surface integrals

(1.7 hours to learn)

Summary

A surface integral is the integral of a function over a surface. Important cases include surface area and flux, where the function is the dot product of the surface normal with a vector field.

Context

This concept has the prerequisites:

Goals

  • Know the definition of a surface integral in three dimensions.
  • Be able to integrate a function over a surface in three dimensions.
  • As a special case, be able to compute surface area.
  • Be able to compute the flux across a surface in three dimensions.
  • Derive the formula for a surface integral for a surface given as z = f(x, y).

Core resources (read/watch one of the following)

-Free-

MIT Open Courseware: Multivariable Caclulus (2010)

-Paid-

Supplemental resources (the following are optional, but you may find them useful)

-Paid-

See also

-No Additional Notes-