The following files are either handouts I wrote for lecture, or
visualizations projected from my laptop in lecture.
File formats
are as follows: pdf = Adobe, nb = Mathematica (version ≥ 6 only!),
gcx = Apple Grapher (todo: replace with Mathematica).
- vector operations demo: vectors.nb
- the plane normal to a vector demo: normalplane.nb
- paramtetrizing lines and planes demo: lineplaneparam.nb
- a bundle of plots z = f(x,y): functionsoftwovars.gcx
- quadric curves and surfaces demo: quadricsurfaces.nb
- a cheat sheat on quadric surfaces: quadrics.pdf
- Frénet frame and curvature: curvature.nb
- Examples of parametric surfaces: parametricsurfaces.nb
- A Mathematica notebook file showing how to make the Moebius strip
as a parametric surface can be found here.
- An explanation of how gradients, critical values, and Lagrange
multipliers interrelate can be found here.
- A guide to the various multivariable integrals can be found here.
- A guide to the various multivariable fundamental theorems of
calculus can be found here.
- A systematic explanation/unification of the multivariable
fundamental theorems of calculus, for those who are very very
curious, can be found here.