Recent content by Vishera

For anyone reading this in the future: I've figured it out. The unit vector ##\hat{a}_{\rho}## does not mean: ##\rho=1##, ##\phi=0##, ##z=0##. ##\hat{a}_{\rho}## actually depends on ##\phi## as it's ##\left( cos\phi,sin\phi,0 \right)##.

So to simplify things, would I be correct in saying that ##{ { \hat { a } } }_{ ρ }## depends on ##\varphi## because the cylindrical coordinate system has ##\varphi## as one of its components but ##{ { \hat { a } } }_{ x }## does not depend on ##\varphi## because the rectangular coordinate...

Alright, thank you for mentioning that vector integrals work like scalar integrals. You said earlier that "If you use curvilinear coordinates, the basis used depends on the point in space." I'm not sure what you're referring to when you say "the point in space" since the integral in the...

It seems this is going over my head. Do you know what I can read to understand vector integrals? I already completely Calculus 3, and I did double integrals, triple integrals, line integrals, surface integrals, green's theorem, stoke's theorem, divergence theorem, etc. But I don't recall ever...

Sorry, I'm having trouble understanding. I'm a little rusty on linear algebra. The basis is "vectors that are linearly independent and every vector in the vector space is a linear combination of this set". But you can only take the basis of a vector space. Are you saying I should take the basis...

Question: Solution: The notation used is: ##(x,y,z)## is for rectangular coordinates, ##(\rho,\varphi,z)## for cylindrical coordinates and ##(r,\theta,\varphi)## for spherical coordinates. ##{ { \hat { a } } }_{ ρ }## represents the unit vector for ##\rho## (same applies to ##x, y, z##...

It seems to me that both PN junctions and transistors act as switches. And both switches are voltage-controlled. So what advantage does a transistor have over a PN junction? When the voltage is high on a PN junction, it is in forward bias and it allows current to pass though. When the voltage is...

Is there any reason why logic gates are built using transistors instead of PN junctions? Wouldn't it be more cost-efficient to use PN junctions? I am referring to CMOS logic gates. Also, what can a transistor do that a PN junction can't?

Do LUTs need to look exactly like this below? Or can LUTs be any sort of box that has 2 inputs and 1 output? Also, do LUTs need those pink squares? i.e. stored 1's and 0's inside the LUT as memory.

Homework Statement Homework EquationsThe Attempt at a Solution [/B] The multiplexer that is closest to the top of the page has ~x3 as an input but I am not allowed to use the negation of a logical variable as an input. Any way to get rid of this negation?

Homework Statement Homework EquationsThe Attempt at a Solution Here is my solution: Is this the most efficient solution? I have to minimize the number of multiplexers I use so I think this is optimal, correct?[/B]

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Is there any more efficient way to solve this problem? The resultant functions are quite complicated and I was wondering if there is any way to make them simpler so it would be easier to draw the circuit.

Homework Statement Homework EquationsThe Attempt at a Solution I am unsure how to proceed from here. Here is what I understand LUTs to look like: Here is my attempt so far: [/B]

I just did it this way and it seems to be correct. Is there anything I did wrong with my method? Actually, I think I figured out what I did wrong. I substituted C=0.25 instead of C=1 and I substituted L=1 instead of L=0.25. Opps.

The problem is that the provided solution doesn't derive the differential equations from scratch. It uses equations that we are supposed to memorize. I would prefer to just solve the problem from scratch instead of plugging in and chugging. I am trying to derive the differential equations from...