Mathematics

### Material on Test 2

11.1 Functions of several variables: domain, level curves, level surfaces.

11.2 Limits and continuity: showing a limit does not exist; where a function is continuous.

11.3 Partial derivatives: interpretation of partial derivative, estimating partial derivatives from tables and contour maps, calculating first and second partial derivatives, checking that a function is a solution of a partial differential equation.

11.4 Tangent planes and linear approximations: tangent plane to z=f(x,y); approximation.

11.5 Chain rule: using the chain rule, implicit differentiation.

11.6 Directional derivatives and the gradient: calculating directional derivatives, direction of maximum rate of change; tangent plane and normal line to level surface of a function of three variables.

11.7 Maximum and minimum: finding critical points and checking whether max, min, or saddle; applications.

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