Lectures for Mathematics 211, Fall 2009-10

  • Monday, 8/31: Overview
  • Tuesday, 9/1: Review from one variable, start Taylor's Theorem
  • Wednesday, 9/2: Finish Taylor's Theorem, approximate ln(1.1)
  • Friday, 9/4: Taylor series: exp, ln(1+x), exp(-1/x^2)

  • Monday, 9/7: Labor Day Holiday
  • Tuesday, 9/8: 2.1 -- algebra of Euclidean space; discuss homework
  • Wednesday, 9/9: 2.2 -- geometry of Euclidean space
  • Friday, 9/11: [Add/section-change deadline] Go over homework

  • Monday, 9/14: Skim through 2.3
  • Tuesday, 9/15: Go over homework
  • Wednesday, 9/16: 2.4 through sequential characterizations of closed sets, bounded sets
  • Friday, 9/18: Go over homework

  • Monday, 9/21: Finish 2.4
  • Tuesday, 9/22: Go over homework
  • Wednesday, 9/23: 3.1 up through T(x)=Ax
  • Friday, 9/25: Finish 3.1, 3.2 through matrix multiplication, quickly over homework (First quiz out, due Monday at classtime)

  • Monday, 9/28: Finish 3.2, start 3.3 up through Ex=0
  • Tuesday, 9/29: Finish 3.3
  • Wednesday, 9/30: Characterization of the determinant; its consequences
  • Friday, 10/2: Go over homework, uniqueness and existence of the determinant

  • Monday, 10/5: [No-W drop deadline] More on uniqueness and existence, determinant algorithm
  • Tuesday, 10/6: Skim inverse formula, go over homework, start determinant and volume
  • Wednesday, 10/7: Determinant and volume, determinant and orientation
  • Friday, 10/9: Go over homework; start 3.10 (cross product)

  • Monday, 10/12: Finish 3.10, review chapter 3, preview homework
  • Tuesday, 10/13: Go over homework (Second quiz out, due Friday at classtime)
  • Wednesday, 10/14: 4.1 -- definition, uniqueness of the multivariable derivative, simple examples
  • Friday, 10/16: 4.2 -- Chain rule

  • Fall break week

  • Monday, 10/26: Review, linearity of derivative, product and quotient rules
  • Tuesday, 10/27: Go over homework
  • Wednesday, 10/28: Start 4.3 -- necessary and sufficient conditions for the derivative
  • Friday, 10/30: Go over homework; example of necessary, sufficient conditions

  • Monday, 11/2: Finish 4.3; 4.4: equality of mixed partial derivatives
  • Tuesday, 11/3: Polar Laplacian; go over homework
  • Wednesday, 11/4: Start 4.5: optimization
  • Friday, 11/6: Go over homework, more optimization

  • Monday, 11/9: [Withdraw/leave deadline] Finish optimization; directional derivative, gradient
  • Tuesday, 11/10: Go over homework
  • Wednesday, 11/11: Level sets and graphs, integral curves, tangent planes
  • Friday, 11/13: Go over homework, review chapter 4 (Third quiz out, due Tuesday at classtime)

  • Monday, 11/16: Preview Chapter 5, start 5.1
  • Tuesday, 11/17: Estimating Lemma, Inverse Function Theorem - injectivity
  • Wednesday, 11/18: Inverse Function Theorem - surjectivity, differentiability of inverse
  • Thursday, 11/19: Discuss optional homework, motivate Implicit Function Theorem
  • Friday, 11/20: More motivation of Implicit Function Theorem, InvFT => ImpFT

  • Monday, 11/23: Go over homework, ImpFT => InvFT
  • Tuesday, 11/24: ImpFT loose ends, preview Lagrange multipliers
  • Wednesday, 11/25: Lagrange multipliers: heuristic argument, specific examples
  • Friday, 11/27: Thanksgiving Holiday

  • Monday, 11/30: Go over homework, another Lagrange example
  • Tuesday, 12/1: Lagrange multipliers: rigorous argument, general examples
  • Wednesday, 12/2: No meeting
  • Friday, 12/4: Go over homework (sessions run by Ben Fischer from now on)

  • Monday, 12/7: Miscellany, go over homework
  • Tuesday, 12/8: No meeting (college on Thursday schedule)
  • Wednesday, 12/9: Go over homework (Last quiz out, due Wednesday 12/16 at L317, 3:00 p.m.)

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