Homework Statement
Although not a computational problem, I still have difficulties understanding emission of characteristic X-rays.
Can someone please clear up my confusions about the topic? Here's where I'm stuck, with two texts as an example:
Source for the above...
Solved
Finally I understood where I've done wrong. For anyone's interest, here it is:
\sum_{1}^{\infty}a^{-k}e^{iw}=-\frac{a^{-1}e^{iw}}{1-a^{-1}e^{iw}}
From here one can solve the thing easily, which gives the correct condition that a>1 as well.
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Homework Statement
My book writes the following: using pair for the Discrete Time Fourier Transform:
-a^{k}u[-k-1] <---(DTFT)---> \frac{1}{1-ae^{-iw}} for \left | a \right | > 1
Homework Equations
Well, for the simple similar pair such as:
a^{k}u[k] <---(DTFT)--->...
Whoops!
So let me try it out in this case, and please correct me if I am wrong:
dy/dx=-\frac{(2xy+sin(x))}{x^{2}+1}
is 0 for x=0, y=2.
dF/dy=-\frac{(2x)}{x^{2}+1}
is 0 for x=0, y=2. However, this still means that the solution is unique, because both functions are continuous and defined...
Thanks for your effort!
However I am still confused with this, especially with implicit solutions.
As a last try, let me rephrase my question:
The paper says: "no solution if x0=0 and y0≠0." . But here, I do have a solution for the differential equation. Maybe that last summary is...
dF/dy=\frac{-2x}{x^{2}+1}
So you are saying that the "test" against the hypotheses of uniqueness states the fact, independent whether the differential equation (IVP) has any solution - as it does in this case?
Thank you LCKurtz for the fast reply! I have studied the sheet, as I have with my coursebook, but didn't get any smarter. Here's where I don't get it:
Yes, the paper says and explains clearly why there is y(0)≠0 gets no solution. But how does this applies to this particular equation, meaning...
Hi folks! This one got me in doubts...
Homework Statement
Solve IVP (Initial Value Problem): (2xy+sin(x))dx+(x^{2}+1)dy=0, y(0)=2
Is the solution unique? Motivate why!
Homework Equations
Relevant equations for solving the exact equation...
The Attempt at a Solution
I can...
Thanks for the advice but I'm sorry - this is not enough for me to understand. I need to find out the way to derive it, because I am certain that I will get this on the coming test.
Here's what I found out on the them internets - but I got stuck here as well. I understand the general way to...
Homework Statement
Verify that the vector functions x_{1}=\begin{bmatrix}e^{t}\\ e^{t}\end{bmatrix} and x_{2}=\begin{bmatrix}e^{-t}\\ 3e^{-t}\end{bmatrix} are solutions to the homogeneous system
x'=Ax=\begin{bmatrix}2 & -1 \\ 3 & -2 \end{bmatrix} on (-\infty ,\infty )
and that
x_{p}...
Homework Statement
Consider a surface ω with equation:
x^2 + y^2 + 4z^2 = 16
Find an equation for the tangent plane to ω at point (a,b,c).
Homework Equations
Tangent plane, 3 variables:
f_{1}(a,b,c)(x-a) + f_{2}(a,b,c)(y-b) + f_{3}(a,b,c)(z-c)= 0
The Attempt at a Solution
I get at the...
Homework Statement
Consider this control system below:
R = set point
E = remaining error
V = interference
My question is, if both R and V are unit step \frac{a}{s}, what will the value of U be when time t\rightarrow\infty ?
Homework Equations
This question is based on the...
Homework Statement
Consider following: a three-phase synchronous generator which is under excited and drives a load with the power factor of 0.9 .
U = 380 V (Main supply voltage)
Ia = 75 A
Xd = 3 Ω / phase
Find the excited voltage E and the load angle δ.
Homework Equations
Under...