Lecture Notes

These notes will be updated during the quarter, and possibly after that. Please let me know of errors, typos, inaccuracies, suggestions, etc at neptamin@uw.edu.

• Double integrals over rectangles

• Double integrals over general regions and properties

• Polar coordinates

• Applications

• Triple integrals

• Cylindrical coordinates

• Spherical coordinates

• Change of variables

• Chain rule

• Directional derivatives and the Gradient

• Vector Fields

• Line Integrals

• The Fundamental Theorem of Calculus

• Div, Curl and Laplacian

• Green’s Theorem

• Parametric Surfaces and Surface Area

• Orientations

• Surface integrals of scalar functions and vector fields

• Stokes’ Theorem

• The Divergence Theorem

Some additional materials

• The types of integrals discussed in Math 324.

• A Handout on Parametrization of Curves

• A Handout on Parametrization of Surfaces.