Recent content by physmatics

Thank you for replying! I figured out how to solve it on my own though, and if anyone is interested I can obviously describe the solution here :)

Homework Statement Hi! Not sure if I'm posting in the right section, this problem is from a course in scientific computing. Anyway, we're considering a set of PDEs: u_t + Au_x = 0 \quad 0<x<1, \ t>0 \\ u(x,0) = f(x) \quad 0 \leq x \leq1 \\ u_1(0,t) = 0 \quad t \geq 0 \\ u_2(1,t) = 0 \quad t...

Homework Statement So we have a source (OP) that emits single photons of a constant wavelength and angular frequency. The photons hit a 50-50 beam splitter, and are then reflected in the mirrors. Where is says (L) ou (SP) (yay for studying in French!) there is a beam splitter. What I...

Pardon me, it should obviously be point x instead of point p!

Hi! I'm not sure this is exactly the right subforum, but here goes: Homework Statement So we have a source (OP) that emits single photons of a constant wavelength and angular frequency. The photons hit a 50-50 beam splitter, and are then reflected in the mirrors. Where is says (L)...

Homework Statement We're supposed to convolve the signal x[k] = u[k] - u[k-8] with its impulse response h[k] = sin(pi*k/4)*( u[k] - u[k-8] ) with the help of MATLAB. Homework Equations - The Attempt at a Solution The thing is that we don't know how to do this in MATLAB...

Homework Statement So, I want to find the pivot columns to the matrix A: A= -1 1 -5 0 2 3 0 6 1 -1 2 -1 7 2 1 2 -7 25 5 1 and after that I want to solve Ax = b where b is (I kind of want to solve Ax = 0 as well, but let's skip that...): b= a+3 2a -a-1 -9a-5 My thought was...

Woah... That's quite embarrasing! Anyway, I'm happy that that was the only mistake I made... Thank you, ehild!

Homework Statement A cylinder with radius r = 0.6 m hangs in a horisontal frictionless axis. A string is winded around it and a constant force, F = 50.0 N, is acting on the string from t1 = 0 s to t2 = 2.00 s. During this time, L = 5 m of the string unwinds. The system starts from rest. a)...

Homework Statement Calculate the integral I = \int (t^x - 1)/ln(t) dt, boundaries: 0 \leq t \leq 1, x \geq 0 by differentiating first with respect to x. Homework Equations - The Attempt at a Solution I have no idea how to solve this, but it's on our sample exam and there are no...

I wrote the Jacobian as a fraction instead, it turned out to work perfectly :) Should have looked closer at it!

Homework Statement Calculate the double integral over D \int\int x*ln(2x + y)/y^3 dx dy D is the finite area in the xy-plane within the straight lines 2x + y = 1 2x + y = 3 x = y x = 2y Homework Equations - The Attempt at a Solution I thought it was obvious to make the variable substitution u...

Homework Statement Calculate the surface integral I = \int\int f dS of the function f(x,y,z) = \sqrt{1/2 + y^{2}} over the surface S given by x^{2} + 2*y^{2} = 1, 0 \leq z \leq x^{2} + y^{2}. (Clue: parametrize the surface.) Homework Equations - The Attempt at a Solution The surface...

Thank you all! I get 5^{x} = 3/5 so x = log_5 3/5 which I should have realized earlier. Now I can be less ashamed as a tutor...

After some rearrangements, I get: x+log_5 (2*5^{x+1}-1) = log_5 3 This is what I mean by "always ending up with something on the form log5(a+bx) or log5(a+b*x)". Now, I could use a subtraction identity that will give me: x+log_5 (2*5^{x+1}) + log_5 ((1-1/(2*5^{x+1}))) = log53 even...