I play around with Mathematica a bit, and sometimes create notebooks I think are pretty cool.
The ones I create for use in class can be found on the class webpages. Not all of those reach a high level of coolness. But some of them are very cool, and if you never take my class you never get to see them--how sad is that? Also, sometimes I create things that aren't associated with a class, and this is where I can share those (only the cool ones, of course).
Some of these have significant discussion of the mathematics involved, others have less documentation, so it might be harder to parse out what the heck is going on. That's life, I guess. Maybe I will add more documentation in the future to the ones which are lacking if any is interested.
| Mathematica File | Comments |
|---|---|
| Battle Simulations | The documentation is so sparse here I feel bad; check out this pdf file for some explanations. |
| Fractional Calculus | The 1/2 derivative of cos x and more! Hypergeometric anyone? |
| Lagrange Multipliers | Example of Lagrange multipliers to find a constrained extrema in 3D. Some sweet 3D graphics showing what Lagrange multipliers do. |
| Newton's Method: solve a system of equations | The documentation in this file is pretty good. I must have had a good night's sleep when I wrote this. Vector fields and graphical picture of the method of solution. |
| Newton's Method: Roots of Unity | Solving zn - c = 0 for a complex number c. If c=1 these are the roots of unity! The complex plane is partitioned based on initializing Newton's method with a random point, and then determining which root Newton's method finds. Points in the complex plane are coloured differently based on this partitioning, and pretty pictures (like the one above) result. |
| Newton's Method: Polynomials in the Complex Plane | This generalizes the Roots of Unity notebook to work with any polynomial. Sweet. More pretty pictures. |
| The Norm of a vector and matrix | A Norm is not just the guy from Cheers. They measure distance, and there are more of them than just the Euclidean norm
|
| Pade Approximants | Let's generalize a Taylor series to something else--how about trying to expand a function as a ratio of two power series? A Pade approximant can do that, and can lead to some surprising results. Come here little divergent series, I want to sum you. |
| Photodissociation Dynamics | This has almost no documentation, since it is a file I used in conjunction with a talk I gave to the Chemistry Discipline at UMM on my research. But the animations are so cool! If you want to know a bit more about why I am calculating the things I am in this file, you can check out the associated pdf file (but I am afraid it might not be much help either!). This notebook is in Mathematica's Slide Show environment. |
| Vibrating Circular Drumhead | This has lots of documentation, since I wrote it for a pde directed study. Cool animation at the end. The example is self contained, so you can skip to that directly if you like. |