Engineering

## Topics in Partial Differential Equations

The present book on ‘‘Partial Differential Equations’’ 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: (i) The language of the book is simple and easy to understand. (ii) Each topic has been presented in a systematic, simple, lucid and exhaustive manner. (iii) 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. (iv) 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. (v) A large number of ‘notes’ and ‘remarks’ have been added for better understanding of the subject.
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-93-5274-102-1
• Chapter 1

Contents

• Chapter 2

Preface

• Chapter 3

Symbols

• Chapter 4

### Chapter 1 - Partial Differential Equations Price 0.11  |  0.11 Rewards Points

Partial differential equations arise in applied mathematics and mathematical physics when the functions involved depend on two or more independent variables. The use of partial differential equation is enormous as compared to that of ordinary differential equations. In the present chapter, we shall learn the method of solving various types of partial differential equations.

• Chapter 5

### Chapter 2 - Partial Differential Equations of The first Order Equations Linear in P and Q Price 0.11  |  0.11 Rewards Points

In the last chapter, we studied the methods of forming partial differential equations. The next step is to solve partial differential equations. Solving a partial differential equation means to find a function which satisfies the given partial differential equation. A function satisfying a partial differential equation is called its solution (or integral). In the present chapter, we shall confine ourselves to the solution of partial differential equations of first order and at the same time linear in p and q.

• Chapter 6

### Chapter 3 - Partial Differential Equations of The first Order Equations Non-Linear in P and Q Price 0.11  |  0.11 Rewards Points

By now we have learnt the method of solving first order partial differential equations which are linear in partial derivatives p and q. A partial differential equation of first order need not be linear in p and q. In the present chapter, we shall study the methods of solving such equations. In the first part, we shall study the method of solving some special types of equations which can be solved easily by methods other than the general method. In the second part, we shall take up Charpit’s general method of solution.

• Chapter 7

### Chapter 4 - Homogeneous Linear Partial Differential Equations with Constant Coefficients Price 0.11  |  0.11 Rewards Points

Till now we have been discussing the methods of solving partial differential equations of the first order. A partial differential equation of the first order involves, only the first order partial derivatives (p and q) of the dependent variable z. Now we shall consider the solution of partial differential equations of order higher than one.

• Chapter 8

### Chapter 5 - Non-Homogeneous Linear Partial Differential Equations with Constant Coefficients Price 0.11  |  0.11 Rewards Points

From the last chapter, we have been solving linear partial differential equations with constant coefficients. In that chapter we found the general solution of only such equations in which the orders of all partial derivatives involved in the equation were same. In other words, we solved only homogeneous linear partial differential equations with constant coefficients. In the present chapter, we shall learn the methods of finding general solution of linear partial differential equations which are not homogeneous.

• Chapter 9

### Chapter 6 - Partial Differential Equations Reducible to Equations with Constant Coefficients Price 0.11  |  0.11 Rewards Points

Now we shall consider the method of solving a particular type of linear partial differential equations with variable coefficients that are capable of reducing to linear partial differential equations with constant coefficients.

• Chapter 10

### Chapter 7 - Monges Method Price 0.11  |  0.11 Rewards Points

In the last chapter we discussed the methods of solving some special type of linear partial differential equations with variable coefficients which were capable of being reduced to linear partial differential equations with constant coefficients by changing the independent variables. Solving any given partial differential equation with variable coefficients is not an easy task. We are moving in this direction step by step.