trig identities

derivatives

integrals

vectors

surfaces

name equation
ellipsoid $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$
elliptical paraboloid $\frac{x^2}{a^2} + \frac{y^2}{b^2} = \frac{z}{c}$
hyperbolic paraboloid $\frac{x^2}{a^2} - \frac{y^2}{b^2} = \frac{z}{c}$
cone $\frac{x^2}{a^2} + \frac{y^2}{b^2} = \frac{z^2}{c^2}$
hyperboloid of 1 sheet $\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2} = 1$
hyperboloid of 2 sheets $-\frac{x^2}{a^2} - \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$

polar coordinates

curvature

partial derivatives