We have modified the author's description so that you can click on any of the highlighted areas below to download that piece of the program. The purpose of this series is to make available to students computer programs which review those materials from the prerequisite courses that are essential for success in the present course. This is a collection of screen images, primarily graphical, which anyone can view. These are usually images of functions which would be difficult, or impossible, to draw on the board. This shows Newton's method graphically.
Some images demonstrate how it works, while others display how it can go wrong.
This displays the Taylor polynomials, of various degrees, corresponding to exp x, sin x, cos x, etc. It also contains some visual demonstrations of convergence and divergence. This has examples from ordinary differential equations, including a one parameter family of curves, the US Population and logistic growth, the cooling of coffee and Newton's law, the Euler and Runge Kutta methods and their fallibility, damped free vibrations, building a function from its series solution, and Bessel functions. This shows the partial sums of Fourier series for the triangular wave, the square wave, the saw tooth wave, the cosine expansion of sin x, and an interrupted square wave. The Gibbs phenomenon and other non-uniform convergence are quite apparent.