Mathematics 551

Differential Geometry.

Wardlaw College 114 MWF, 9:40am--10:30am

Instructor:

Ralph Howard

• Office: LC 304
• Phone: 777-7471
• E-mail: howard@math.sc.edu
• Office Hours: TTh 2:30pm-3:30pm and by appointment.
• Syllabus. It contains the basic information about prerequisites, grading, test dates, the text and so forth.

Text: Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition by Manfredo P. do Carmo, which is less than $20 at Amazon, and Differential Geometry: A First Course in Curves and Surfaces by Theodore Shifrin which is free.

• LaTeX basics..

• Geodesics on Surfaces.
• The Gauss-Bonnet Theorem

Tests:
• Take home part of test 1.

Quizzes:

Homework:

• Homework 1
  
• Homework 2
  
• Homework 3
  
• Homework 4
  
• Homework 5
  
• Homework 6
  
• Homework 7
  
• Homework 8
  
• Homework 9
  
• Homework 10
  
• Homework 11
  
• Homework 12
  
• Homework 13
  
• Homework 14
  
• Homework 15
  
• Homework 16
  
• Homework 17
  
• Homework 18
  
• Homework 19
  

Some Extra Credit Problems:

• Rational Points on Conics and Pythagorean Triples.
  
• The curvature of level set of a function of two variables.
  

Jupyter Notebooks:
If you have Jupyter installed on your computer these notebooks can be down loaded and run.
• plot_from_curvature.ipynb This notebook plots the curve given the curvature function.
• plot_and_find_curvature.ipynb This notebook takes the parametric form of a planar curve, plots it and computes the unit tangent, unit normal, and the curvature.
• polar_curvature.ipynb This notebook plots the graph of a curve given in polar coordinates as r = f(theta) and computes its curvature.
• evolute.ipynbThis notebook plots a curve together with its evolute.
• plot3d_curve_find_curvature_torsion.ipynb A notebook that plots a 3D curve given parametrically, and computes its Frenet frame, curvature, and torsion.