Animated Equations is a collection of examples that show differential equations at work. Each example uses a sequence of animations to illustrate features of the system. An animation is indicated by a highlighted picture, like this:
Click on the picture. Your browser should start a helper or plug-in to display the animation. If it didn't, you will have to configure your browser.
Highlighted text, like this, is a link to another part of the Animated Equations Web site, or even to another Web site. Click on the highlighted text to follow the link.
When you have finished reading a page, click on your browser's [Back] button to go back to the previous page. You can also use the Animated Equations link at the top of each Animated Equations page to return to the table of contents.
Most of the examples are from Edwards & Penney (1996); full descriptions of the problems and solutions can be found in the book.
In December 1997 there was no standard for displaying mathematical symbols and equations in web pages. Equations are therefore written as ordinary text with subscripts and superscripts. Fractions are written as a / b, with brackets (), [] and {} used for grouping. Variables are emphasised. Here are some example equations that demonstrate the notation:
1 / x + y = (1 / x) + y[x + y] / 2 = x / 2 + y / 2
sqrt (a + b) = [a + b]1/2
cos (a + b) = cos a cos b - sin a sin b
i = sqrt (-1) = [-1]1/2
exp [i pi] - 1 = e i pi - 1 = 0
Now go back to the Animated Equations table of contents and select an example.