Learning expectations for first midterm

• This midterm will primarily test the material listed below, but anything from the list of learning expectations for midterm 1 will also be fair game on this midterm.
• Find the directional derivative of a function in the direction of a unit vector and understand the meaning of a directional derivative.
• Be able to compute the gradient of a function.
• Know the relationship of the gradient to directional deriviatives.
• Know properties of the gradient: that it is perpendicular to contour lines (or contour surfaces) and that it points in the direction of maximal rate of change of a function.
• Be able to find the critical points of a function, and for functions of two variables, classify criticals point using their discriminant (into local max, local min, saddle, or non-ordinary critical point).
• Find the global maximum and/or minimum of a function on a closed and bounded domain (recall this includes finding critical points on the interior, and also finding max/min of the function restricted to the boundary).
• Solve optimization word problems.
• Use Lagrange multipliers to solve constrained optimization problems.
• Compute iterated integrals.
• Compute double integrals over domains of type I or type II by expressing them as iterated integrals.
• Be able to reverse the order of integration in an iterated integral.
• Express and/or compute double integrals using polar coordinates.
• Use double integration to find the volume under the graph of a function, or area of a domain.