Vector Calculus Independent Study Path

Unit 8: Fundamental Theorems of Vector Calculus

In single variable calculus, the fundamental theorem of calculus related the integral of the derivative of a function over an interval to the values of that function on the endpoints of the interval. In this unit, we will examine two theorems which do the same sort of thing. Gauss' theorem relates the integral of the divergence of a vector field over a solid region to the integral of the vector field over the boundary of the region, and Stokes' theorem relates the integral of the curl of a vector field over a surface to the integral of the vector field around the boundary of the surface. In this unit, you will learn: For more detailed instructions, see the Xdvi or PDF pages.

For a collection of all of the Theorems on one HTML page, with gaudy color figures, see the Fundamental Theorems of Vector Calculus. The form of the theorems, and the notation, is that of Calculus with Analytic Geometry, Second Edition, by George F. Simmons, and page references are to this volume.

Similarly, an outline of a proof of Stokes' Theorem, using Simmons' notation, is available (PDF only).

Suggested Procedure


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Last modified July 28, 1998