Lectures for Mathematics 202, Spring 2020-21

  • M 1/25: Overview
  • T 1/26: 2.1-Euclidean space algebra, start 2.2-Euclidean space geometry (Optional preface exercises due)
  • W 1/27: Finish 2.2-Euclidean space geometry, start 2.3-Euclidean space analysis
  • F 1/29: Finish 2.3-Euclidean space analysis, go over homework (2.1, 2.2 exercises due)

  • M 2/1: Start 2.4-Euclidean space topology
  • T 2/2: Go over homework (2.2, 2.3 exercises due), preview rest of 2.4
  • W 2/3: Finish 2.4-Euclidean space topology, skim 3.10-Cross product
  • F 2/5: [Add/section-change deadline] 3.10 Point-to-plane, point-to-line distances, 4.1-Symbol-pattern breakown, go over homework (2.4 exercises due) (Chapter 2 quiz out)

  • M 2/8: Start 4.2-Bachmann-Landau scheme (Chapter 2 quiz due)
  • T 2/9: Finish 4.2-Bachmann-Landau scheme, 4.3-Definition of multivariable derivative
  • W 2/10: Start 4.4-Basic results and the chain rule, go over homework (4.2 exercises due)
  • F 2/12: Finish 4.4-Basic results and the chain rule, 4.5-Calculating the derivative: necessity, go over homework (4.3 exercises due)

  • M 2/15: 4.5-Review the necessity theorem, prove the sufficiency theorem, examples
  • T 2/16: 4.5-Chain rule in coordinates, go over homework (4.4, some 4.5 exercises due)
  • W 2/17: 4.6-Higher-order derivatives: equality of mixed partial derivatives, polar Laplacian
  • F 2/19: Start 4.7-Extreme values, go over homework (rest of 4.5 exercises due)

  • M 2/22: Finish 4.7-Extreme values
  • T 2/23: Go over homework (4.6 exercises due), start 4.8-Directional derivatives and the gradient
  • W 2/24: Finish 4.8-Directional derivatives and the gradient
  • F 2/26: Go over homework (4.7 exercises due), start 6.1-Integration machinery

  • M 3/1: Finish 6.1-Integration machinery, 6.2 Definition of the integral
  • T 3/2: Go over homework (4.8 exercises due), start 6.3-Continuity and integrability
  • W 3/3: Finish 6.3-Continuity and integrability
  • F 3/5: Go over homework (6.1, 6.2 exercises due), Start 6.4-Review of one-variable integration (Chapter 4 quiz out)

  • M 3/8: Finish 6.4-Review of one-variable integration, start 6.5-Integration over nonboxes (Chapter 4 quiz due)
  • T 3/9: Finish 6.5-Integration over nonboxes, start 6.6-Fubini's theorem
  • Th 3/11: Go over homework (6.2, 6.3 exercises due), more 6.6-Fubini's theorem
  • F 3/12: Go over homework (6.3, 6.5 exercises due), more 6.6-Fubini's theorem (Chapter 6a quiz out)

  • M 3/15: Start 6.7-Change of variable theorem (Chapter 6a quiz due)
  • T 3/16: Finish 6.7-Change of variable theorem
  • W 3/17: Go over homework (6.6 exercises due)
  • F 3/19: Go over homework (6.6 exercises due)

  • M 3/22: 9.1-Definition of k-surface in n-space, 9.3-Differential forms syntactically and operationally
  • T 3/23: Go over homework (6.7 exercises due)
  • W 3/24: 9.4-One-forms, start 9.5-Two-forms
  • Th 3/25: OPTIONAL first of four lectures on chapter 5-Inverse function theorem, implicit function theorem, Lagrange multiplier method
  • F 3/26: Go over homework (6.7 exercises due)

  • M 3/29: [No-W drop deadline, withdraw/leave deadline] Finish 9.5-Two-forms, 9.6-Basic properties, 9.7-Multiplication
  • T 3/30: Go over homework (9.3, 9.4 exercises due)
  • W 3/31: 9.8-Differentiation of differential forms, start 9.9-Pullback
  • Th 4/1: OPTIONAL second of four lectures on chapter 5
  • F 4/2: Go over homework (9.5 exercises due) (Chapter 6b quiz out)

  • M 4/5: (Chapter 6b quiz due)
  • T 4/6: Start 9.9-Pullback of differential forms
  • W 4/7: Go over homework (9.7 exercises due)
  • Th 4/8: OPTIONAL third of four lectures on chapter 5
  • F 4/9: Go over homework (9.8 exercises due), more 9.9-Pullback

  • Spring break week

  • M 4/19: 9.10-Change of variable for differential forms, 9.12-Cubes and chains, start 9.13-Boundary
  • T 4/20: Go over homework (9.9, 9.10 exercises due), more 9.13-Boundary
  • W 4/21: 9.14-The general FTIC, 9.16-Green's theorem
  • Th 4/22: OPTIONAL fourth of four lectures on chapter 5
  • F 4/23: Go over homework (9.13 exercises due), 9.16-Stokes's and Gauss's theorems

  • M 4/26:9.11-Closed forms, exact forms, and homotopy
  • T 4/27: Go over homework (9.14 exercises due), FTC examples, course evaluations
  • W 4/28: Maxwell's equations
  • F 4/30: Go over homework (9.16 exercises due) (Chapter 9 quiz out, due 5pm Wed May 5)

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