MVVC Week 8 – Problem Set Assignments and Learning Goals
Reading:
- Boas 6.10: The Divergence and the Divergence Theorem (skip Gauss’s Law pp. 320-322)
- Schey: Flux (pp. 31-33)
- Schey: The Divergence (pp. 37-42)
- Schey: The Divergence Theorem (pp. 45-49)
- Math Lab 10 Part 4 directs you to read some Parts of https://mathinsight.org/thread/math2374. For the purposes of this reading assignment, make sure to read/review Part 12 (particularly those sections related to divergence) and Part 23.
Learning Goals:
- Determine the unit normal direction to a surface by inspection or by using the gradient.
- Set up flux integrals by: a) finding the integrand by taking the dot product of the vector field with the unit normal direction(s) to the surface(s); b) writing down the appropriate surface area element(s); c) determining the appropriate limits of integration. For straightforward geometries, evaluate the integral.
- Set up volume integrals involving divergence of vector fields by: a) calculating the divergence of the vector field; b) writing down the appropriate volume element(s); c) determining the appropriate limits of integration. For straightforward geometries, evaluate the integral.
- Use the divergence theorem to equate a flux integral for a closed surface to the volume integral for the divergence of the vector field for the volume enclosed by the closed surface. Evaluate whichever is easier.
- Interpret the divergence of a vector field geometrically/physically as related to “sources” or “sinks”.
MVVC Problem Set, Week 8:
- Schey Ch. II: II-10, II-15(a)(b), II-23
- Boas 6.10: 3, 4, 6, 7, 10
To see which problem(s) you’ve been assigned to contribute to the Collaborative Solution Set, visit this shared Google folder and navigate to the appropriate subject and assignment in the directory structure. This is also the document to which you will post your solutions by Friday 6pm.