(Sections
15.1-16.5)
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 of two variables.
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?
Know
what the linearization of a function of several variables is.
No
questions about differentials will be asked.
15.5
Know how to use the
chain rule.
Know
exactly how to compute d/dt F(x(t), y(t), z(t)).
15.6 Know and UNDERSTAND
what a directional derivative is.
Know
how to compute directional derivatives.
Know
and UNDERSTAND the proof of Theorem 15 on page 982.
Know and UNDERSTAND WHY the gradient vector is
perpendicular to the tangent plane to a level surface (that is, know and
understand the proof on pages 983/984).
What
is the definition of a level surface?
Know how to
find the equation of a tangent plane and a normal line 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.
16.4 Know how to use polar coordinates for double
integration.
16.5
Know how to find the
mass and the center of mass of a lamina.
Make statements on your test.
(For instance: Write equal signs whenever you think two expressions are equal.)
Use a pencil and write legibly.