Calendar for 2019 - 2020 Fall Semester MATH 1350 Section 100 (Class Number 7969), taught by Mark Barsamian

Week 1: Mon Aug 26 - Fri Aug 30

• Reading: Pressley Chapter 1: Curves in \( \mathbb{R}^{2} \) and \( \mathbb{R}^{3} \)
  • 1.1: What is a curve? Cartesian -vs- Parametrized presentation of curves. Tangent vector to a curve.
  • 1.2: Arc Length, speed
  • 1.3: Reparametrizations, Regular Curves
  • 1.4: Closed Curves, T -Periodic Curves
• Homework: H01 Due Tue Sep 3
  • 1.1 # 3,4,7,8,9
  • 1.2 # 1,2,3,4
  • 1.3 # 1,2,3
  • 1.4 # 1,2,3,4,5

Week 2: Mon Sep 2 - Fri Sep 6

• Reading: Pressley Chapter 2: How much does a curve curve?
  • 2.1: Curvature
  • 2.2: Plane Curves, Signed Curvature, Osculating Circle
  • 2.3: Space Curves, Principal Normal Vector, Binormal Vector, Torsion, Frenet-Serret Equations
  • 2.1: Curvature
• Homework: H02 Due Wed Sep 11
  • 2.1 # 1,2
  • 2.2 # 1,2,6,7
  • 2.3 # 1,2,3,4,5 (typo in #4: should be \( \frac{d}{dt} \))

Week 3: Mon Sep 9 - Fri Sep 13

• Reading: Pressley Chapter 3: Global Properties of [Plane] Curves
  • 3.1: Simple Closed Curves
  • 3.2: The Isoperimetric Inequality
  • 3.3: The Four Vertex Theorem
• Homework: H03 Due Mon Sep 16
  • 3.1 # 1
  • 3.2 # 2
  • 3.3 # 2,3

Week 4: Mon Sep 16 - Fri Sep 20

• Exam 1: Take-home exam covering Chapters 1 - 3, Assigned Tue Sep 17 at noon; Due Thu Sep 19 at noon
• Reading: Pressley Chapter 4: Surfaces in \( \mathbb{R}^{3} \)
  • 4.1: What is a Surface? Surface Patch, Atlas, Transition Map
  • 4.2: Smooth Surfaces
  • 4.3: Smooth Maps Between Surfaces, Smooth Functions from a Surface to \( \mathbb{R} \)
• Homework: H04 Due Mon Sep 23
  • 4.1 # 2,3,4
  • 4.2 # 2,3,5,6
  • 4.3 # 1,2

Week 5: Mon Sep 23 - Fri Sep 27

• Reading: Pressley Chapter 4: Surfaces in \( \mathbb{R}^{3} \)
  • 4.4: Tangent Vector to a Surface, Tangent Plane, Derivative of a Map Between Surfaces
• Homework: H05 Due Fri Sep 27
  • Revisit 4.2 #6. Write an outline for the author's solution. (Just write an outline.)
  • 4.4 # 1,2,3 (Be sure to include outline-type headings in your solutions.)
    • In 4.4#2, note that the book is often casual about reparametrizations. We need to be more precise. A reparametrization of \( \sigma \) is a map \( \tilde{\sigma} \) that can be expressed as \( \tilde{\sigma} = \sigma \circ \phi \) where \( \phi : \tilde{U} \rightarrow U \)

Week 6: Mon Sep 30 - Fri Oct 4

• Reading: Pressley Chapter 5: Examples of Surfaces
  • 4.5: Normals and Orientability, Oriented Surface
  • 5.1 Level Surfaces
• Homework: H06 Due Mon Oct 7
  • 4.5 # 1,2
  • 5.1 # 2,3

Week 7: Mon Oct 7 - Fri Oct 11

• Reading: Pressley Chapter 6: The First Fundamental Form
  • 6.1 Lengths of Curves on Surfaces
• Homework: H07 Due Fri Oct 11
  • 6.1 # 1,2,3,4

Week 8: Mon Oct 14 - Fri Oct 18

• Reading: Pressley Chapter 6: The First Fundamental Form
  • 6.2 Isometries of Surfaces
  • 6.3 Conformal Mappings of Surfaces
• Homework: H08 Due Fri Oct 18
  • 6.2 # 1,2,3
  • 6.3 # 1,2,4,5,6,7

Week 9: Mon Oct 21 - Fri Oct 25

• Reading: Review Chapters 4,5,6
• Homework: None
• Exam 2: Take-home exam covering Chapters 4,5,6, Assigned Thu Oct 24 at 3pm; Due Mon Oct 28 at noon

Week 10: Mon Oct 28 - Fri Nov 1

• Reading: Pressley Chapter 7: Curvature of Surfaces
  • 7.1 The Second Fundamental Form
  • 7.2 The Gauss and Weingarten Maps
  • 7.3 Normal and Geodesic Curvatures
  • 7.4 Parallel Transport and the Covariant Derivative
• Homework: H09 Due Mon Nov 4
  • 7.1 #1,2,3,4
  • 7.2 #1,2,3
  • 7.3 #1,2,3,4
  • 7.4 #1

Week 11: Mon Nov 4 - Fri Nov 8

• Reading: Pressley Chapter 8: Gaussian, mean, and principal curvatures
  • 8.1 Gaussian and mean curvatures
• Homework: H10 Due Fri Nov 8
  • 8.1 #1,2,4,5,7

Week 12: Mon Nov 1 - Fri Nov 15

• Reading: Pressley Chapter 8: Gaussian, mean, and principal curvatures
  • 8.2 Principal curvatures of a surface
  • 8.3 Surfaces of constant Gaussian curvature
  • 8.4 Flat Surfaces
  • 8.5 Surfaces of constant mean curvature
• Homework: H11 Due Fri Nov 15
  • 8.2 #1,2,3,4
  • 8.4 #1
  • 8.5 #1,2

Week 13: Mon Nov 18 - Fri Nov 22

• Reading: Pressley Chapter 9: Geodesics
  • 9.1 Definition and basic properties
  • 9.2 Geodesic equations
  • 9.3 Geodesics on surfaces of revolution
  • 9.4 Geodesics as shortest paths
• Homework: H12 Due Mon Nov 25
  • 9.1 #1,2,5
  • 9.2 #1,2,3,4,6
  • 9.3 #1,2
  • 9.4 #1,2

Week 14: Mon Nov 25 - Fri Nov 29 (Wed, Thu, Fri is Thanksgiving Break.)

• Reading: Pressley Section 9.5 Geodesic Coordinates and Section 10.2 Gauss's Theorem
• Exam 3: Take-home exam covering Chapters 7,8,9, Assigned Tue Nov 26 at 3pm; Due Thu, Dec 5 at 9am.

Week 15: Mon Dec 2 - Fri Dec 6

• Reading: Chapter 13 (The Gauss-Bonnet theorem)
• Final Exam: Take-home exam covering Chapter 13, Assigned Thu Dec 5 at 3pm; Due Thu Dec 12 at 9am.