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# Introduction

A Partial Differential Equation (PDE) is an equation relating a function of two or more independent variables and its partial derivatives. Consider the general equation (1.1)

where , , , , and may be functions of , and even . The order of the equation is given by the order of the highest derivative. Thus, if one of the functions, , or are non-zero, then the PDE is second order. If but or are non-zero, then the PDE is first order.

If the functions , , , , and do not depend on the dependent variable , then Equation (1.1) is linear otherwise it is non-linear. We are mainly concerned with linear PDEs in this course.

If , then Equation (1.1) is honogeneous otherwise it is inhomogeneous.

Example 1. .1First order Partial Differential Equations.

1. linear PDE.

2. non-linear PDE.

3. linear, inhomogeneous PDE.

Example 1. .2Second order Partial Differential Equations.

1. linear PDE.

2. linear, inhomogeneous PDE.

3. non-linear PDE.   Next: Revision of Partial Differentiation Up: Partial Differential Equations of Previous: Partial Differential Equations of
Prof. Alan Hood
2000-10-30