MATH 2401: WEEK 9

Topics for this week are:

• Double integrals as iterated integrals and as the limit of Riemann sums
• Polar coordinates and applications of double integrals -- areas, volumes, mass, centers of mass and centroids, kinetic energy and moments of inertia

Text coverage:     Sections 16.2 - 16.5 of Salas, Hille, and Etgen

Reference:   These topics are also discussed in Chapter 13, More Integration, of the Cain-Herod textbook.

Online resources:

• Maple Worksheets
  • Pappus' theorem: To simplify the computation of volumes of revolution.
  • Polar coordinates: Most useful when dealing with problems with the right symmetry.
  • Intersecting cylinders: An illustrative example in the computation of volumes.
• Solved Problems
  • Chapter 13, Section 1
  • Chapter 13, Section 2
  • Chapter 13, Section 3
• Projects
  • Centroids and centers of mass.
• Java applets
  • Applet on two dimensional integration in Cartesian coordinates with Riemann sums.

---

Last Modified: . School of Mathematics, Georgia Institute of Technology.