- Problems pp. 358, #3, 6, 8, 9 (due today, 4/7)
- Third Exam next Friday, 4/16
- Today's activity, and new assignment:
Wed 4/7 Continue basic integration - Read sections 41-43
- Problems: pp. 129, #1bc, 3, 7, 10 (due Wed., 4/14)
- Section 102: A related problem
- Derive the form of the isotherms
- Discuss other "easy" problems, using Appendix 2. What's an easy temperature
distribution to solve for?
- How about a rectangular box with two opposing insulated sides, and constant values on the other sides?
- How about a rectangular box insulated on all sides? (Really easy! -- where will it equilibrate?)
- Now what transforms into a finite rectangular box, and what can a finite rectangular box turn into?
- Section 36
- We're working with parametric curves
- Many of the usual rules work
- Some don't, however (e.g. Mean Value Theorem)
- Section 37
- Anti-derivatives are working for these parametric curves
- Complex integration allows us to get a "twofer" sometimes. As an example, we've got
- An inequality
- Section 38: Contours
- Definitions:
- Arc - parametrized curve
- Simple/Jordan arc -- arc w/o self intersections
- Simple closed curve / Jordan curve -- intersects with itself only to close
- Smooth arc -- differentiable,
on (a,b), and continuous on [a,b].
- Contour: piecewise smooth arc
- Simple Closed Contour: closed piecewise smooth arc (divides the complex plane into an inside and an outside)
- Parametric curves are not unique
- Definitions:
- Section 39: Contour integrals
- Transforming contour integrals into parametrized curves
- Most of the usual rules apply
- Section 40: Examples
- #1a, p. 129
- #2a, p. 129
- #6