MATH 3240/6250, Review for exam 1

The exam will be based on the homeworks (problem sets 1-6). Here is a list of definitions, examples, and theorems you should know for the exam.

(1) Curves

(a) Definitions:
regular curve
tangent line
arc length
involute
evolute
Frenet frame
curvature
torsion

(b) Examples:
straight line
circle
ellipse
helix
catenary
astroid

(c) Theorems:
straight line <-> shortest distance
straight line <-> velocity = constant vector
Frenet equations
T, N, B, kappa, tau for non-unit speed curves (If they're needed, I will give you these formulas on the exam.)
helix <-> tau/kappa is constant

(2) Surfaces

(a) Definitions:
coordinate patch (simple surface)
Monge patch
regular surface
reparametrization
tangent plane
normal vector
coordinate curves
surface (atlas)
coordinate transformation
metric tensor (gij)

(b) Examples:
ruled surface
surface of revolution
sphere: geographic coordinates, stereographic coordinates
helicoid
hyperboloid of one sheet