My WorkPlace

I am currently working on a project called Book Mode with Professors Willian F. Schelter and Maorong Zou in the Mathematics Department, University of Texas at Austin. The Book Mode project intends to bring the students enrolled in Mathematics courses in our department to a closer hands-on experience with the computational aspects of Mathematics.

Emacs Book Mode allows you to interface with a large number of mathematics packages within an Emacs file. In these files the yellow-green highlighted regions are mouse sensitive. They present properties such that a simple click on these regions with right-mouse-button can execute commands defined on packages such as Maxima, LISP, Gnuplot, Octave, Maple, Pari, fplot, Zplot, etc.

Several projects were written as a suplemetary material for some undergraduates courses offered by the Mathematics Department. These projects offer the student an interactive experience with the computational aspects that the subject may present.

How can I access these projects?

These projects will on any UNIX based systems with the appropriate software installed. In our computer labs, these projects are called "books". They can be accessed by clicking on the icon "books" located on the right hand side of the screen, or by typing book & in a terminal window on a graphics terminal. A list of undergraduate classes and a sublist of books will be displayed. Choose one according to your interest. For beginners, I recommend the project under "Schelter --> math_books.bk". If you start by choosing a book related to an specific class (e.g. 427k), "master.bk" will give you a list of all the books according to the subject and links for each book listed. To go back to "master.bk" click on BACK on the top of the Emacs file. You can always call a new book by pulling down the "BOOK" menu and choosing "Find a Book".

Working within a project.

This is an excerpt from a book page (maxima.bk). In these examples, you can have Maxima evaluating limits, derivatives and integrals by simply clicking on the highlighted regions with the right-mouse-button. Notice that the last one is already evaluated since this is a page of a started book . The best characteristic of a book is that they are dynamic and interactive. You can easily edit and add to those files. For example, if you want to differentiate sin(x) with respect to x, instead of cos(x), just replace the function on the first example and click on the highlighted region. This time, Maxima will evaluate the derivative of sin(x) with respect to x.

The Projects

Emacs books range from small projects to detailed interactive lecture notes for some courses. There are a number of interesting projects installed. I would like to introduce a few of them here.

Taylor Series

This project is under taylor.bk. By executing these commands, one obtains a plot of the functions sin(x) and the taylor polynomial of sin(x) with n terms about a . The value of the parameters a and n can be changed through the use of sliders, and one can watch the graph being replotted simultaneously.

This is the output. You will see the re-plot while values of n or a changes. Reload it, if the image is not moving.

Direction Fields

This is a neat project using dfplot. It can be accessed by choosing "Direction Fields --> 427k-1.bk". Given an ODE, clicking with mouse-button-2 on the yellow region will plot the direction fields. To plot an orbit click on the plot window, and a trajectory through the point where you click will be computed.

Here you see the orbits being plotted as initial conditions vary. Again, I would like to point out that you can easily edit and add to those files. This means you may change the equation and obtain a new solution.

Selected Topics in Differential and Integral Calculus (M408D)

This is the project that I have been working on. It is very true that there is still a lot of work to be done, but right now I am trying to organize the Book Mode Workshop and writing this homepage.... Ok, no complaints! I will resume work on the project very soon.

The topics are:

• Polar Coordinates
• Sequences
• Infinite Series
• Taylor & Maclaurin Series
• Graphs
• Quadric Surfaces

Click here to see a brief description of my projects (old).

I use for most of my projects a cool C-Library: the EZ-Widgets and Graphics Library written by Dr. Maorong Zou (Departmant of Mathematics, University of Texas at Austin).