Lectures for Mathematics 212, Spring 2007-08

  • Monday, 1/28: Logistics; overview: Green's, Stokes's, Gauss's theorems
  • Tuesday, 1/29: General remarks about integration, start 6.1
  • Wednesday, 1/30: Finish 6.1, 6.2 through definition of integrability
  • Friday, 2/1: Go over homework, Integrability Criterion

  • Monday, 2/4: Rest of 6.2: subbox result; start 6.3: equivalence of sequential and e-d continuity
  • Tuesday, 2/5: Go over homework
  • Wednesday, 2/6: More 6.3: examples of e-d continuity, continuity on compacta is uniform
  • Friday, 2/8: [Add/section-change deadline] Go over homework, finish 6.3

  • Monday, 2/11: Start 6.4
  • Tuesday, 2/12: Finish 6.4, go over homework, preview 6.5
  • Wednesday, 2/13: 6.5: motivation, Volume Zero Criterion, some graphs have volume zero
  • Friday, 2/15: Go over homework; finish 6.5: Near-continuity implies integrability

  • Monday, 2/18: Review proof of Theorem 6.5.4; iterated integrals
  • Tuesday, 2/19: Go over homework, prove Fubini's Theorem (first quiz out, due Sat 5:00)
  • Wednesday, 2/20: Geometry of the Fubini proof, unequal iterated integrals, more 6.6
  • Friday, 2/22: Differentiation under the integral sign; start 6.7

  • Monday, 2/25: More 6.7
  • Tuesday, 2/26: Go over homework, finish 6.7 examples
  • Wednesday, 2/27: Spherical volume element geometrically; discuss Change of Variable proof
  • Friday, 2/29: Go over homework, discuss Change of Variable proof

  • Monday, 3/3: [No-W drop deadline] Discuss Change of Variable proof
  • Tuesday, 3/4: Go over homework
  • Wednesday, 3/5: Skim approximation by smooth functions
  • Friday, 3/7: Go over homework (second quiz out, due Wednesday 5:00 p.m.)

  • Monday, 3/10: Start parameterized curves
  • Tuesday, 3/11: More on parameterized curves
  • Wednesday, 3/12: More on parameterized curves
  • Friday, 3/14: More on parameterized curves

  • Spring break week

  • Monday, 3/24: 7.1
  • Tuesday, 3/25: 7.2
  • Wednesday, 3/26: 7.3, start 7.4 (third quiz out, due Sat 5:00 p.m.)
  • Friday, 3/28: Finish 7.4, 7.5

  • Monday, 3/31: Forms: basic properties, product, derivative
  • Tuesday, 4/1: Go over homework
  • Wednesday, 4/2: Preview homework
  • Friday, 4/4: Go over homework; motivate pullback

  • Monday, 4/7: [Withdraw/leave deadline] Pullback
  • Tuesday, 4/8: Go over homework
  • Wednesday, 4/9: Change of variable for forms, antidifferentiation
  • Friday, 4/11: Go over homework,

  • Monday, 4/14: Cubes and chains, boundary, special cases of General FTIC
  • Tuesday, 4/15: Go over homework
  • Wednesday, 4/16: General FTIC
  • Friday, 4/18: Go over homework, miscellany

  • Monday, 4/21: The classical theorems
  • Tuesday, 4/22: Cauchy-Riemann equations, div and curl
  • Wednesday, 4/23: Go over homework, start Maxwell's equations
  • Friday, 4/25: More Maxwell's equations

  • Monday, 4/28: Finish Maxwell's equations
  • Tuesday, 4/29: Loose ends, evaluations
  • Wednesday, 4/30: Recreational lecture
  • Friday, 5/2: (No meeting)

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