and infinite series. Organized into eight chapters, this book begins with an overview of the theory of functions of a complex variable. This text then examines the properties of analytical functions, which are all consequences of the differentiability of the function. Other chapters consider the converse of Taylor's Theorem, namely that convergent power series are analytical functions in their domain of convergence. This book discusses as well the Residue Theorem, which is of fundamental significance in complex analysis and is the core concept in the development of the techniques. The final chapter deals with the method of steepest descent, which is useful in determining the asymptotic behavior of integral representations of analytic functions. This book is a valuable resource for undergraduate students in engineering and mathematics.

Author : Peter K.F. Kuhfittig
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 46,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489922014

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Introduction to the Laplace Transform by Peter K.F. Kuhfittig Pdf

The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily. The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.

Author : Hilary A. Priestley
Publisher : Oxford University Press
Page : 343 pages
File Size : 40,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9780198525615

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Introduction to Complex Analysis by Hilary A. Priestley Pdf

This second edition of Priestley's well-known text is aimed at students taking an introductory core course in Complex Analysis, a classical and central area of mathematics.

Author : Vladimir Eiderman
Publisher : CRC Press
Page : 399 pages
File Size : 40,7 Mb
Release : 2021-12-20
Category : Mathematics
ISBN : 9781000511116

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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 : T. K. V. Iyengar, B. Krishna Gandhi, S. Ranganatham & M.V.S.S.N. Prasad
Publisher : S. Chand Publishing
Page : 128 pages
File Size : 51,5 Mb
Release : 2024-06-26
Category : Science
ISBN : 9789352838219

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Laplace Transforms, Numerical Methods & Complex Variables by T. K. V. Iyengar, B. Krishna Gandhi, S. Ranganatham & M.V.S.S.N. Prasad Pdf

Laplace Transforms, Numerical Methods & Complex Variables

Author : Kalyan Chakraborty,Shigeru Kanemitsu,Takako Kuzumaki
Publisher : World Scientific Publishing Company
Page : 208 pages
File Size : 47,7 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 : P.P.G. Dyke
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105053

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An Introduction to Laplace Transforms and Fourier Series by P.P.G. Dyke Pdf

This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.

Author : Wilbur R. LePage
Publisher : Courier Corporation
Page : 516 pages
File Size : 54,9 Mb
Release : 2012-04-26
Category : Technology & Engineering
ISBN : 9780486136448

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Complex Variables and the Laplace Transform for Engineers by Wilbur R. LePage Pdf

Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.

Author : R. Beals
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 54,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781468498868

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Advanced Mathematical Analysis by R. Beals Pdf

Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for science and engi neering" from what might be called "advanced mathematical analysis for mathematicians." It seems to me both useful and timely to attempt a reconciliation. The separation between kinds of courses has unhealthy effects. Mathe matics students reverse the historical development of analysis, learning the unifying abstractions first and the examples later (if ever). Science students learn the examples as taught generations ago, missing modern insights. A choice between encountering Fourier series as a minor instance of the repre sentation theory of Banach algebras, and encountering Fourier series in isolation and developed in an ad hoc manner, is no choice at all. It is easy to recognize these problems, but less easy to counter the legiti mate pressures which have led to a separation. Modern mathematics has broadened our perspectives by abstraction and bold generalization, while developing techniques which can treat classical theories in a definitive way. On the other hand, the applier of mathematics has continued to need a variety of definite tools and has not had the time to acquire the broadest and most definitive grasp-to learn necessary and sufficient conditions when simple sufficient conditions will serve, or to learn the general framework encompass ing different examples.

Author : Luis Barreira,Claudia Valls
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 40,6 Mb
Release : 2012-04-23
Category : Mathematics
ISBN : 9781447140085

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Complex Analysis and Differential Equations by Luis Barreira,Claudia Valls Pdf

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.

Author : Richard Beals
Publisher : Unknown
Page : 230 pages
File Size : 44,8 Mb
Release : 1973
Category : Mathematical analysis
ISBN : 7506200422

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Advanced Mathematical Analysis by Richard Beals Pdf

Author : R. Beals
Publisher : Springer
Page : 128 pages
File Size : 44,6 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 3540780300

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Advanced Mathematical Analysis by R. Beals Pdf

Author : Stephen D. Fisher
Publisher : Courier Corporation
Page : 448 pages
File Size : 52,6 Mb
Release : 2012-04-25
Category : Mathematics
ISBN : 9780486134840

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Complex Variables by Stephen D. Fisher Pdf

Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.