General:  The Midterm will cover sections 10.1-11.4. I will curve the test, Depending on how hard the test is (after I get done writing it), the cutoff for a "C" might be anywhere from 40-70 percent. So don't panic if you feel like you are struggling--just do the best you can. (I will post a description of the curving procedure on my web page).

The following breakdown of the material should help guide you in your studying.

Bare Essentials (You must be able to do the following to pass the test)

• Vectors
  1. Given a directed line segment, find the component form of the vector it represents.
  2. Find the length and direction (angle with the x-axis) of a given 2-D vector in component form.
  3. Find the component form of a vector of a given length and direction.
  4. Write a vector as a linear combination of unit vectors (i,j,k).
  5. Determine whether two vectors are parallel.
  6. Calculate the dot product of two vectors.
  7. Use the dot product to test whether two vectors are orthogonal.
  8. Determine the norm of a vector.
  9. Find a unit vector in the same direction as a given vector.
  10. Calculate the cross-product of 2 vectors in 3 dimensions.
  11. Use the cross-product to find a vector orthogonal to two given vectors.
• 3-D geometry
  1. Find a parametric equation for a line in space that passes through a given point and is parallel to a given vector.
  2. Find a parametric equation for a line passing through two given points in space.
  3. Find the equation of a plane passing through a given point and normal to a given vector.
  4. Given an equation for a plane, sketch the plane (using the xy-, yz-, and xz-traces).
• Cylindrical and Spherical Coordinates
  1. Convert a point from cylindrical to rectangular coordinates, from rectangular to cylindrical, from rectangular to spherical, or from spherical to rectangular coorinates. (You do not have to be able to convert from cylindrical to spherical or spherical to cylindrical).
  2. Convert an equation from cylindrical to rectangular coordinates, from rectangular to cylindrical, from rectangular to spherical, or from spherical to rectangular coordinates.
• Vector-valued functions.
  1. Evaluate a vector-valued function r(t) at a given value of t.
  2. Calculate the derivative of a vector-valued function.
  3. Calculate indefinite integrals of vector valued functions (be careful to include a constant of integration for each component of the vector).
  4. Calculate the antiderivative of a vector-valued function (given initial conditions).
  5. Calculate a definite integral of a vector-valued function.
  6. Find the unit tangent vector of a curve at a given value of t.

"B"-level Material (In addition to the above, you should be able to do most of the following to get a B on the exam).

1. Find the angle between two vectors.
2. Draw a picture illustrating how to find the sum of two vectors graphically, or what effect scalar multiplication has on a vector.
3. Find the projection of a vector onto another vector (MEMORIZE the formula!!).
4. Calculate direction angles in 3-dimensional space.
5. Find the component of a vector orthogonal to another vector.
6. Use vectors to determine whether three points are collinear.
7. Find the equation of a sphere given two points on either end of a diameter.
8. Use the cross-product to calculate the area of a parallelogram having two given vectors as adjacent sides
9. Find the equation (standard or general form) of a plane in space containing three noncolinear points.
10. Applications
    • Force (see 10.1, example 7)
    • Velocity (10.1, example 8)
    • Work (calculate the work done by a force acting on a moving object).
11. Calculate the angle between two planes given normal vectors to each plane.
12. Match a vector valued function with its graph.
13. Sketch a plane curve defined by a vector-valued function.
14. Sketch a simple space curve defined by a vector-valued function.
15. Represent a 2-D graph by a vector-valued function.
16. Calculate the velocity and acceleration vectors of an object whose motion is described by a vector-valued function.
17. Apply properties of derivatives (Thm 11.2) to determine derivatives of expressions involving vector valued functions.
18. Determine the motion of an object given the acceleration, initial velocity and initial position of the object.
19. Find the tangent line at a point on a curve.
20. Find the principal unit normal vector for a curve at a given point.
21. Given the equation of a surface, sketch the surface using the xy-, yz-, and xz-traces.
22. Find the domain of a vector-valued function.
23. Evaluate the limit of a vector-valued function.
24. Determine intervals on which a vector-valued function is continuous.
25. Sketch a simple space curve defined by a vector-valued function.
26. Represent a 2-D graph by a vector-valued function.

"A"-level Material (In addition to being able to do all of the above, you should be able to do most of the following to get an A on the exam).

1. Calculate the triple scalar product of three vectors.
2. Use the triple scalar product to calculate the volume of a parallelpiped with three given vectors as adjacent sides.
3. Calculate the moment of a given force (Torque) about a point.
4. Find the line of intersection of two planes.
5. Find the distance between a point and a plane.
6. Find the distance between two parallel planes.
7. Find the distance between a point and a line in space.
8. Match an equation with its 3-D graph (see 10.6: exercises 1-6).
9. Represent a 3-D curve (defined by a set of equations) by a vector-valued function. (See section 11.1, problems 49-56).
10. Find tangential and normal components of acceleration for a given position function.