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...
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
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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...
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
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The Attempt at a Solution
I have no idea how to solve this, but it's on our sample exam and there are no...
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
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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
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The Attempt at a Solution
The surface...
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...