Math 005C Review 4

Vector slope of plane (m), r, df

Directional slope of plane (and tan plane), u, definition

When is directional derivative 0, max, max value

magnitude of gradient, level lines

gradient of g

r, u, f, gradient of f, rephrase

gradient of g

expanded form, matrix form, graph

a, b, c, d

partial derivatives

Determinant of Hessian, deviation

D, half Laplacian/average

Critical point, D, half Laplacian

constraint, components, solve,

lagrange

lagrange

Volume under surface and double integrals (rectangle R, V, dA, dV)

treat x and y as constant (a, b; c, d)

R, dA, inside endpoints/differential, integral, bounded by…

dA

D, dA

D, dA

draw D, x, y, direction of arrow, bottom/top, left/right

graph of g1, g2

(misc.)

Area of D (misc.):

Volume between surfaces (misc.)

R, x, y

dA

using r and theta

General polar regions (D, r, dA, circle, line)

Centroid

dA

dS (vector and non-vector), dr, tan. plane, z = f(x,y), surface area (S)

Solve for the inside