Recent content by demonelite123

Math and physics degrees usually require the same lower division math courses such as linear algebra, multivariable and vector calculus, differential equations, etc. As for upper division courses, math and physics will be quite different. pure math courses will be more heavily focused on...

i haven't used spivak myself, but how much analysis was covered in your course? for instance, did you learn about compactness, cauchy sequences, completeness, convergence, continuity in metric spaces and normed spaces? it seems to me that going from spivak directly to rudin's Real and...

i think i figured it out. i didn't calculate the potential correctly for the case that m was inside the earth. while my -CM'/r was correct, the term D was incorrect. after correctly calculating the potential due to all the shells that enclose the mass m, i do indeed get the same value of CM as i...

So I am given that the gravitational potential of a mass m a distance r away from the center of a spherical shell with mass m' is -Cm'/r for m outside the shell and constant for m inside ths shell. I am to find the potentials inside and outside a solid sphere (the earth) of radius R as well...

depending on the schools, you may find an introduction to general relativity covered in an undergraduate differential geometry class from the math department. you can also check to see if your school offers a graduate general relativity course.

rudin's exercises are known to be pretty difficult and may require more ingenuity than just simply applying the theorems and propositions in the text. you shouldn't have to do all of the exercises either. i would say scan through the exercises and find ones that you don't know how to do right...

personally, i didn't like number theory so much. but then again, i only took an introductory course in it which covered topics such as divisibility, linear congruences, and primitive roots. if you've taken an algebra course, there's going to be quite a bit of overlap in the beginning. have...

i'm trying to understand how the electrosatic potential expressed as an integral satisfies poisson's equation. i know that i have to take the laplacian of both sides of (Eq 1.17) page 35 in Jackson. i understood how jackson took the laplacian of \frac{1}{\sqrt{r^2 + a^2}} but after Eq 1.30...

i've been thinking about this and i am still confused on this issue. i recently came across a similar issue that is really making me doubt my competence with the chain rule. my book wants to take the partial derivative of f(y + an, y' + an', x) with respect to a. So it simply writes...

for the derivative g' which variable is the derivative with respect to? also, how come in your expansion of the chain rule for g' you have fh and fk but they are being multiplied by just h and k respectively? shouldn't it be something like fhh' + fkk'? also, thank you for your reply.

yes i meant for tx and ty to be t*x and t*y (normal multiplication) respectively.

sorry, what do you mean by t_x = x ? partial derivative of t with respect to x? could you explain a little more?

Let g(t) = f(tx, ty). Using the chain rule, we get g'(t) = (\frac{\partial f}{\partial x})(tx, ty) * x + (\frac{\partial f}{\partial y})(tx, ty) * y this was actually part of a proof and what i don't understand is that why didn't they write (\frac{\partial f}{\partial (tx)}) and...

ah ok. what you said earlier makes sense now. thanks!

sorry about my late response. I'm still a bit confused. for the case "going up" i agree that F = (-mg)j and d = (y - y0)j since as you said it was final point (y) - initial point (y0). but for the "going down" case, F = (-mg)j but how come d = (y0 - y)j? isn't final point - initial point...