Recent content by eckiller

doubleIntegral( |cos(x+y)| dx dy ) over the rectangle [0, pi]x[0,pi] I tried several ways to split the integral up so that I could remove the absolute value sign and integrate. However, I did not get the correct answer, so I must be splitting it wrong. Can someone show me how to split the...

Hi, how do I find the Fourier transform of this function sin x / x, i.e., f* = Integral( sin x / x * exp( i*w*x) dx from -infinity to +infinity ). I've been using Jordan's Lemma up to this point, but it doesn't seem to apply here as a way to evaluate the integral. Thanks for any help.

I need help completing this problem: y'' - 4k^2 y^2 = 0, y(0) = 2, y'(0) = 4k, k > 0 and fixed constant Let v = y' dv/dx = dv/dy * dy/dx = dv/dy * v dv/dy * v - 3k^2 y^2 = 0 Integral( v dv ) = Integral( 3k^2 y^2 ) v^2 = 2k^2 y^3 + C0 v(0) = 4k ==> C0 = 16k^2 dy/dx = sqrt(...

I am to reduce the following PDE to 2 ODEs and find only the particular solutions: u_tt - u_xx - u = 0; u_t(x,0) = 0; u(0,t) = u(1,t) = 0 I guess u = X(x)T(t), and plug u_tt, u_xx into PDE and divide by u to get: T''/T = X''/X + 1 = K I solve X'' + (1-K)X = 0 first. From...

I have the tridiagonal matrix (which comes from the backward Euler scheme) A = [ 1+2M - M 0 ... ] [ -M 1+2M 0 ... ] [ ... ] [ -M 1+2M ] I am given that the...

I have the transformation: z' = g(z) = f*z / (f-n) - f*n / (f-n) f >= 0 , n>= 0 constants that define an interval [n, f]. I want to prove, z' <= z.

I have formula for 1D wave equation: (*) u(x, t) = 1/2 [ f(x + ct) + f(x - ct) ] + 1 / (2c) Integral( g(s), wrt s, from x-ct to x+ct ) I am trying to find u(1/2, 3/2) when L = 1, c = 1, f(x) = 0, g(x) = x(1 - x). However, for (*) to work, the initial position f(x) and initial velocity...

Hi, I have that |T(p)| <= sqrt(10)*|p| where T is a linear mapping. The question is: How small must |p' - p''| be in order that |T(p') - T(p'')| <= 1/10. This is what I did: T linear, so |T(p') - T(p'')| = |T(p' - p'')|. Applying the bound: |T(p' - p'')| <=...

Hi, I am in an undergrad numerical analysis course. Our instructor lectured on some material not found in the book. Specifically, he talked about a way to check stability of finite differencing schemes (for PDE) by studying how each Fourier mode evolves in time. Then you can find an...

Thanks for the reply. But note that mu union is finite. j = 1 to finite number p.

Yes, I overwrote it by accident when I copied my new version of the proof in.

Hi, I think this proof is easy, but would like someone to check my work since sometimes I miss technicalities on these "easy" proofs. Let K1, ..., Kp be compact sets in R^n. Show that union( Kj, j = 1 to p) is a compact set in R^n. Proof. We show that if K1 and K2 are compact then...

Hi everyone, Let T be a linear operator on nxn Matrices with real entries defined by T(A) = transpose(A). Show that +-1 are the only eigenvalues of T. Any tips on how to start this. I thought about writing the matrix representation relative to the standard basis, but it seemed...

Hello, I have the inequality t > (1/2) + a / |w|^2 where w is a complex number, w = a + bi. So the a in the inequality is the real part. So I need to find t such that all w are in a sector around the negative real axis. Note t in [0, 1]. I am having trouble figuring out the...

Hello, I am given the method: y_(n+1) = y_n + h f(t_n + w h, (1-w)y_n + w y_(n+1). I am to determine the region of absolute stability; I am also to determine for which w in [0, 1] is the method A(a) stable, i.e., the region of absolute stability contains a sector about the negative...