My course notes
Chapter 1 notes
Chapter 2 notes
Chapter 3 notes
Chapter 5 notes
Chapter 6 notes
Chapter 7(path and line) notes
Chapter 7 surface integrals, chapter 8 examples
Final study notes for first half of the semester
Miscellaneous
Here is a proof of
Kepler's laws
using vector calculus and Newton's laws.
The proof of Kepler's second law is the easiest.
Surfaces in three space can be quite beautiful and complicated.
Take a look at the examples (minimal surfaces) in the
Virtual Math Museum
Saddle Surface Contour Plot
Maps from R^n to R^m; the big picture
Worked examples
Distance between skew lines
A function where all directional derivatives exist but is discontinuous
Computing the gradient in polar coordinates using the chain rule
When does a vector field have a potential function?
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