Mathematica Resource Pages
I really need to put together an updated version of my Mathematica Resource Pages (after an initial burst of energy, I kind of ran out of steam and only added material needed for my Calculus IV and Differential Equations classes). When Wolfram Research came out with version 6 of Mathematica, I really became excited (in a sad, math teacher sort of way) about doing some new work with this. So that I spend more of my time working in Mathematica rather than trying to polish up a new version of my website, I plan to post those new demos here as-is for now. No warranties are implied (so if your computer blows up while using these, I just don't want to know about it) and I haven't spent a whole lot of time polishing the demos up for general release. If something is seriously not ready for prime time yet (or has some rough edges), I'll try to mention it here. When I have time and it is possible, I will also post Adobe Flash previews for the animations, so that you can view them on the web, before downloading if you wish. All of these files are Copyright 2008 © by Marcus McGuff, but anyone is free to make use of them for educational purposes, as long as you give proper attribution. (If you figure out a way to make money off of them, then I want a cut...) Constructive comments and suggestions are welcome; feel free to let me know of any problems you encounter (and I will add those to my list of things to fix when I have time). Enjoy...
Computer Lab Assignments for my classes can be found here.
General purpose
- The unTutorial - If you are looking for a tutorial on how to use Mathematica, you'll have to wait until I have more time (and get motivated). However, in the meantime, here are a set of quick examples showing you which commands to use to draw which types of graph and how to do other things you might want to do in an upper level community college math course. I will expand this as I have time and think of things that need to be added. (Right now, this is mostly graphs, but I will probably add to it as I get around to it...) Mathematica notebook Warning - BIG file (12 MB). Alternative: html version (kind of ugly; eventually, I will see if there is a way to format the web pages Mathematica outputs more nicely, but you can read through this version for now if you don't want to download the big notebook or you don't have Mathematica)
Calculus III and IV
- Visualizing level curves and sections/slices of surfaces - A couple of fancy demonstrations (I suggest most of you not bother looking at the code behind these; just use them as demos), plus a few simpler demonstrations of how to use Mathematica to show level curves on a surface and level surfaces in 3-space. One warning - On the demos where you can enter an arbitrary expression to graph, you must use standard Mathematica notation (square brackets, capitalize built-in functions, etc.). Mathematica notebook (Flash demos and html version are coming later)
- Investigating Limits of functions of 2 variables - A couple of fancy demonstrations that help you visualize and graphically investigate the limist of several weird functions of 2 variabes as (x,y) approaches (0,0). Mathematica notebook (Flash demos and html version are coming later)
- Tangent plane - Move the tangent plane around the surface (function). Mathematica notebook (Flash demos and html version are coming later)
- Visualizing the Gradient, Divergence, and Curl - Several demos to help you visualize the Div, Grad, and Curl. I'm still working on better versions of these, but they are a start. Mathematica notebook (Flash demos and html version are coming later)
Differential Equations
- Slope fields - This lets you enter a differntial equation with some optional parameters and allows you to examine what effect this has on its slope field and solution curves (you can set the intial conditions by clicking on the graph with the mouse). Mathematica notebook (Flash demos and html version are coming later)
- Phase portraits - This lets you graph systems of autonomous differential equations (linear and non-linear) to see their slope field, equilibrium (critical) points, eigenvalues/eigenvectors at the equilibrium points (well, the eigenvalues/eigenvectors of the "local linearization" at the equilibrium points), and plot solution curves just by clicking on the graph with the mouse. You can also enter parameters in your equations and see what effect varying these has on everything in real time. (I think this is a pretty cool demo, actually.) This will not work if your system gets too nonlinear, but powers of x and y should be fine (trig functions, probably not). Mathematica notebook (Flash demos and html version are coming later)
Calculus I and II
- Slopes of secant and tangent lines - Enter a function and move the points around to see the slope of secant and tangent lines to that curve at those points. Mathematica notebook (Flash demos and html version are coming later)
- Numerical integration - Visual/numerical comparison of several different methods of numerically approximating the definte integral (left sum, right sum, trapezoid rule, midpoint rule, Simpson's rule). One of the few examples I have seen that actually shows the parabolas of Simpson's rule... (One confession: The "actual area" isn't really; it is the area you get if you use Mathematica's built-in numerical integration routine. I could have had Mathematica compute the indefinite integral and then evaluate it, but I decided that might be too slow or limiting for certain integrals. It wouldn't be hard to change it, so if my conscience bothers me enough, I might do that or make it a selectable option...) Mathematica notebook (Flash demos and html version are coming later)
- Taylor series - Mathematica notebook (Flash demos and html version are coming later)
- Slope fields - This lets you enter a differntial equation with some optional parameters and allows you to examine what effect this has on its slope field and solution curves (you can set the intial conditions by clicking on the graph with the mouse). Mathematica notebook (Flash demos and html version are coming later)
Precalculus / Trigonometry / Calculus (a mixed bag)
- Parametric grapher - This is a "graphing calculator" type application designed to help you visualize the graphing of sets of parametric equations (in 2 dimensions). This is actually a pretty cool application; it has a lot of flexibility. You can graph 2 sets of equations simulataneously, watch how the graph depends on its parameter, look at how points of intersection depend on the parameters, and investigate families of curves (or animate them) pretty easily. Mathematica notebook (Flash demos and html version are coming later)
- Polar grapher - This is a "graphing calculator" type application designed to help you visualize the graphing of polar plots. You can show 2 graphs simulataneously, watch how the graph depends on its angle, look at how points of intersection depend on the angle, and investigate families of curves (or animate them) pretty easily. There are several things I still want to add to this, but I decided to go ahead and put it up as-is for now. Mathematica notebook (Flash demos and html version are coming later)
If you want to view the material on my old Mathematica Resource Pages site, it is still available here.
