Math Help Forum - Advanced Applied Math

Numerical Integration of Fourier Transform.

nirmal323 — Fri, 20 Nov 2009 19:59:12 GMT

Hi Everyone,
I have the complicated function in Fourier Domain. I want to find the inverse fourier of the complicated function. This function is a vector potential of the electrodynamic wheel for magnetic levitation in Fourier domain. I am trying to get the function in the rectangular coordinate system, f(x). F(w) is a function in fourier domain. I want to find the function f(x) which is a fourier inverse of F(w).
I tried Mathematica, Maple and MATLAB to get the straight foruier inverse, but could not get the result.
I am wondering if there is any way to get the inverse fourier of F(w). I did not get any idea , so I am thinking of integrating it by Numerical Technique. But, I still do not know which of the numerical technique works well for the highly oscillatory function like this (i.e. For the Integrand: 1/(2*pi)*F(w)*exp(i*w*x)).

F(w)= [exp(t/2*w)*w^4*heaviside(-w)*cosh(r*y)] / [w*cosh(r*t/2)+r*sinh(r*t/2)]

Where, r=sqrt(w^2+i*mu(we+v*w)), here r is a function of w as well.
mu=permeability of the surface
y=distance along y-axis, we=angular velocity of the wheel, t=thickness of the guide-way, v=translational velocity of the wheel, x=distance in x-axis (which is a variable)
Now,
f(x)=Integration(-Inf,Inf,1/(2*pi)*F(w)*exp(i*w*x)*dw)

Could you please suggest me some ideas to find the Inverse Fourier of F(w) or Integrate by Numerical Technique (suggest me the best method for highly oscillatory Integrand).

Thank you !!!

Eigenvectors of a Jacobian matrix

chella182 — Thu, 19 Nov 2009 22:08:41 GMT

Sorry, if this is the wrong subforum, firstly.

So I have a dynamical system with fixed points , and .

The bit I'm stuck on is this; I have the Jacobian matrix for and as (so the trace and the determinant ) and the eigenvalues as and .

To find the eigenvectors and I know I need to solve

and

and this is what I'm stuck on. I've found both lines of the simultaneous equations to be

but I can't get anywhere with it. I did give it a go and got but I get the feeling that's not right (Worried) this was never my strong point when we initially learned it, but I think it's the complex number that's confusing me. Any ideas? Cheers in advance.

homework help

mlemilys — Wed, 18 Nov 2009 03:49:15 GMT

applied harmonic analysis

i am really struggling in this course and don't know where to begin.
if anyone could give me some hints or leads it would be greatly appreciated.
we don't really have a text and we just finally got a course outline that our professor wrote himself.
and even though i am an excellent note taker, i have hardly any due to the nature of my instructors teaching style.

thanks in advance for any help.
please see the attached assignment and pdf of the outline

Attached Files

	h3.pdf (43.8 KB)
	outline.pdf (516.1 KB)

zeros of an analytic function

dymin3 — Tue, 17 Nov 2009 09:17:26 GMT

let f, g be analytic on a domain containing a simple closed curve ɣ and its inside. Show that if |f(z)| > |g(z)| for all z in ɣ, then the two equations f(z)=g(z) and f(z)=0 have an equal number of solutions inside ɣ.

I do not know how to prove this T-T plz help me!!! (Crying)

and use above to determine how many solutions are there for z^3 = z^2 + z + 6 in |z|<1. I know answer for this is "no solution" but why??? :confused:

plz!!!

Calculus and Baseball

ReneePatt — Mon, 16 Nov 2009 17:17:44 GMT

An outfielder fields a baseball 280 ft away from home plate and throws it directly to the cather with an initial velocity of 100 ft/s. Assume that the velocity v(t) of the ball after t seconds satisfies the differential equation dv/dt = -1/10v because of air resistance. How long does it take for the ball to reach home plate? (Ignore any vertical motion of the ball).

I apologize if this question has already been posted. But I've spent some time searching and haven't found anything yet.

[SOLVED] Diffusion equation with a death rate

wglmb — Sun, 15 Nov 2009 23:29:22 GMT

I've been given this equation:

0, \mu >0" title="\frac{\partial n}{\partial t} = D_0 \frac{\partial}{\partial x}\left [ \left ( \frac{n}{n_0} \right ) ^m \frac{\partial n}{\partial x} \right ]- \mu n, D_0>0, \mu >0" style="border: 0px; vertical-align: middle;" />

(where "" is the death term)

Then I'm told:
Suppose . Show by appropriate transformations in and that this question can be reduced to one equivalent to

ie with no death term.

