Mathematics

### Material on Test 3

12.1 Approximating double integrals by Riemann sums: OMIT.

12.2 Iterated integrals over rectangles: calculating iterated integrals; evaluating double integrals as iterated integrals; finding volumes by double iterated integrals.

12.3 Iterated integrals over more general regions: same topics as 12.2, plus figuring out the limits and reversing the order of integration.

12.4 Double integrals in polar coordinates: sketching the region, figuring out the limits. Don't forget the extra r.

12.5 Mass, moment, center of mass of a lamina. Omit moment of inertia, probability, expected value.

12.7 Triple integrals: calculating triple iterated integrals; evaluating triple integrals as triple iterated integrals; figuring out the limits; finding volumes, mass, center of mass of solids by triple iterated integrals.

9.7 Cylindrical and spherical coordinates. This section is just background for the next section.

12.8 Triple integrals in cylindrical and spherical coordinates, with applications. Don't forget the extra factors.