(Sections
13.1-17.10)
13.1
Know the distance
formula.
Know the equation of a sphere
with center C(a,b,c) and radius r.
13.2
Know the properties of
vectors (addition, scalar product, length, unit vector, position vector).
13.3
Know the definition of
the dot product.
Know
the geometric properties of the dot product.
Know
the properties of the vector projection.
13.4
Know the definition of
the cross product.
Know the geometric
properties of the cross product.
Know the properties
collected in Theorem 8 on p. 854.
13.5
Know the equation of a
line.
Know
how to parameterize a line segment connecting two given points.
Know the equation of a plane.
Be
able to do all the HW assignments.
13.6
Be able to sketch
surfaces by using the method of traces.
You donŐt need to know or to
memorize Table 1 on p. 872.
13.7
Know the definition and
meaning of cylindrical and spherical coordinates.
14.1
Be able to draw space
curves.
Be
able to match parametric equations with given graphs.
Know
the parametric equations of a circle (in the xy-plane, for instance).
14.2 Be able to find tangent
vectors and unit tangent vectors.
Be
able to find the equation of a tangent line.
14.3
Know how to compute the
length of a curve.
No questions about arc length
and curvature will be asked.
14.4
Know how to compute the
velocity and the acceleration.
Know
how to find the position vector if the acceleration is given.
15.1 Be able to sketch the
graph of a function.
Be able to
sketch level curves.
15.2
Be able to decide
whether a limit exists. Be able to use the squeeze theorem.
Know
the definition of continuity.
15.3
Know how to compute
partial derivatives.
Be able to
compute higher order partial derivatives.
15.4
Know the equation of 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
that the gradient vector is perpendicular to level surfaces.
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.
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.
16.7 Know how to do triple
integrations.
Know how to use arrows to find the bounding surfaces.
Know how to find the planar region D.
Know how to
find the volume, the mass, and the center of mass of a solid.
16.8
Know how to use
spherical and cylindrical coordinates for triple integration.
Know how to use arrows to find
the limits of integration.
17.1
Know the definition of a
conservative vector field.
You will not be asked to
sketch vector fields.
17.2
Be able to compute line
integrals for functions and for vector fields.
Know the meaning of line integrals (work, mass and
center of mass of a wire).
Know how to parameterize a circle.
Know how to
parameterize a line segment connecting two given points.
17.3
Know and understand the
statement of the Fundamental Theorem for Line Integrals
(that is, Theorem 2 on page 1110). KNOW and UNDERSTAND
its proof.
Know that the line integral of a conservative vector field over a
closed curve is 0 (why?)
Know that the line integral of a conservative vector field is path
independent (why?)
Know how to
find a potential function f.
17.4
Know GreenŐs Theorem.
17.5
Know the definition of
div and curl.
Know
that a vector field F defined on
R^3 is conservative if curl F=0
(why?)
Know how to
find a potential function if F is
conservative.
17.6
Know how to find
parametric equations of a sphere, a cylinder (along the x, y, or z-axis), and
of
a
surface given by z=g(x,y), y=g(x,z), and x=g(y,z).
Know how to find the equation of a tangent plane for a parametric
surface.
Know how to
compute the surface area of a surface.
17.7
Know how to evaluate the
surface integral of a function.
Know how to
evaluate the surface integral of a vector field.
17.8 Know
and understand the statement of StokesŐs Theorem.
Be
able to do the HW assignments.
17.9 Understand the
statement of the divergence theorem.
Be able to evaluate the surface integral of a vector field over a
closed surface by using
both sides in
the divergence theorem.
Make statements on your test.
(For instance: Write equal signs whenever you think two expressions are equal.)
Use a pencil and write legibly.