Suggested topics
for the test:
1. Equation of a plane through three points,
normal vector to a plane, vectors parallel to a plane, area of a parallelogram;
parametric equations of lines, distance formula, length of a vector, unit
vector.
2. Contour Graphs
3. Partial Derivatives, Tangent Planes for
z=f(x,y), Mixed Partials, Chain Rule (in the simplest possible form),
Directional Derivatives, Direction of Max/Min Increase at a given point, Magnitude
of Max Increase (=length of the gradient at the point).
4. Max/Min problem or Lagrange Multipliers.
5. Motion, Velocity and Acceleration (not Length or Distance traveled).
6. Double and Triple Integrals, Polar coordinates,
Cylindrical Coordinates, Jacobian of a transformation.
7. Gradient Vector Field, Potential Function
(in the plane)
8. Line Integrals in the Plane and in Space
(you should know well that a gradient vector field is path independent (and conservative)
and therefore a line integral can be computed with the help of the Fundamental
Theorem of Calculus).
9. Green's Formula and Line Integrals.
10.
Flux of a
vector field through a surface given by z=f(x,y).(not through a cylindrical or spherical
surface), determining from a
picture if the flux of vector field is positive, negative or zero.
11.
The Curl Test
and the Divergence test for Vector Fields in 3-space.
12.
Fundamental
Theorem of Calculus in the plane and in Space.
13.
Stokes' Theorem, Divergence Theorem (you will be able to choose one of them).