Elements Of Ordinary 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 Differential Equations And Group Theory From Riemann To Poincare
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Author : Jeremy Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-07
Linear Differential Equations And Group Theory From Riemann To Poincare written by Jeremy Gray 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 2010-01-07 with Mathematics categories.
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Special Functions And Analysis Of Differential Equations
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Author : Praveen Agarwal
language : en
Publisher: CRC Press
Release Date : 2020-09-08
Special Functions And Analysis Of Differential Equations written by Praveen Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-08 with Mathematics categories.
Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.
Elements Of Ordinary Differential Equations
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Author : Wilfred Kaplan
language : en
Publisher:
Release Date : 1964
Elements Of Ordinary Differential Equations written by Wilfred Kaplan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.
This book is intended to serve as a text for a first course on differential equations. It provides more than enough material for a one-semester course. The book is a much shortened version of the author's Ordinary Differential Equations (525 pp., Addison-Wesley Publishing Company 1958). The principal differences are as follows: the section on matrices and the chapters on exact differential equations of higher order, phase plane analysis, and fundamental theory (proofs of existence theorems) are omitted; the treatment of linear equations from the point of view of the systems designer (input-output analysis) is considerably abbreviated; the material is regrouped in 10 short chapters. With all these changes, the present volume still retains the principal aspects of the longer work: the emphasis on gaining insight and understanding as opposed to pure manipulative skill; the use of physical examples both as illustrations of the mathematical methods and as aids to understanding these methods. Chapter 1 presents the important concepts and the main problems. By a study of simple numerical methods, an understanding of the existence theorem is gained. Chapter 2, devoted to equations of first order and first degree, gives some special procedures for solving problems in explicit form but also emphasizes understanding the processes. Chapter 3 gives a number of applications of first order equations; for the linear equations, some discussion of the systems point of view is given. Chapter 4 considers linear equations of arbitrary order, presents the main theorems, and methods for equations with constant coefficients; additional methods, based on differential operators and Laplace transforms, are given in Chapter 5. Chapter 6 treats applications of linear equations, including such topics as stability, transients, response to sinusoidal forcing functions, with illustrations in mechanics and circuit theory. Chapter 7 is devoted to simultaneous linear equations, with emphasis on the method of exponential substitution; operational methods are also introduced; applications are treated briefly. Chapter 8 discusses equations not of first degree and introduces the concept of singular solution. Chapter 9 covers power series solutions, and includes solution of linear equations at regular singular points.
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
Elements Of Partial Differential Equations
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Author : Ian N. Sneddon
language : en
Publisher: Courier Corporation
Release Date : 2013-01-23
Elements Of Partial Differential Equations written by Ian N. Sneddon and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-23 with Mathematics categories.
This text features numerous worked examples in its presentation of elements from the theory of partial differential equations, emphasizing forms suitable for solving equations. Solutions to odd-numbered problems appear at the end. 1957 edition.
Elements Of Ordinary Differential Equations
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Author : Michael Golomb
language : en
Publisher:
Release Date : 1965
Elements Of Ordinary Differential Equations written by Michael Golomb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.
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.