Worked examples

Surfaces, fluxes and the theorems of Gauss and Stokes

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Normal vector and tangent plane to parametric surfaces
• 2Areas of Cartesian surfaces
• 3Areas of surfaces of revolution and portions of spheres and cylinders
• 4Surface integrals of scalar functions
• 5Divergence and curl of a vector field
• 6Fluxes by direct computation
• 7Fluxes with the divergence theorem
• 8Circulations with Stokes' theorem