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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 nonzero, then the PDE is second order. If
but or are nonzero, 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 nonlinear. 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.

linear PDE.

nonlinear PDE.

linear, inhomogeneous PDE.
Example 1. .2Second order Partial Differential Equations.

linear PDE.

linear, inhomogeneous PDE.

nonlinear PDE.
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Prof. Alan Hood
20001030