- Colloquium
- “Making Infinity Finite - Zeno’s Paradoxes, Sequences, and Filters”
- John Reynolds, Kansas University
- Wednesday, Dec. 2, 2:45
- Newton 204
- Extra credit for write-ups
- Problem set question 1—how to find bounds for integrals?
- Problem doesn’t constrain parameterizations in any way, so you can pick them to be convenient
- The bounds you find for t values give bounds for integrals
- Work, flow/circulation, flux
- Summary of section 16.2 from “Work Done by a Force over a Curve
in Space” to end
- Definitions and calculation formulas
- Definitions and calculation formulas
- Examples
- Work done on electron “falling” across vacuum tube
- (Keep in mind that “units” in this problem are completely
made up to make the math simple, they have no connection to actual physics)
- (Keep in mind that “units” in this problem are completely
made up to make the math simple, they have no connection to actual physics)
- Velocity field V(x,y) = ⟨ y - x/2, -x - y/2 ⟩ is my
attempt to be inspired by water circling a drain
- i.e., at least an inward-spiralling field, no attempt to model speeds realistically
- Did I at least get inward vs outward flow right?
- Look at flux to decide: negative means inward flow, positive means outward
- Work done on electron “falling” across vacuum tube
- Finish flux calculation to see if it’s positive or negative
- Do as much of this as you can before class
- Conservative vector fields
- Read section 16.3