Spring 2014, TuTh, Science Center 116
My name: Andrew Cotton-Clay (please call me Andy)
Office: Science Center 527
Office Hours: To be determined
E-mail: acotton at math
TF: John Sheridan, john.sheridan4579 at gmail
Syllabus: Math 132 Syllabus
Course iSite: Math 132 iSite
Due Feb 6
Due Feb 13
Due Feb 20
Due Feb 27
Midterm practice problems and solutions
Due Mar 27
Due Apr 24
Mon 1/28: Section 1.1 of [GP]. See also our figure
eight curve, its
resolution in R^3, and a cross cap. If you take the expressions and enter them in an
actual copy of Mathematica, you'll be able to rotate the figures around.
Here's another
cross cap viewed from a better angle. The
the fourth coordinate in the resolution is Sin[2t]. To see this in
Mathematica, you can make it a color. Namely, try
ParametricPlot3D[{(2-Cos[2t])*Sin[s]*Cos[t], (2-Cos[2t])*Sin[s]*Sin[t],
(2-Cos[2t])*(1-Cos[s])}, {s,0,Pi}, {t,0,2*Pi}, ColorFunctionScaling ->
False, ColorFunction -> Function[{x,y,z,u,v}, Hue[(1+Sin[2v])/4+1/4]]].
Here I've rescaled and shifted the fourth coordinate a bit to get it to
play nicely with Mathematica's Hue function.
Wed 1/30: Cutoff and bump functions (see [GP problem 1.1.5]). Definition
of derivative of maps from R^k to R^l. Chain rule. Proof that continuous
partials implies differentiable. (See Rudin or Spivak for this background
material.) Beginning of 1.2 of [GP] and tangent spaces, with preliminaries
on other definitions of tangent spaces.