W4T Undergraduate Analysis

Web Sites for Teaching Undergraduate Analysis

The Chaos Hypertextbook, by Glenn Elert at Columbia University.

This contains illustrated tutorials on iteration, with focus on chaotic dynamics. There is good motivation for Julia and Mandelbrot sets, followed by "What is Dimension?" The last section, "Measuring Chaos," is a good introduction to Lyapunov stability.

Chaos Gallery, by Leon Poon at University of Maryland.

This provides attractor and basin pictures and has some search capability. At first each picture is small (for reasonable load time), and the size of the full version is given to let you know how long it will take to load (by clicking on the small one). The annotation is brief, but there is a link to a searchable "Chaos Database" (in bibtex).

Computational Mathematics: Models, Methods and Analysis, by R.E. White at North Carolina State University.

This is a collection of notes (pdf files), which you can obtain by sections within four chapters. Chapter 1 is Time Dependent Matrix Models, illustrated by heat and mass transfer. Chapter 2 is Steady State Matrix Models, illustrated by heat diffusion. Chapter 3 is Laplace Equation Models, -Du = f with boundary conditions on u. Chapter 4 is Other Partial Differential Equaiton Models, F(u) = f, applying Picard and Newton methods, among others. The author also has Matlab, Fortran 90 and Cray codes, which you can download.

Consortium of ODE Experiments, by Harvey Mudd College

This Newsletter has articles that can be useful in an ODE course. Recent issues are in HTML; back issues are in compressed postscript (need to be unzipped with gunzip in unix). For example, the Fall 1995 issue has:

Three Activities from Exponential Growth and Decay Lab
Exploration of the Parachute Problem with STELLA
How Long Does It Take a Harmonic Oscillator to Come to Rest?
Why Numerical Methods Don't Always Work

Dynamical Systems Lab, by Evelyn Sander at University of Minnesota.

This uses Geometer's Sketchpad, as part of the Geometry Center's "Technology in the Geometry Classroom." The sections include Periodic Points, Iteration, Linear and Nonlinear Functions, and Bifurcation.

Famous Curves Index, from the Mathematical MacTutor system.

This gives a list and provides a search function. With each curve, its equation and a picture are given, plus links for history and related curves. With Java, the student can also change the parameters and visualize the effect.

Fractint, by Noel Giffin at TRIUMF.

This contains fractal freeware to run under MS Windows. You can also get the C++ source code, and students can modify it for their projects.

Interactive Real Analysis, by Bert G. Wachsmuth at Seton Hall University.

This is a complete book. Some of the interactivity consists of asking the student questions right after some material, such as an example, and providing the answer with a click. The materials include a glossary, which remains an active button in a frame. Some Java and JavaScript are used for letting the student plot a function, check continuity, or find a root.

S.O.S. Mathematics - Differential Equations, from the University of Texas at El Paso.

This is one of the complete modules, essentially a full book on differential equations, with lots of interesting applications. Other modules are under development, and the faculty are listed with related links to special areas. (It's not clear who authored this module.)