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Author: A. Chakrabarti Publisher: New Age International ISBN: 9788122408805 Category : Languages : en Pages : 172
Book Description
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.
Author: A. Chakrabarti Publisher: New Age International ISBN: 9788122408805 Category : Languages : en Pages : 172
Book Description
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.
Author: Luis Manuel Braga da Costa Campos Publisher: CRC Press ISBN: 0429641648 Category : Mathematics Languages : en Pages : 359
Book Description
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
Author: Gerhard Kristensson Publisher: Springer Science & Business Media ISBN: 1441970207 Category : Mathematics Languages : en Pages : 219
Book Description
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.
Author: Sergeĭ I︠U︡rʹevich Slavi︠a︡nov Publisher: Oxford University Press, USA ISBN: 9780198505730 Category : Mathematics Languages : en Pages : 318
Book Description
The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlevé equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a useful text and reference work.
Author: Aloknath Chakrabarti Publisher: John Wiley & Sons ISBN: Category : Mathematics Languages : en Pages : 164
Book Description
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.
Author: Luis Manuel Braga da Costa Campos Publisher: CRC Press ISBN: 0429638477 Category : Mathematics Languages : en Pages : 192
Book Description
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
Author: Steven Holzner Publisher: John Wiley & Sons ISBN: 0470543892 Category : Mathematics Languages : en Pages : 315
Book Description
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
Author: R.P. Agarwal Publisher: Springer Science & Business Media ISBN: 9401730040 Category : Mathematics Languages : en Pages : 412
Book Description
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.
Author: Ravi P. Agarwal Publisher: Springer Science & Business Media ISBN: 0387791469 Category : Mathematics Languages : en Pages : 422
Book Description
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.
Author: Katsunori Iwasaki Publisher: Springer Science & Business Media ISBN: 3322901637 Category : Technology & Engineering Languages : en Pages : 355
Book Description
This book gives an introduction to the modern theory of special functions. It focuses on the nonlinear Painlevé differential equation and its solutions, the so-called Painlevé functions. It contains modern treatments of the Gauss hypergeometric differential equation, monodromy of second order Fuchsian equations and nonlinear differential equations near singular points.The book starts from an elementary level requiring only basic notions of differential equations, function theory and group theory. Graduate students should be able to work with the text."The authors do an excellent job of presenting both the historical and mathematical details of the subject in a form accessible to any mathematician or physicist." (MPR in "The American Mathematical Monthly" März 1992.
Author: A. Chakrabarti
Author: A. Chakrabarti
Author: Luis Manuel Braga da Costa Campos
Author: Gerhard Kristensson
Author: Sergeĭ I︠U︡rʹevich Slavi︠a︡nov
Author: Aloknath Chakrabarti
Author: Luis Manuel Braga da Costa Campos
Author: Steven Holzner
Author: R.P. Agarwal
Author: Ravi P. Agarwal
Author: Katsunori Iwasaki