Method of Green’s Functions 18.303 Linear Partial Differential Equations
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چکیده
We introduce another powerful method of solving PDEs. First, we need to consider some preliminary definitions and ideas. Definition [Delta Function] The δ-function is defined by the following three properties, δ (x) = 0, ∞, x � = 0, x = 0, ∞ δ (x) dx = 1 −∞ ∞ f (x) δ (x − a) dx = f (a) −∞ where f is continuous at x = a. The last is called the sifting property of the δ-function. To make proofs with the δ-function more rigorous, we consider a δ-sequence, that is, a sequence of functions that converge to the δ-function, at least in a pointwise sense. Consider the sequence
منابع مشابه
The method of characteristics applied to quasi-linear PDEs 18.303 Linear Partial Differential Equations
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تاریخ انتشار 2006