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] go over homework, 3.5-Consequences of the determinant properties (2.4 exercises due)

  • M 2/11: 3.5-Consequences of the determinant properties
  • T 2/12: 3.8-Determinant and volume, go over homework (3.5 exercises due)
  • W 2/13: 3.9-Determinant and orientation, 3.10-Cross product, rest of section as time allows
  • F 2/15: Go over homework (3.8, 3.9 exercises due), 4.1-Symbol-pattern breakown, 4.2-Bachmann-Landau scheme (Chapter 2 quiz out)

  • M 2/18: 4.2-Bachmann-Landau scheme, 4.3-Definition of multivariable derivative (Chapter 2 quiz due)
  • T 2/19: Review 4.2 and 4.3, derivative of p(x,y)=xy, go over homework (3.10 exercises due)
  • W 2/20: 4.4-Basic results, chain rule, start 4.5-Calculating the derivative
  • F 2/22: Sample derivative calculation, go over homework (4.2, 4.3 exercises due), preview derivative sufficiency theorem

  • M 2/25: 4.5-Calculating the derivative: sufficiency, chain rule in coordinates
  • T 2/26: Go over homework (4.4, 4.5 exercises due)
  • W 2/27: 4.6-Higher-order derivatives
  • F 3/1: Go over homework (4.6 exercises due)

  • M 3/4: [No-W drop deadline] 4.7-Extreme values
  • T 3/5: 4.8-Directional derivative and gradient
  • W 3/6: Go over homework (4.7 exercises due)
  • F 3/8: Go over homework (4.8 exercises due) (Chapter 4 quiz out)

  • M 3/11: 6.1-Integration machinery, 6.2-Definition of the integral (Chapter 4 quiz due)
  • T 3/12: 6.3-Continuity and integrability
  • W 3/13: 6.3-Continuity and integrability, go over homework (6.1, 6.2 exercises due)
  • F 3/15: Skim 6.5-Integration over nonboxes, go over homework (6.2, 6.3 exercises due)

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

  • Spring break week

  • M 4/1: 6.7-Change of variable theorem (Chapter 6a quiz due)
  • T 4/2: 6.7-Change of variable theorem
  • W 4/3: Go over homework (6.6 exercises due)
  • 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
  • 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)
  • 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 4/19: OPTIONAL lecture on 9.11-Closed forms, exact forms, and homotopy
  • 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: Optional extra lecture: 8.1-Euclidean and non-Euclidean constructions
  • F 5/3: Go over homework (9.16 exercises due) Course evaluations (Chapter 9 quiz out, due Wednesday May 8)

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