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...Math fourier series and boundary value problems chapter ii separation of variables greg fasshauer department applied mathematics illinois institute technology fall iit edu outline model problem linearity heat equation for a finite rod with zero end temperature other laplace s much the following discussion we will use d constant values c k as q x t tu xu l initial condition u f conditions play very important role in our work denition theoperator is linear if any constants functions differentiation integration are operations example consider ordinary univariate function i e then dx...