Recent content by rexasaurus

I was able to solve for the following: du/ds=1 integrate to get u=s+K1 dx/ds=x integrate to get x=K2es dy/ds=y integrate to get y=K3es I am unsure how to use the IC's

1. Use the method of characteristics to solve: xux+yuy=1 2. given condition of u(x,y)=1 when x2+y2=1 3. I know I need to transpose into the s-t domain. Using: du/ds=uxdx/ds+uydy/ds=aux+buy so a=x & b=y... please help

1. Show that, if the velocity field (V) is a fixed (spatially constant) vector, then the characteristic curves will be a family of parallel-straight lines. 2. ut+V1ux+V2uy=f f=S-[dell dotted with V]u characteristic curves: dX/dt=V1(X,Y) & dY/dt=V2(X,Y) 3. really looking for...

[b]1. I am looking for some examples on how to perform ray-tracing and extensions for a function. u_{tt}=u_{xx} for 0<x<1 with homogeneous Dirichlet conditions (i.e., the boundary conditions are that u(t,0) and u(t,1) are 0 for all t). As initial data we assume that u(0,x)= x for 0 < x <...

[b]1. For the 1-D wave equation, the d’Alembert solution is u(t, x) = f (x + ct) + g(x − ct) where f , g are each a function of 1 variable. Suppose c = 1 and we know f (x) = x^2 and g(x) = cos 2x for x > 0. Find u(t, x) for al l t, x ≥ 0 if you are also given the BC: u ≡ 1 at x = 0...

Sin(K*u)?? Second derivative would be -K2sin(K*u) I am not sure which variable should be inserted for "u" since u is a function of x,y,z.

Thx for your help.

the last substitution should read λ=α2+β2

I checked the problem statement The question actually states: u(t,x,y)=e-λtsin(αt)cos(βy) Could the instructor possibly have made a typo?? When I set ut=uyy (from simplifying Δu) I was able to substitute: λ=2+β2 My last line reads: αcos(αt)+β2sin(αt)=(α2+β2)sin(αt) Any thoughts?

The original equation was posted incorrectly. The actual question states: u(t,x,y)=e-λtsin(αt)cos(βy) My apologies

[b]1. verify that u(t,x,y)=e-λtsin(αt)cos(βt) (for arbitrary α, β and with λ=α2+β2) satisfies the 2-D Heat Equation. [b]2. ut=Δu [b]3. I began with: Δu=uxx+uyy. note the equation does not contain variable "x" so uxx=0 i.e. Δu=uyy uy=e-λtsin(αt){-βsin(βt)}...

[b]1. A function "v" where v(x,y,z)≠0 is called an eigenfunction of the Laplacian Δ (on some region Ω - with specified homogenous BC) if v satisifies the BC ad also Δv=-λv on Ω for some number λ. Part A: Give an example of an eigenfunction of Δ when Ω is the cube [0,∏]3 with Dirichlet BCs...

Thank you for your help. I was able to plot the graph for x^2 and the odd/even BC's not sure where to go from there. Any help is appreciated.

1. Homework Statement : A function f : R → R is called “even across x∗ ” if f (x∗ − x) = f (x∗ + x) for every x and is called “odd across x∗ ” if f (x∗ − x) = −f (x∗ + x) for every x. Define f (x) for 0 ≤ x ≤ ℓ by setting f (x) = (x^2) . Extend f to all of R (i.e., define f (x) for all real x)...