Homework Statement
I need to find an expression for the gain in this circuit. I know it is an interting amplifier, because with the models we were given to look at, this one fits the inverting amlpifier. I've also constructed a simulation in a simple Java applet that I have.
My problem...
You guessed it, we're using Griffith's. If you can call it "using."
We aren't assigned reading, we aren't assigned problems out of the book. 99% of the time when that happens in a class, you think to yourself, "why do I even need this book, then?"
I have purchased all of the books for all of...
Hello all,
I'm taking my first actual quantum course this semester. I went over "briefly" some quantum mechanics Fall of 2012 in a Modern Physics course during my sophomore year, currently I'm a junior.
To get straight to the point, this course is making me miserable. I had high hopes for...
Homework Statement
I need to prove for arbitrary functions φ(x) that:
\lim_{\lambda \to 0} \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi} \lambda} exp\left( \frac{-x^{2}}{2 \lambda^{2}} \right) \varphi(x) dx = \varphi(0),
which, in the sense of distributions is basically the delta...
Thank you, I think I got what I needed from there. It just seemed like too simple of a problem.
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Now, would anyone happen to be able to tell me why a signal inverts iitself when coming back down the coaxial cable if we've shorted the other end?
I know the math that explains...
Homework Statement
We measured the time between a signal source, and it's reflection coming back through our probe after going through an open-ended coaxial cable.
My teacher told us this: the cable has a polyethylene insulator between central wire and the grounding web, which has a...
Homework Statement
Noether's theorem asserts a connection between invariance principles and conservation laws. In section 7.8 we saw that translational invariance of the Lagrangian implies conservation of total linear momentum. Here you will prove that rotational invariance of L implies...
It's an assignment, I'm much more than capable of solving this with more traditional means, but I can't submit that work.
I don't have my notebook at the moment but from memory, when using power series, you assume
y = \sum_{n=0}^{\infty} a_{n}x^{n}
Which means
y' =...
Homework Statement
When solving a D.E. with power series, I've encountered something along the lines of:
(2 - r)^{2}g'' = -2
Homework Equations
Power Series
The Attempt at a Solution
I know I am just supposed to assume such a series exists, and work from there. But I'm really...
Maybe I'm jumbling up notation.. The value I was calling x0 is where the function is a minimum value, and then I need to approximate the function for when |x - x0| is <<< than x0
I was assuming I needed to use some sort of series because it's included in the "series" part of the assignment
But how am I supposed to find this value of x-zero to use in the series? I thought I had to use the series to find it.
Or do I take its limit as it approaches zero, or..? I'm still lost
Homework Statement
I have the equation
f(x) = \frac{\lambda^{2}}{ax^{2}}-\frac{\gamma ab}{x}
What I am assigned to do is find a value of x at it's smallest, then approximate the value of the function when x - x(smallest) is much much greater than x(smallest).
Homework Equations
f(x) = f(0)...
Homework Statement
Compare the wavelengths of a particle when it passes a barrier of height (a) +V0 and (b) -V0 where E > |V0|. Calculate the momentum and kinetic energy for both cases.
Homework Equations
(see below)
The Attempt at a Solution
I know the wavelength changes in the...
Homework Statement
Compare the wavelengths of a particle when it passes a barrier of height (a) +V0 and (b) -V0 where E > |V0|. Calculate the momentum and kinetic energy for both cases.
Homework Equations
(see below)
The Attempt at a Solution
I know the wavelength changes in the...
Homework Statement
Find absolute maxima and minima of the function in the given region:
T(x,y) = x2 + xy + y2 - 6x
Region: Rectangular plate given by: 0 ≤ x ≤ 5, -3 ≤ y ≤ 3
Homework Equations
First derivative test, fx =0, fy = 0
Second derivative test, fxxfyy - fxy2 = ?
The...
It's great that I've worked out what I have done so far, I've come to some realizations that I didn't really notice before.
But my question was (and I guess I should have worded it better), does the order of the eigenvalues in the diagonal matter? Seeing how, for example, calculating the...
I've actually found that the diagonal of the 5x5 is just its eigenvalues down the main diagonal.
But, is the order important? I found the eigenvalues of the 2x2 and 3x3's, and they're all the same as the eigenvalues of the 5x5, which would mean they are the elements of the diagonal 5x5.. but...
How can I triangularize a matrix like this.. I don't see how it's possible.
{0, 2}
{2, 0}
The diagonal is already zero..and the outside bits are all non-zero. Is it literally impossible to triangularize this by roiw reductions? Same with the 3x3.. Maybe this way isn't the right way :(
So, just to make sure again..
Let's call the 3x3 matrix M, and the 2x2 matrix N.
I have to triangularize M and N, to get what was previously called V and W, not diagnalize M and N to get V and W?
So,
A = \begin{pmatrix}
M & 0 \\
0 & N
\end{pmatrix}
and
D =...
So, in reality, as opposed to treating the 5x5 as a whole and using its eigenvectors to fulfill [P-1AP = D], I should triangularise the 3x3 and the 2x2 and then put the resultant triangularised matrices back into a 5x5, which will then be equivalent to the Diagonal of the original 5x5?
If...
I'm required to diagonalize a 5x5 matrix by hand, using 'appropriate similarity transformations.' I'm not asking for an answer to a homework question, I'm asking is there any sort of easier (by hand) way of doing this than how I'm approaching it?
If it matters, the matrix is as follows:
A= {...
Homework Statement
Solve for x: Ax = y.
A = {{2 0 1},
{1 1 4},
{2 2 1}}
y = {{1},
{1},
{1}}
Homework Equations
Basic Matrix operations
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I have a vague idea how I'm supposed to do this, but I have no attempt yet.. eigenvalues and eigenvectors come...
Homework Statement
Find the gradient of the function at the given point. Then sketch the gradient together with the level curve that passes through the point.
g(x,y) = x2/2 - y2/2; (√2, 1)
Homework Equations
∇f = (∂f/∂x)i + (∂f/∂y)j
The Attempt at a Solution
∇g = <x, -y>
∇g(√2, 1) = <√2...
In K the event is seen as T0 = t2 - t1 = (3a / 2c) - (2a / c), and in K'.. um, T' = gamma*T0? If that's so then I don't know how to calculate this because gamma relies on velocity which is what I'm trying to find
Homework Statement
Find a system K' in which the following events in frame K appear at the same time:
i) x1 = a; t1 = (2a) / c; y1 = 0; z1 = 0
ii) x2 = 2a; t2 = (3a) / (2c); y2 = 0; z2 = 0
Describe the motion of K'.
Homework Equations
Lorentz transformations; time dilation...
Pardon my issues with the BB code and Latex, I've pretty much never used it before a week ago. Yes, you were able to pick out my errors quite nicely.
As for my main question, I've tried to invision what is going on. It seems this question is inherently trivial because...
Homework Statement
Evaluate the following expression:
\sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk}
Homework Equations
\delta_{ij} = [i = j]
The Attempt at a Solution
I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing has to do...
Homework Statement
Evaluate the following expression:
\sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk}
Homework Equations
\delta_{ij} = [i = j]
The Attempt at a Solution
I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing...