Recent content by hbweb500

I am studying complex variables with Brown and Churchill. In it, they define the principal value of z^c, with both variables complex, to be e^{c\; \text{Log }z} , where \text{Log} is the principle value branch of the complex logarithm. Now, suppose z = i and c = 3 . We know that \text{Arg...

Yes, that is what I mean. In any case, I thought about it, and the determination of the probabilities isn't as hard as I thought it would be. For example, the probability of getting at least one 2 is the complement of getting no twos. The probability of getting no twos is: \frac{{1...

Ah, you forgot to divide out a (1/4) in order to get the summand into the form x r^{x-1} . In particular: \sum_{x=0}^\infty x r^{x} Divide out an r, dropping the power in the summand down by 1: r \sum_{x=0}^\infty x r^{x-1} Recognize that this is the derivative of the series with...

I am working on correcting an exam so that I may study for my probability final. Unfortunately, I don't have the correct answers, so I was hoping that someone here might be able to check my thought process. 1) Pick three numbers without replacement from the set {1,2,3,3,4,4,4}. Let T be the...

Alright, that makes sense! Thanks.

Ah, I think I see part of my confusion now. It is necessary for the stress tensor field to be divergenceless for equilibrium, not the tensor being zero... Perhaps you could answer this to solidify my understanding: Say you have some object that you are accelerating straight up in the z...

Alright, this sort of helps... I am trying to get a better understanding of the stress tensor mainly because we are reviewing the Maxwell stress tensor in my E&M class. The professor talks about the stress tensor as representing "momentum flow", i.e, the amount of momentum crossing a surface...

I understand all that. I guess my question is, if I look at a point in the medium, and there is a force from the left pointing toward to point, and a force from the right also pointing towards the point, do the forces cancel such that T_xx is zero...

I have a couple of questions about the stress tensor. I am not an engineering student, so this is the first time I have dealt with internal forces, stress, shears, and such. It is my understanding that the entries in the stress tensor are forces per unit area. I assume this means the total...

Yep, that's the case. I must have plugged it into Mathematica wrong.

Homework Statement Find the open circuit voltage across A & B: Homework Equations V = IR The Attempt at a Solution If I0 is the current leaving the voltage source and passing through the first resistor, I1 is the current through the left resistor in parallel, and I2 through...

Thanks!

Going from cylindrical coordinates to cartesian coordinates, we can use the transformations x = r \cos(\theta) , y = r \sin(\theta) , and, of course, z = z_{\text{cyl}}. Now, going from cartesian to cylindrical isn't as obvious, but is still simple. For example, the radius, r, is simply r...

I think you are on the right track. What I would do, instead of minimizing the distance, is to take advantage of the geometry. Draw a vector \vec{p} from the origin to the point. Draw another vector from the origin to the parameterized vector function: \vec{r}(t) = (3t-1, 2-t, t). Now, let...

I am working on a problem that uses the notation: \sum_{i,j=1}^n A_{i,j} Where A is an (n x n) matrix. I am a little unsure of what the summation is over, due to the odd notation "i,j = 1". My first guess is that this is shorthand for \sum_{i=1}^n \sum_{j=1}^n A_{i,j} But I...