MATH 241 SPRING 2006- PROBLEM LISTS and TOPICS (planned)
List 1
vector-valued functions of 1 variable and parametrized curves/ tangent
line/ reparametrization/
arc length and arc-length parameter/ unit tangent and unit normal;
curvature/ velocity and acceleration;
tangential and normal components/ integration of functions along
curves/mean-value inequality.
List 2
functions of 2 and 3 variables/partial derivatives/ chain
rule/differentials and tangent-plane approximation/
mean-value theorem
List 3
Directional derivatives/ gradient vector/ level curves and level
surfaces; quadric surfaces/ tangents to curves or surfaces defined
implicitly
List 4
Functions defined implictly/ coordinate changes and mappings/
parametrized surfaces
List 5
Solutions of equations and systems/Newton's method
List 6
critical points/ the Hessian, local max, local min and saddle points/
global max/min in bounded regions/ constrained max/min
and Lagrange multipliers
List 7
multiple integrals: computation by iteration/ change of variable
formula/improper integrals/surface area and scalar functions on surfaces
List 8
calculus of vector fields I: line integrals, work/ independence
of path, potentials
List 9
calculus of vector fields II: Green's theorem and the divergence
theorem in the plane/ Stokes' theorem in R^3/ flux and
the divergence theorem
List 10
The Laplacian/ Maxwell's equations/ potentials and vector potentials