Vector Calculus Independent Study Path

Unit 7: Surfaces

We studied surfaces before when we investigated the graphs of scalar valued functions of two variables. In this unit, we generalize to the notion of parameterized surfaces. Parameterized surfaces are defined by a mapping from two space to three space -- think of the straight longitude and latitude ``lines'' on a flat map being sent to the curved longitude and latitude lines on a sphere. While parameterized surfaces are a bit awkward at first, they soon allow you to do all sorts of things, including integrating scalar functions and vector fields over the surface. In this unit, you will learn: For more detailed instructions, see the Xdvi or PDF pages.

Suggested Procedure

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Last modified July 28, 1998