[Chris Hibner]

I wanted to make this a separate post, just so it doesn't get lost in the above post.

The concept that I pointed out in my first post (about writing a function as a linear combination of other functions) is a very powerful concept. In fact, it is the basis of virtually all approximation methods.

If you've ever heard of Wavelet Transforms, Spline Functions, Finite Element Methods, Element-Free Methods, etc.; these are all applications of using a set of functions like vectors. All of these methods try to approximate complex functions as linear combinations of simpler functions. And they also all use the concept of projecting a function onto these simpler basis functions.

If you're going into a masters program involving control or computational engineering of any sort (i.e. any sort of computer simulation), you should take a good theoretical linear algebra class and a linear systems class. After this, your other classes will make a lot more sense and will be much easier to understand. My Finite Elelment Methods course (the course in which we had to write our own finite element solvers in Matlab and compare the results to commercially available solvers like Nastran and Abaqus), the drop-out rate was over 50%. Since I had a good understanding of the math, I thought the class wasn't too bad. I have my boss at work (a PhD) for giving me the advice to take the other classes first - it helped a lot.