2 examples of the method of characteristics for solving PDEs

1. Use the method of characteristics to solve the advection equation du/dt=-kdu/dx-ru subject to the initial condition u(x,0)=f(x). 2. Use the method of characteristics to solve du/dt+te^(-t^2))du/dx=usin(t) subject to the initial condition u(x,0)=e^(-x^2)) (See attachment for the above questions formatt ...continues

Solving the wave equation using separation of variables

See the attachment for the questions.

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

Fourier Series and Boundary Value Problems

Please help with the following problems : # 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 < ∞ ...continues

PDE - The convolution of two functions

See attached problem (convolution of two functions)

Nature of a turning point of a function of 2 variables

Could you please do the problem attached? Thank you.

Differential Equation

Find general solutions for the attached differential equations.

Quasi-linear pde

I'm having trouble with a PDE problem, I've indicated in the attached file what specifically.

Use Green's function for the first quadrant of R^2 to solve Laplace's equation with boundary conditions.

Please see the attachment for full description.