Differential Equations

Differential Equations. From Linear Differential Equations. See attached file for full problem description.

Finding Green's functions - parabolic equations - heat equation

I am having great difficulty understanding how you derive Green's functions, particularly how the boundary conditions are incorporated. I've also not studied Fourier series before and it appears that these are also used particularly in developing solutions for parabolic PDEs. My text does not have any specific worked examples (only the theory) and so I can't see how it all works. The question I have is to find in 00 the Green's function G(x,t,x',t') satisfying P=v_xx + v_t and the additional conditions G_x'(x,t,a,t') = G(x,t,0,t') = 0. I've also attached two files (one in Word format, one PDF) where the equations/formulae are in a more readable format, along with the act... click for more

Differential Equations

From First Order Systems--Modeling via Systems. Please explain each step of your solution and double check your final answers. Thank you.

Differential Equations

From First Order Systems--The Geometry of Systems Please explain each step of your solution and double check your final answer. Thank you.

Spherical Symmetry and the Wave Equation

I'm a graduate student trying to study for an upcoming prelim exam and need help solving the attached practice problem. I accept the possibility that there is a typo in part (c) and that instead it asks you to show that u_t is discontinuous at (0,a/c) instead of u.