A solution of the 2d Laplace equation using separation of variables.

Solve Laplace of u = 0 subject to the conditions: u(x,0) = f1(x) u(0,y) = 0 u(x,b) = 0 u(a,y) = 0 0

Fourrier Series and Boundary Value Problem

Dear OTA, I attached to this posting a list of 8 Problems from which I need help only of three of them. They are: # 4, # 6 and # 8.

PDE

1. Consider the first order PDE, ∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0 a) Find the fundamental solution b) Use the fundamental solution and convolution to find a formula for the solution to: ∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0 u(x,0) = f(x) c) Use the method of characteristics to find the solution to part b.(Make sure your answers agree)

PDE - The convolution of two functions

See attached problem (convolution of two functions)

Nature of a Turning Point of a Function of Two Variables

Could you please do the problem attached? Thank you.