Calculus and Mathematica

You may be wondering just who I am, so please allow me to tell you a little about myself. I am currently a graduate student in organic chemistry at Caltech. I received my BS in chemistry from the U of I in 1994 andI took all of my Calculus classes with C&M. When I came out of the C&M courses, I was worried that advanced math and chemistry would be very difficult because of the way that I had taken my previous classes. And to be honest, some of the other classes may "seem" a little more difficult, but the reason is probably not what you might think. C&M stresses the concepts of the mathematics more than the actual mechanics of calculation. What this means is that when you walk away from C&M and head out into more advanced classes you have an understanding of the meaning behind the math, you know what the integrals mean, not just how to calculate them by hand. This is extremely important to a chemist, because most of the types of problems that we try to calculate are not amenable to doing by hand. In a typical quantum chemistry course, you learn how to calculate the exact solution to the Schrodinger equation by hand. (The Schrodinger equation is used to calculate, among other things, the electron distributions of molecules and give the pretty pictures of orbitals that you see in your general chemistry textbook). The funny thing is that for the most part you can only solve the equation exactly for all but the simplest of molecules (such as H2). Anything more complicated (i.e. most of chemistry) cannot be solved exactly. How do we get around this? We use numerical approximations and we solve the many easy to set up,but complicated to calculate, equations using computers.