Singular Differential Equations And Special Functions

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Elements Of Ordinary Differential Equations And Special Functions

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Author : A. Chakrabarti
language : en
Publisher: New Age International
Release Date : 2006

Elements Of Ordinary Differential Equations And Special Functions written by A. Chakrabarti and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Ordinary Differential Equations And Special Functions Form A Central Part In Many Branches Of Physics And Engineering. A Large Number Of Books Already Exist In These Areas And Informations Are Therefore Available In A Scattered Form. The Present Book Tries To Bring Out Some Of The Most Important Concepts Associated With Linear Ordinary Differential Equations And The Special Functions Of Frequent Occurrence, In A Rather Elementary Form.The Methods Of Obtaining Series Solution Of Second Order Linear Ordinary Differential Equations Near An Ordinary Point As Well As Near A Regular Singular Point Have Been Explained In An Elegant Manner And, As Applications Of These Methods, The Special Functions Of Hermite And Bessel Have Been Dealt With.The Special Functions Of Legendre And Laguerre Have Also Been Discussed Briefly. An Appendix Is Prepared To Deal With Other Special Functions Such As The Beta Function, The Gamma Function, The Hypergeometric Functions And The Chebyshev Polynomials In A Short Form.The Topics Involving The Existence Theory And The Eigenvalue Problems Have Also Been Discussed In The Book To Create Motivation For Further Studies In The Subject.Each Chapter Is Supplemented With A Number Of Worked Out Examples As Well As A Number Of Problems To Be Handled For Better Understanding Of The Subject. R Contains A List Of Sixteen Important Books Forming The Bibliography.In This Second Edition The Text Has Been Thoroughly Revised.

Elements Of Ordinary Differential Equations And Special Functions

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Author : Aloknath Chakrabarti
language : en
Publisher: John Wiley & Sons
Release Date : 1990

Elements Of Ordinary Differential Equations And Special Functions written by Aloknath Chakrabarti and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Ordinary differential equations and special functions form a central part in many branches of Physics and Engineering. This book brings out some of the most important concepts associated with linear ordinary differential equations and the special functions of frequent occurrence. Each chapter is supplemented with a number of worked examples and problems to give the student a greater understanding of the subject.

Ordinary And Partial Differential Equations

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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-13

Ordinary And Partial Differential Equations written by Ravi P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-13 with Mathematics categories.

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.

Linear Ordinary Differential Equations

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Author : Earl A. Coddington
language : en
Publisher: Cambridge University Press
Release Date : 1997

Linear Ordinary Differential Equations written by Earl A. Coddington and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

A thorough development of the main topics in linear differential equations with applications, examples, and exercises illustrating each topic.

Singular Differential And Integral Equations With Applications

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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-31

Singular Differential And Integral Equations With Applications written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Mathematics categories.

In the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This mono graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.

Second Order Differential Equations

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Author : Gerhard Kristensson
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05

Second Order Differential Equations written by Gerhard Kristensson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-05 with Mathematics categories.

Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online.

Singular Differential Equations And Special Functions

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Author : Luis Manuel Braga da Costa Campos
language : en
Publisher: CRC Press
Release Date : 2019-11-05

Singular Differential Equations And Special Functions written by Luis Manuel Braga da Costa Campos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.

Singular Differential Equations and Special Functions is the fifth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This fifth book consists of one chapter (chapter 9 of the set). The chapter starts with general classes of differential equations and simultaneous systems for which the properties of the solutions can be established 'a priori', such as existence and unicity of solution, robustness and uniformity with regard to changes in boundary conditions and parameters, and stability and asymptotic behavior. The book proceeds to consider the most important class of linear differential equations with variable coefficients, that can be analytic functions or have regular or irregular singularities. The solution of singular differential equations by means of (i) power series; (ii) parametric integral transforms; and (iii) continued fractions lead to more than 20 special functions; among these is given greater attention to generalized circular, hyperbolic, Airy, Bessel and hypergeometric differential equations, and the special functions that specify their solutions. Includes existence, unicity, robustness, uniformity, and other theorems for non-linear differential equations Discusses properties of dynamical systems derived from the differential equations describing them, using methods such as Liapunov functions Includes linear differential equations with periodic coefficients, including Floquet theory, Hill infinite determinants and multiple parametric resonance Details theory of the generalized Bessel differential equation, and of the generalized, Gaussian, confluent and extended hypergeometric functions and relations with other 20 special functions Examines Linear Differential Equations with analytic coefficients or regular or irregular singularities, and solutions via power series, parametric integral transforms, and continued fractions

Special Functions

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Author : Z. X. Wang
language : en
Publisher: World Scientific
Release Date : 1989

Special Functions written by Z. X. Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

Contains the various principal special functions in common use and their basic properties and manipulations. Discusses expansions of functions in infinite series and infinite product and the asymptotic expansion of functions. For physicists, engineers, and mathematicians. Acidic paper. Paper edition (unseen), $38. Annotation copyrighted by Book News, Inc., Portland, OR

Singular Integral Equations

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Author : Ricardo Estrada
language : en
Publisher: Springer Science & Business Media
Release Date : 2000

Singular Integral Equations written by Ricardo Estrada and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This work focuses on the distributional solutions of singular integral equations, progressing from basic concepts of the classical theory to the more difficult two-dimensional problems.

Differential Equations Workbook For Dummies

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Author : Steven Holzner
language : en
Publisher: John Wiley & Sons
Release Date : 2009-06-29

Differential Equations Workbook For Dummies written by Steven Holzner and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-29 with Mathematics categories.

Make sense of these difficult equations Improve your problem-solving skills Practice with clear, concise examples Score higher on standardized tests and exams Get the confidence and the skills you need to master differential equations! Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more! More than 100 Problems! Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series THE DUMMIES WORKBOOK WAY Quick, refresher explanations Step-by-step procedures Hands-on practice exercises Ample workspace to work out problems Online Cheat Sheet A dash of humor and fun