Math 103L.02

Plan for Week 14

Week 14 (December 1-5). On Monday we will take a rapid survey of vector fields in space and derivatives and integrals connected to them. There are class notes. In the lab on Tuesday, we will examine vector field diagrams of four basic vector fields in space and derivatives and integrals associated with them. These calculations will form the basis for the class discussion for the rest of the week.

Homework due on Wednesday, December 3.

1. Calculate the divergence and curl for the four vector fields listed on the class notes.
2. Chapter 16 Exercises: 1, 2, 4, 16, 17, 18, 19, 35

Homework due on Friday, December 5.

1. Show that if phi(x,y,z) has continuous second partial derivatives, then curl(grad(phi)) = 0 (vector)

2. Assume that P(x,y,z), Q(x,y,z), and R(x,y,z) have continuous second partials. Show that div(curl(Pi + Qj + rk))=0

3. If phi(x,y,z) has continuous second partial derivatives, show that div(grad(phi))= d²phi/dx² + d²phi/dy² +d²phi/dz²

4. Let F(x,y,z) = yi + zj + xk and let S be the first octant portion of the plane x = y = z = 1 with unit normal N pointing away from the origin. Calculate the surface integral of FdotN over S.

5. Section 16.5: 7, 8, 17, 18

Last modified: December 3, 1997