Science And Technology

## Topics In Power Series Solution and Special Functions

The present book on ‘‘Power Series Solution and Special Functions’’ has been written as a textbook according to the latest guidelines and syllabus in Mathematics issued by the U.G.C. for various universities. The text of the book has been prepared with the following salient features. The language of the book is simple and easy to understand. Each topic has been presented in a systematic, simple, lucid and exhaustive manner. A large number of important solved examples properly selected from the previous university question papers have been provided to enable the students to have a clear grasp of the subject and to equip them for attempting problems in the university examination without any difficulty. Apart from providing a large number of examples, different type of questions in ample quantity have been provided for a thorough practice to the students. A large number of ‘notes’ and ‘remarks’ have been added for better understanding of the subject.
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-93-5274-101-4
Total Price: 0
• Chapter 1

Contents

• Chapter 2

Preface

• Chapter 3

### Chapter 1 - Series Solution of Differential Equations Price 0.11  |  0.11 Rewards Points

We know that linear differential equations with constant coefficients can be solved and their solutions are elementary functions.* There also exists some methods in which linear differential equations (with some specific types of variable coefficients) can be solved and their solutions are elementary functions. In general, a linear differential equation with variable coefficients may not admit of any solution which is expressible in terms of elementary functions. In the present chapter, we shall learn the method of solving linear differential equations and obtaining solutions in the form of an infinite series.

• Chapter 4

### Chapter 2 - Legendre Equation Price 0.11  |  0.11 Rewards Points

With the knowledge of series method of solving second order differential equations, we are ready to solve three very important differential equations of Physics. The present chapter and the next two chapters would be devoted to these differential equations. In this chapter, we shall consider the differential equation known as Legendre equation*.This differential equation occurs particularly in boundary value problems for spheres.

• Chapter 5

### Chapter 3 - Bessel Equation Price 0.11  |  0.11 Rewards Points

In this chapter, we shall study a very important differential equation called Bessel equation. This differential equation appears in problems relating to electric fields, viberations, heat conduction, etc.

• Chapter 6

### Chapter 4 - Hypergeometric Equation Price 0.11  |  0.11 Rewards Points

In this chapter, we shall study the third very important differential equation used very widely in applied mathematics. This differential equation is called Gauss hypergeometric equation or simply hypergeometric equation.

• Chapter 7

### Chapter 5 - Sturm-Liouville Problems Price 0.11  |  0.11 Rewards Points

In the present chapter, we shall study the solution of a special type of second order differential equations with given conditions. This type of differential equations with given conditions are called Sturm-Liouville problems. These problems will introduce us to the concepts of ‘eigen value’ and ‘eigen function’.