Recent content by Brian T

Does anyone have recommendations for reading/resources on Discrete Exterior Calculus and/or Finite Element Exterior Calculus? In particular, I want to learn the topics to use in a project for a course and so would like to learn how to implement these methods (specifically geared toward...

I have several recommendations for differential geometry / forms: For a classical dg text, you can try "Tensor Analysis on Manifolds". For a more physics oriented text (specifically relativity), see "Differential Forms and the Geometry of General Relativity". This is a good book to see some...

As said above, you need to use the correct limits. It is not good enough to choose limits which agree at the boundaries (which yours doesn't even do), you need to have the correct domain throughout (e.g. for a triangle use linear functions).

I'm currently attending UCSD as a double major in math and physics. I can't tell you which school as I'm obviously biased. However, I will say that UCSD has a great program in the Math dept for applied math, Computational Science and Math (CSME) at the Center for Computational Maths. The grad...

Draw the region in the xy plane and then draw the region in the uv plane to determine bounds. From there, use the standard change of variables...

The first term ## r \times p## comes from the definition of angular momentum of any particle (or center of mass), while the second term comes from the fact that this object has a finite extent (i.e. moment of inertia). However, technically, the formula is incorrect since the first term is a...

Here's a question for you, why do you think one term is positive while the other is negative (i.e. what does it mean physically)?

There are two ways to go about doing that. 1) if you want to determine the normalization constant, you have the fact that the integral of the distribution over all possible values must 1, i.e. $$ \int_0^\infty P(r) dr = 1 $$ Use this integral to solve for C. 2) Again, using the fact that the...

If you have a good math background check out Geometry, Topology, and Physics by Nakahara https://www.crcpress.com/Geometry-Topology-and-Physics-Second-Edition/Nakahara/9780750306065

I'm doing something similar, physics and math double major. I front loaded my GEs so now I'm just doing all physics and math courses (18 to 20 units per quarter). It's time consuming and tiring but possible if you're committed. You should be able to get good grades if, like I said, you're...

Well, one way to do it is take the inner product of V2 and V1 and set that to 0. Note that since you're not in orthogonal coordinates, the product will contain some off diagonal terms. That will give you one equation, you have two unknowns so you'll need one more

I'd say focus on math as much as possible. Your intro science courses are fairly self contained, they don't assume prior physics or chem knowledge but they will expect you to be familiar with the math. If you get your math foundation set then you should be good to go.

The heat equation has the smoothing property which smooths out any discontinuities in the data, so no the solution after t=0 should not be piece wise

I know, that's why I said assume arclength parametrization (as is usual done when discussing geodesics, since they travel at constant speed anyway)

Of course it's not necessary, but op's asking out of interest how it's related. Here's another way you can think of it. Consider two contour lines (say f=a and f=b, b>a). You're currently on a point on the f=a contour. Assume you travel at arclength speed (one unit distance per unit time), then...