Recent content by Pinedas42

Homework Statement Given a parallel plate capacitor with sides of size L connected to a constant potential (battery) separated by a distance D A dielectric slab is inserted between the plates to a length x so that there are two areas w/ dielectric constant K L(L-x) for the space without a...

Bumpity. Does anyone even have perhaps a hint that something is wrong?

Homework Statement Find the indicial equation and find 2 independent series solutions for the DE: xy''-xy'-y=0 about the regular singular point x=0 Homework Equations y=Ʃ(0→∞) Cnxn+r y'=Ʃ(0→∞) Cn(n+r)xn+r-1 y''=Ʃ(0→∞) Cn(n+r)(n+r-1)xn+r-2 The Attempt at a Solution Finding the...

OK, thank you! I had thought that there always had to be a function for \lambda>0, but I wasn't sure and I couldn't find any literature specifically mentioning it.

Homework Statement Find the eigenvalues and eigenfunction for the BVP: y'''+\lambda^2y'=0 y(0)=0, y'(0)=0, y'(L)=0 Homework Equations m^3+\lambdam=0, auxiliary equation The Attempt at a Solution 3 cases \lambda=0, \lambda<0, \lambda>0 this first 2 give y=0 always, as the only...

Homework Statement Assume f(1,1,1)=3 and f(1.1,1.2,1.1)=3.1 a) Which directional derivative Duf at (1,1,1) can be estimated from this information? Give vector u b) Estimate the directional derivative in part a Homework Equations Duf = del f (dot product) vector u del f =...

Thanks, I think I just looked deeper than what the question actually pertained to. I need to learn to drop expectations I suppose. :P Thanks again!

So what I get is a=-2c and b=c the actual numbers inside will be arbitrary? just as long as a=-2c and b=c above are true?

Homework Statement Find nonzero scalars a, b, c, such that au+b(u-v)+c(u+v)=0 for every pair of vectors u and v This isn't a homework question, more of a conceptual exercise, but I want to understand it thoroughly.The Attempt at a Solution I've gone to u(a+b+c) + v(c-b)=0 then I couldn't quite...

So I beat at it until I solved it :D ( I don't give up dammit) I put the integral into terms of u so u=cos(0)=1 u=cos(pi/2)=0so integral 0-->1 u(u^2+49)^-1/2 du I took the second sub of t=u^2+49 dt=2udu to give 1/2 integral0-->1 (t)^-1/2 dt 1/2 * 2 (t)^1/2 giving the function (u^2+49)^1/2...

Homework Statement Use 2 or more substitutions to find the following integrals hint : begin with u=cosx Homework Equations Integral 0--->pi/2 (cosxsinx)/swrt(cos2x+49 dx The Attempt at a Solution I'm still a little fuzzy on using multiple substitutions. From what I've read on...