Differential Geometry: Math 340-01A Syllabus Fall 2005
Section 01A : 2-4-6 at 1 - 2.10 pm, HAB 015
Instructor: Kris Nairn Office: PE 239, HAB 17C Phone: (PE) x 3087
Email: knairn@csbsju.edu
My website is http://www.employees.csbsju.edu/knairn
Text: John McCleary, Geometry from a Differentiable Viewpoint. This text is available in paperback on Amazon
Help: Office Hours are to be determined
Grade Breakdown: Homework 30%, Exam I 20%, Exam II 20%, Final 20%, Class Presentations 10%. The class presentations will be on topics related to the homework.
Lecture Plans: The following is merely a guide and can change given the needs of the class.
| Day | Lecture topic |
| August 26 (Day 2) | Intro to course/Lines in Euclidean space |
|
30 |
Notion of Straightness on a sphere/Geodesics |
| September 1 | Straightness on Cones/Cylinders, Intrinsic/Extrinsic curvature |
| 3 | Multidimensional Calculus, Part I |
| 8 | Multidimensional Calculus, Part II |
| 10 | Introduction to Curves in Euclidean Space/Arc-length |
| 13 | Lab Day: Mathematica |
| 15 | Curvature of Plane curves |
| 17 | Curves in Space: Frenet-Serret Apparatus |
| 20 | Rigid Motions/Isometries, Part I |
| 22 | Implications of Curvature/Torsion |
| 24 | |
| 27 | Exam I |
| 29 | 3-body Problem, Part I |
| October 1 | 3-body Problem, Part II |
| 4 | Introduction to Surfaces: regular maps, patches, Inverse Function Theorem |
| 6 | |
| 8 | Tangent Plane, Orientability |
| 11 | First Fundamental Form, Gauss Map |
| 13 | Second Fundamental Form, Gaussian Curvature |
| 18 | Isometries, Part II/Christoffel Symbols |
| 20 | Geodesics/Geodesic Curvature |
| 22 | |
| 25 |