Now, I have absolutely no idea what transformations to use...

Game Theory IESD/IEWD

morganfor — Sat, 14 Nov 2009 04:14:22 GMT

Consider an n-person strategic game where each player picks an integer between 1 and 999. So N ={1,....n} and A_i={1,...,999}. Let a* be the mean of the action profile (a_1,...,a_n), that is a*= the sum of (a_i)/n for i=1,...,n. The winners in this game are those players whose choice of integer is closest to 2/3(a*)

How would one describe the results of IESD and IEWD for this case?

Thanks!

Economics Help:

neek — Fri, 13 Nov 2009 17:45:58 GMT

The question is:

5. Nimbus, Inc., makes brooms and then sells them door to door. Here is the relationship between the number of workers and Nimbus's output in a given day.

Workers | Output | Marginal Cost | Total Cost | Avg. Total Cost | Marginal Cost
0 0
1 20
2 50
3 90
4 120
5 140
6 150
7 155

a) Fill in the column of marginal products. What pattern do you see? How might you explain it?
--> I have filled in the Marginal cost. I think I did it right??

b) A Worker costs $100 per day, and the firm has a fixed cost of $200. Use the information to fill in the column for average for average total cost.

c) Fill in the column for Total Cost. (Recall that ATC = TC/Q) What pattern do you see?

d) Now fill in the column for marginal cost (Recall that MC = ^TC/^Q) What pattern do you see?

e) Compare the column for marginal product and the column for marginal cost. Explain the relationship.

f) Compare the column for average total cost and the column for marginal cost. Explain the relationship.

Workers | Output | Marginal Cost | Total Cost ?
0 0 20
1 20 30
2 50 40
3 90 50
4 120 60
5 140 70
6 150 80
7 155 90

I have gotten the marginal cost but i am having trouble with the total cost?

How do I go about finding the total cost?

I don't need anyone to fully answer these questions, but if someone could guide me through them? Anything would help.

Thanks

Tetrahedron and the dot product

Cabouli — Thu, 12 Nov 2009 00:52:25 GMT

Here is the question
"Two pairs of opposite edges of a tetrahedron are perpendicular. Prove that the third pair is also perpendicular."

I let the 3 sides be a, b and c
assume a is perpendicular to b
assume b and c are perpendicular

then a.b=0 and b.c=o

need to show a.c=o

but I am not sure how to proceed.

Cheers
Cabouli

Twiddle Factors in DFT

Sling434 — Wed, 11 Nov 2009 22:01:24 GMT

Could someone kindly explain to me how to calculate the Fourier Transform with Twiddle Factors?

central difference scheme

calculushelptx — Tue, 10 Nov 2009 18:01:51 GMT

I need a little clarification about how to use this equation.

f'(x)=f(x+h)-f(x-h)/2h + O(h^2)

here is the info
time___ 0 20 40 . . . . . . . . . . . .......................... . . 160 180 200
altitude 60 10170 33835 ........................107892 119626 162095

find the central difference at t=20 and t=180

I know how to find h but how to i put all these x values into the equation?

Complex Numbers

Aladdin — Tue, 10 Nov 2009 15:27:29 GMT

To every complex number , z different from -i . assign
f(z) = [tex]\frac{iz}{z+i}[/tex]
Denote by M the point of the plane with affix z .
A) a) Find the coordinates of the point B whose affix z0 is the solution of the equation f(z0)= 1 + 2i.
Work !

Affix of B is z0 = xB + iyB
f(z0) = yB = 1 + 2i ..
From the question : Solution : means that if I replace the values I will get zero

complex variables]Isolated singularities

dymin3 — Mon, 09 Nov 2009 22:45:14 GMT

Find the Laurent series for the given function about the indicated point and give the residue of the function at the point

1/(e^z-1)
zo=0 (four terms of the Laurent series)

I need help!!!plz

Green�s theorem

bashirsaad — Mon, 09 Nov 2009 07:33:33 GMT

please if any one can help me in this i will be thankful(Wait)

Attached Files

HW6_Math_514_Fall_2009[1].pdf (697.8 KB)

Divergence and Curl???

orendacl — Mon, 09 Nov 2009 04:52:01 GMT

Take the Divergence and curl of the following:

E = 5y^2 * xhat + 6xy * yhat

I suppose that my terminology for the "xhat & yhat" could look like x^ and y^; (has the hat symbol above the x and y values)...

I think that E is basically a vector field..