(Sections 15.1-16.3)
15.1 Be able to find the domain and range of a function of several variables.
Be able to sketch the graph of a function.
Be able to sketch level curves and level surfaces.
Be able to match graphs or level curves with functions.
15.2 Be able to decide whether a limit exists. Be able to justify your conclusions.
Know the definition of continuity.
15.3 Know how to compute partial derivatives.
Be able to compute higher order partial derivatives.
Know ClairautÕs Theorem on p. 952 (You donÕt need to know the proof.)
15.4 Know the equation of a tangent plane.
What is a tangent plane?
15.5 Know how to use the chain rule.
15.6 Know how to compute directional derivatives.
Know the geometric properties of the gradient vector.
Know and UNDERSTAND the proof of Theorem 15 on page 982.
Know and UNDERSTAND WHY the gradient vector is perpendicular to
level surfaces (that is, know and understand the proof on pages 983/984).
What is a level surface?
Know how to find the equation of a tangent plane to a level surface.
15.7 Know how to find the critical points of a function of two variables.
What is a critical point?
Know
the second derivative test.
Know how to find the maximum and minimum values for a function defined on a bounded and closed region D.
16.1 Know the geometric meaning of double integrals (volume of a solid under the graph of f).
16.2 Be able to do the HW assignments.
16.3 What is a type I (type II) region?
Know how to change the order of integration. (Use arrows to find the bounding curves.)
Know how to find the volume of a solid.
Know how to find the area of a two dimensional region.
Make
statements on your test. (For instance: Write equal signs whenever you think
two expressions are equal.) Use a pencil and write legibly.