Mathematics 551
Differential Geometry.
LeConte 348, 1:10--2:00pm
- Instructor:
- Ralph Howard
- Office: LC 352
- Phone: 777-7471
- E-mail: howard@math.sc.edu
- Office Hours: MW 2:30--3:30, Tue 2:00--3:00pm and
by appointment.
- Syllabus. It contains the basic information about prerequisites, grading, test dates, the text and so forth.
- Text:
Differential Geometry: A First Course in Curves and Surfaces
by
Theodore Shifrin which is free.
Jupyter Lab Notebooks:
Below are Jupyter Lab notebooks for doing some calculations of
things such as curvature, torsion, Gauss curvature, mean curvature
of curves and surfaces and for plotting pictures. These can be
downloaded and run on your machine if you have Jupyter installed.
Jupyter is free and runs on Windows, Mac OS, and Linux. It is available
at the Jupyter website. If
you have downloaded one of the files file.ipynb open it by opening
a terminal and then running the command.
jupyter lab file.ipynb
plot_from_curvature.ipynb If
you enter a function \(f(s)\) then this plots the graph of
a curve with curvature \(\kappa(s) = f(s) \).
Curve_plot_len.ipynb
You can enter a curve \(\mathbf c(t) = (x(t),y(t))\) and
and this will plot the curve and compute its arc length.
plot_and_find_curvature.ipynb
You can enter a curve \(\mathbf c(t) = (x(t),y(t))\) and
and this will plot the curve and compute its curvature.
evolute.ipynb
You can enter a curve \(\mathbf c(t) = (x(t),y(t))\) and
and this will plot the curve and its evolute.
osculating_circle.ipynb
You can enter a curve \(\mathbf c(t) = (x(t),y(t))\) and
and this will plot the curve and its osculating circle
at selected points.
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