William F. Coleman
Wellesley College, Wellesley, MA 02481

These movies are designed to help students visualize various numerical approaches to evaluating functions or solving equations. The methods themselves may be familiar to students from their mathematics courses, but they may have forgotten the material or never made the connection between a statement such as "the derivative of a curve at a given point is the slope of the line tangent to the curve at that point" and the way that one might evaluate such a derivative.

All of the movies have VCR-style controls that enable the student to step through them one frame at a time and to move backwards as well as forwards.

Quadratic shows how the roots of a quadratic change as the b term in the equation changes. The equation was chosen to illustrate the fact that only real roots are seen as points where the curve crosses the x-axis. This can lead to a useful discussion of what is meant by a physically meaningful solution.

Tangent Curve compares the slope of the tangent line to the value of the derivative obtained using symbolic differentiation at various points along a particular function.

Numerical Integration obtains the integral of a function by summing the areas of a number of rectangles, and then compares the result to the value of the integral obtained using symbolic integration. It is interesting to note that agreement between the two values of the integral to the fourth decimal place requires over 200 rectangles.

Newton-Raphson introduces the user to the Newton-Raphson method for evaluating the root(s) of a function. This procedure is demonstrated for a particular function in Newton Test.

	View	Quadratic Tangent Curve Numerical Integration Newton-Raphson Newton Test
	Review	Comment on Visualizing Numerical Methods
	Requires	Flash plug-in, available at www.macromedia.com.