REMINDER: Midterm for Calc IIIa will be on Thursday 9/21/00 in class. The test will cover up through Section 11.4. (That's right, the test does not include section 11.5).

Homework:  Read Sections 11.3-11.5, and work the following problems. You should work all of the problems, since any of them may appear on the midterm. But you will only be handing in the problems marked with an asterisk (*). (These will be due on Wednesday Sept. 20).

• Section 11.3:   4, 10, 15,21,22,25*,41,42,43,44
• Section 11.4:   1, 5, 9, 18, 24, 29*, 34, 39, 42
• Section 11.5:   5, 10, 19, 24, 75, 85

Overview:  The main goals for this week are to master differentiation and integration of vector-valued functions, and to apply these to study velocity and acceleration of projectiles moving in space. We will also study tangent and normal vectors for space curves, and apply this to find the tangential and normal components of acceleration. Finally, in section 11.5, we will study arc length and curvature.

Things to learn this week: 

Terminology:  derivatives and integrals for vector-valued functions, smooth curves, tangent and normal vectors for curves, centripetal component of acceleration, arc length, curvature.

Essential Skills (which will be on the Midterm):

1. Calculate the derivative of a vector-valued function.
2. Apply properties of derivatives (Thm 11.2) to determine derivatives of expressions involving vector valued functions.
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. Calculate the velocity and acceleration vectors of an object whose motion is described by a vector-valued function.
7. Determine the motion of an object given the acceleration, initial velocity and initial position of the object.
8. Find the unit tangent vector of a curve at a given value of $t$.
9. Find the tangent line at a point on a curve.
10. Find the principal unit normal vector for a curve at a given point.
11. Find tangential and normal components of acceleration for a given position function.

Essential Skills from section 10.5. These will not be on the Midterm, but I will be lecturing on this material on Tuesday, Sept. 20:

1. Find the arc length of a space curve.
2. Find the arc length function of a space curve.
3. Rewrite a smooth curve as a function of its arc length.
4. Calculate the curvature of a smooth curve.