Recent content by Pavoo

DrClaude and Jonathan Scott That certainly clears up my confusion! Thanks for pointing that out!

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. The thread may be locked now.

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)--->...

Thanks to both of you for your hints and guidance!

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...

Thanks for tip! I solved it through dependence on r , and integrated it at the end. I understand that this will be a rough approximation, because of the different speeds of the disc. I'll look for some constant that I can add to the equation to make it more accurate and will work with the...

EDIT: Would a further approximation be accurate (F = the braking force)? F = σ*v*B2 , where v is the rotating speed of the disc (average). OR, should I move back to the Farraday Law for integrating solutions? Thanks for any tips!