Advanced Calculus II
Prerequisites: Math 200. Math 221 is recommended.
Instructor
Joel Feldman
Text
-
James Stewart, Multivariable Calculus, fourth edition.
I will post all handouts, problem sets, final grades, etc. on the web
here.
Topics
- Curves
(§14):
curves, velocity, acceleration, arc length.
Exclude curvature, normal
and binormal vectors, tangential and normal components of acceleration
and Kepler's laws.
- Vector Fields and Line Integrals
(§17.1, 17.2, 17.3):
vector fields, field lines (not covered well
in the text), conservative fields, line integrals.
- Surface integrals (§17.6, 17.7):
surfaces, tangent planes (also review the
subsection of §15.4 entitled "Tangent Planes" and the subsection
of §15.6 entitled "Tangent Planes to Level Surfaces"),
flux integrals, surface area.
- Integral Theorems (§17.5, 17.9, 17.4, 17.8):
gradient, divergence and curl (also review the
subsection of §15.6 entitled "Significance of the Gradient Vector"),
divergence theorem, Green's theorem, Stokes' theorem, applications.
Grading
- There will be two midterms (tentatively scheduled for Monday, February 10 and Friday, March 14) accounting for about 40% of the final mark.
- There will be weekly problem sets accounting for about 5% of the final mark.
- The final exam will account for about 55% of the final mark.
- Grades will probably be scaled.