| concept |
| curvature of space curve |
| via v cross a, e.g. (hyper)cycloid |
| normal and tangential components of acceleration |
| line integrals |
| jacobian |
| mass, moments c of g of semi-circular rod |
| implicit specification of sets |
| implicit plane curves |
| "signplot" |
| classification of quadratic curves (review) |
| parametric surfaces |
| cylinders |
| sphere, torus |
| implicit surfaces |
| quadric |
| 3 generics: ellipsoid, 1- and 2-sheet hyperboloids |
| classification |
| hyperbolic paraboloid |
| elliptic (circular) paraboloid |
| elliptic cone |
| sketching: traces in coordinate planes |
| parametric volumes |
| cylindrical and spherical coordinates |
| functions of several variables (further study) |
| implicit domain |
| graphs |
| contours, level sets |
| limit |
| combo rules |
| examples of limit and no-limit lack of limit via path-limits |
| continuity |
| partial derivatives |
| notations, chain rule review |
| higher-order partial derivatives |
| mixed-derivative theorem |
| PDEs, heat equation (1D) |
| linearization |
| find approximation to zero set |
| Newton's method |
| critical points |
| location |
| classification: maxima, minima, saddles |
| exotic critical points: monkey saddle, quartic extremum |
| absolute extrema on bounded region |