Question: 1 (Diffusion on the whole line)

Solve the diffusion equation u_t = ku_xx for x R and t (0, ) subject to the initial condition:

u(x, 0) = e^5x , x > 0

e^5x , x < 0

Express your solution in terms of the error function Erf.

Question: 3 (Complex numbers)

(a) Without using the fundamental theorem of calculus (FTC) for complex functions, evaluate the following integral. Remember to show your working. (Remark: you may use the FTC when your integrand is purely real)

01ieit dt