A solution of the wave equation using D'Alembert's solution
Solve the wave equation subject to the initial conditions u(x,0)=sin(x)/(x^2+1), du/dt(x,0)=x/(x^2+1)
The Fourier coefficients of a derivative
Let f be a 2 pi periodic, differentiable function with Fourier coefficients a_n and b_n. Let (a_n)*, (b_n)* be the Fourier coefficients of f'. a) Show that (a_0)*=0 b) Use integration by parts to find a formula for the Fourier coefficients of f' in terms of the Fourier coefficients of f. (The attachment contains the ...continues
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.
PDE's - separation of variables
I would like to understand how these 2 problems are solved. Thanks.
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.
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 Two Variables
Could you please do the problem attached? Thank you.
