Using either formula (1)--(2) of
http://www.math.toronto.edu/courses/apm346h1/20151/HA3.html or its modification (if
needed)
a. Solve IVP for a heat equation (3) with $g(x)=e^{-\alpha |x|}$; what happens as $\alpha \to +0$?
b. Solve IVP for a heat equation with convection (4) with $g(x)=e^{-\alpha |x|}$; what happens as $\alpha \to +0$?
c. Solve IBVP with the Dirichlet boundary condition for a heat equation (3) with $g(x)=e^{-\alpha |x|}$; what happens as $\alpha \to +0$?
d. Solve IBVP with the Neumann boundary condition for a heat equation (3) with $g(x)=e^{-\alpha |x|}$; what happens as $\alpha \to +0$?
