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...
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 =...
General Question. How would I recognize when to do a full reduction of order versus using the formula y2=y1 integral(e^integral(P(x)dx)/y1^2)
So far I only know by when the homework problem set, specifies to use the formula or the reduction of order. However I want to know if I can tell...
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...