# Interactive Math Programs

These programs are designed to be used with Multivariable Mathematics by R.E. Williamson and H.F. Trotter, and Introduction to Differential Equations by Richard E. Williamson, but are quite generally useful for illustrating concepts in the areas covered by the texts. So have fun, experiment with different values, and let us know if you have any trouble.

These programs were originally written in True Basic for the Macintosh by Richard Williamson. The translation into Java and the writing of a recursive descent equation parser was done by Scott Rankin and Susan Schwarz.

The programs are java applets tested on Macintosh computers running OS 10 using Netscape v7 and Internet Explorer v5.2, and on computers  running Windows 2000 and XP  using Netscape v7 and Internet Explorer v6. The applets will run on Macintosh computers running OS 9 using Netscape 7 but not Internet Explorer.

To run one of the programs in the list below, just click on its  name. Each program displays a brief explanation of how to use it. If you run into difficulties, here are more detailed instructions on running the applets.  The first time you try any of the  programs you may want to look at the link anyway. If you do not see the buttons that are used to run the program, you may need to scroll down in the browser window until the buttons are visible.

Multivariable Calculus

• Ascent - steepest ascent method
• Ascent+ - steepest ascent method with variable step-size
• Cplot-2D - plot parametric curves in 2-space
• Cplot-3D - plot parametric curves in 3-space
• Gplot-3D - plot graph of F(x,y)
• Midpt2 - midpoint rule for double integrals
• Simp2 - Simpson's rule for double integrals
• Splot-3D - plot parametric surfaces in 3-space
• Midpt3 - midpoint rule for triple integrals
• Simp3 - Simpson's rule for triple integrals
• Newt2 - Newton's method in 2 dimensions
• Newt3 - Newton's method in 3 dimensions

First Order Equations

• EULER -demonstration of Euler's method
• DIRFLD -plots direction field and solutions
• 1ORD - numeric output for initial-value problems
• 1ORDPLOT - graphical output for initial-value problems
• NEWTON - Newton's method for solving equations
• RUNKUT - Runge-Kutta method

Second Order Equations

• 2ORD - numeric output for initial-value problems
• 2ORDPLOT - graphical output for initial-value problems
• PHASEPLOT - plots phase curves for second order equations
• BOUNDARY2 - plots trials and final estimates for boundary problems
• CYLINDERREP - cylindrical representation of phase curves
• TIMESECT-plots time sections

Higher Dimensional Systems

• DESYS2PLOT - plots trajectories in two dimensions
• 2BODY - plots orbit of a planet around a star
• 3BODY - plots trajectories for three bodies
• 4BODY - plots trajectories for four bodies
• PLANETS - plots orbits of the nine planets around the sun
• SPRINGS2-1 - plots one mass linked by two springs to fixed points
• SPRINGS3-1 - plots one mass linked by three springs to fixed points
• SPRINGS3-2 - plots two masses linked in series to two fixed points
• DOUBLEPEND - double pendulum motion
• SPHEREPEND - spherical pendulum trajectory
• SWING - pumping on a swing
• VECFIELD - plots 2-dimensional vector field with solution trajectories

Partial Differential Equations

• FOURIER - plots partial sums of Fourier series
• HEAT- plots graph of heat equation solutions
• WAVE - plots graph of wave equation solutions