Recent content by rick1138

John Hubbard's Vector Calculus, Linear Algebra, and Differential Forms is outstanding. I recommend it highly.

I suffer from the same illness as Turbo-1. It is very difficult to deal with, mainly because of the attitude of society towards people who suffer from it.

I'm looking for resources of worked problems in modern differential geometry. There are plenty that have theorems and general formulas but very few that gon into the dirty details of how to solve actual problems. Any information would be appreciated.

I'd like an example of calculating the Lie derivative of a one-form with respect to a vector field, for example, the one-form \omega = 3 dx_1 + 4x dx_2 with the vector field X = 7x \frac{\partial }{\partial x_1} + 2 \frac{\partial }{\partial x_2} Any input would be...

Here is the link: http://www.zebrality.com/media/2005/aaron_broussard.mov

I'm ashamed of my country. We could be so much better. We do have the power to be a true world leader but we have squandered it through greed and corruption.

If you get a copy of Visual Complex Analysis, you will find that it discusses many of the topological issues you are asking about. It was written by a student of Penrose. A good very basic introduction to algebraic topology is A Combinatorial Introduction to Topology.

Absolutely outstanding. It is as good as any of the others. I recommend this to anyone.

Thanks for the links. Funny I saw someone just yesterday with the Mawell t-shirt - I was wondering why it didn't use the differential forms version - it would fit better on a t-shirt.

By the way does anyone know of an in depth and complete refererence on the rules for index shuffling? The treatments I have found so far are somewhat ad hoc.

I like the notes posted above. Excellent suggestion.

Both F and G - they are used in the Jacobian to produce \frac{\partial x}{\partial u} = - \frac{3u}{x}.

Ok here it is. This example is from Kaplan's book - the detail is provided by me. Given a system of two functions: F \equiv ( x^2 + y^2 + u^2 + v^2 - 1) G \equiv ( x^2 + 2y^2 - u^2 + v^2 - 1) Where u and v depend on x and y: u = f(x,y) v = g(x,y) find...

I don't know - perhaps because the equations are implicitly defined. I figured out how the answers were calculated, I can apply the same formula and get the correct answer, but I don't know why it is correct - the "naive" solution appears to work correctly, at least integrating the 2nd...

I have been reviewing Calculus and have tripped up on figuring out to calculate the 2nd partial derivatives of imlicit functions. Kaplan and Spiegel give a cursory treatment to the subject in both of their "Advanced Calculus" books. Simply repeating the methods used to calculate the 1st...