Lectures for Mathematics 202, Spring 2018-19

  • M 1/28: Overview
  • T 1/29: 2.1-Euclidean space algebra, start 2.2-Euclidean space geometry (Optional preface exercises due)
  • W 1/30: Finish 2.2-Euclidean space geometry, start 2.3-Euclidean space analysis
  • F 2/1: Finish 2.3-Euclidean space analysis, go over homework (2.1, 2.2 exercises due)

  • M 2/4: Start 2.4-Euclidean space topology
  • T 2/5: Go over homework (2.2, 2.3 exercises due)
  • W 2/6: 2.4-Euclidean space topology, 3.5-Introduce determinant properties
  • F 2/8: [Add/section-change deadline] Start 3.8-Determinant and volume, go over homework (2.4 exercises due) (Chapter 2 quiz out)

  • M 2/11: Finish 3.8-Determinant and volume, 3.9-Determinant and orientation, 3.10-Cross product up to characterizing property (Chapter 2 quiz due)
  • T 2/12: Finish 3.10-Cross product, lines and planes in 3-space, 4.1-Symbol-pattern breakown, start 4.2-Bachmann-Landau scheme
  • W 2/13: More 4.2-Bachmann-Landau scheme, go over homework (3.8, 3.9 exercises due),
  • F 2/15: Finish 4.2-Bachmann-Landau scheme, 4.3-Definition of multivariable derivative, go over homework (3.10 exercises due)

  • M 2/18: Finish 4.3-Definition of multivariable derivative, start 4.4-Basic results and the chain rule
  • T 2/19: Go over homework (4.2, 4.3 exercises due), 4.5-Calculating the derivative: necessity
  • W 2/20: Review, geometry of the derivative, 4.5-Calculating the derivative: sufficiency,
  • F 2/22: Go over homework (4.4, some 4.5 exercises due), 4.5-Calculating the derivative: example, chain rule in coordinates

  • M 2/25: 4.5-Chain rule in coordinates, start 4.6-Higher-order derivatives
  • T 2/26: Go over homework (rest of 4.5 exercises, some 4.6 exercises due), finish 4.6-Higher-order derivatives
  • W 2/27: 4.7-Extreme values
  • F 3/1: Go over homework (rest of 4.6 exercises due), finish 4.7-Extreme values

  • M 3/4: [No-W drop deadline] Start 4.8-Directional derivative and gradient
  • T 3/5: Go over homework (4.7 exercises due), finish 4.8-Directional derivative and gradient
  • W 3/6: Summary remarks on chapter 4, 6.1-Integration machinery
  • F 3/8: Go over homework (4.8 exercises due), 6.2-Definition of the integral (Chapter 4 quiz out)

  • M 3/11: 6.3-Continuity and integrability (Chapter 4 quiz due)
  • T 3/12: Finish 6.3-Continuity and integrability
  • W 3/13: Go over homework (6.1, 6.2 exercises due), skim 6.5-Integration over nonboxes
  • F 3/15: Go over homework (6.2, 6.3 exercises due), continue skimming 6.5-Integration over nonboxes (Chapter 6a quiz out)

  • M 3/18: 6.6-Fubini's theorem (Chapter 6a quiz due)
  • T 3/19: 6.6-Fubini's theorem
  • W 3/20: Go over homework (6.3, 6.5 exercises due)
  • F 3/22: Go over homework (6.6 exercises due)

  • Spring break week

  • M 4/1: 6.7-Change of variable theorem
  • T 4/2: Go over homework (6.6 exercises due)
  • W 4/3: 6.7-Change of variable theorem
  • Th 4/4: OPTIONAL first of four lectures on chapter 5-Inverse function theorem, implicit function theorem, Lagrange multiplier method
  • F 4/5: Go over homework (6.7 exercises due)

  • M 4/8: [Withdraw/leave deadline] 9.1-Definition of k-surface in n-space, 9.3-Differential forms syntactically and operationally, start 9.4-one-forms
  • T 4/9: Go over homework (6.7 exercises due)
  • W 4/10: More 9.4-one-forms, 9.5-two-forms, 9.6-basic properties, 9.7-multiplication
  • Th 4/11: OPTIONAL second of four lectures on chapter 5
  • F 4/12: Go over homework (9.3, 9.4 exercises due) (Chapter 6b quiz out)

  • M 4/15: More 9.7 multiplication, 9.8-differentiation of differential forms (Chapter 6b quiz due)
  • T 4/16: 9.9-Pullback of differential forms
  • W 4/17: Go over homework (9.5, 9.7 exercises due)
  • Th 4/18: OPTIONAL third of four lectures on chapter 5
  • F 4/19: Go over homework (9.8 exercises due), more 9.9-pullback

  • M 4/22: 9.10-Change of variable for differential forms, 9.12-Cubes and chains
  • T 4/23: Go over homework (9.9, 9.10 exercises due)
  • W 4/24: 9.13-The boundary operator
  • Th 4/25: OPTIONAL fourth of four lectures on chapter 5
  • F 4/26: Go over homework (9.13 exercises due)

  • M 4/29: 9.14-The general FTIC, 9.16-Green's theorem
  • T 4/30: Go over homework, 9-16-Stokes's, Gauss's theorems (9.14 exercises due)
  • W 5/1: 9.11-Closed forms, exact forms, and homotopy
  • F 5/3: Go over homework (9.16 exercises due), course evaluations (Chapter 9 quiz out, due Wednesday May 8)

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