Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations

Partial Differential Equations

Introduction

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Partial differential equations arise in connection with various physical and geometrical problems. When the functions involved depend on two or more independent variables, usually on time t and one or several space variables.

UNIT - I

Partial Differential Equations

Formation of partial differential equations Singular integrals - Solutions of Standard types of first order partial differential equations - Lagrange's linear equation - Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

 

INTRODUCTION

Partial differential equations arise in connection with various physical and geometrical problems. When the functions involved depend on two or more independent variables, usually on time t and one or several space variables. It is fair to say that only the simplest physical systems can be modeled by ordinary differential equations whereas most problems in fluid mechanics, elasticity, heat transfer, electromagnetic theory, quantum mechanics and other areas of physics lead to partial differential equations.

A partial differential equation is one which involves partial derivatives. The order of a partial differential equation is the order of the highest derivative occuring in it.

Throughout this chapter, we use the following notations : z will be taken as a dependent variable which depends on two independent variables x, y so that z = f(x, y). We write


Thus, p + qx = x+y is a partial differential equation of order 1 and r+t = x2+y is a partial differential equation of order 2.

Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations : Tag: : Introduction - Partial Differential Equations

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MA3351 3rd semester civil, Mechanical Dept | 2021 Regulation | 3rd Semester Mechanical Dept 2021 Regulation