Integral Equations: Introduction (L1)

We are familiar with differential equations: an equation involving one (or more) unknown function and its derivatives. Similarly, an integral equation is an equaiton in which an unknown function appears under one or more integral signs.

For example, for a\le s\le b,a\le t\le b, the equations

f(s)=\int_a^b {K(s,t)g(t)dt}

g(s)=f(s)+\int_a^b {K(s,t)g(t)dt}

g(s)=\int_a^b {K(s,t)[g(t)]^2dt}

where the function g(s) is the unknown function while all the other functions are known, are integral equations. Note that f(s), K(s,t) can be complex valued functions of real variables s and t.

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