Topics we have covered and you should know:
functions of several variables
continuity of f(x,y) or f(x,y,z) at a point or in a region, partial derivatives of a function of two
or three variables, higher order derivatives, differentiable vs continuous (example p. 167),
finding partial derivative “by definition” (same example), chain rule(s), gradient (compute,
interpret: direction of maximum/minimum increase), directional derivatives in direction of
unit and non-unit vectors, gradient of f is orthogonal to level curve of f, finding normal line
or tangent plane to a surface F(x,y,z)=c at a point on it, finding normal line or tangent
plane to graph of f(x,y) at a point, max-min problems, critical points, local max/min, saddle
points, second derivative test for f(x,y) at a critical point, global max/min, applied max-min
problems, Lagrange multipliers.
multiple integrals
double integral of f(x,y) over a rectangular region or horizontally or vertically simple region,
switching the order of integration.
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