Author: A. Chakrabarti
Publisher: New Age International
ISBN: 9788122408805
Category :
Languages : en
Pages : 172
Get Book Here
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: Aloknath Chakrabarti
Publisher:
ISBN: 9788122402087
Category : Differential equations
Languages : en
Pages : 148
Get Book Here
Book Description
Author: Aloknath Chakrabarti
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 164
Get Book Here
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: Praveen Agarwal
Publisher: CRC Press
ISBN: 1000078566
Category : Mathematics
Languages : en
Pages : 371
Get Book Here
Book Description
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.
Author: Jeremy Gray
Publisher: Springer Science & Business Media
ISBN: 0817647732
Category : Mathematics
Languages : en
Pages : 357
Get Book Here
Book Description
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.
Author: Wilfred Kaplan
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 296
Get Book Here
Book Description
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.
Author: Sergeĭ I︠U︡rʹevich Slavi︠a︡nov
Publisher: Oxford University Press, USA
ISBN: 9780198505730
Category : Mathematics
Languages : en
Pages : 318
Get Book Here
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: James Morris Page
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
Book Description
Author: Louis Legendre Pennisi
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 792
Get Book Here
Book Description
Author: Michael Golomb
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 382
Get Book Here
Book Description
