Prof. Zeev Rudnick
Fall 2004-2005, Tel Aviv
Thursday 13-15 Melamed auditorium
Recitation session: Mr. Mendy Shoval, Tuesday 14-15, Orenstein 103
The course is an introductory course in the geometry of two and three
It assumes knowledge of the courses calculus 1, linear algebra 1
and that the students have either taken calculus 2 and linear algebra
2 or are studying them in parallel with the course.
The topics include
See here for the details of what was taugh this year !.
- Background from linear algebra:
Inner product spaces, orthogonality,
projections, reflections, isometries eigenvalues and eigenvectors
- Orientation and the vector product
- affine geometry
- Conic sections
- The classification of plane quadrics
- curves in the plane: tangents, normals
- tangents to conic sections
- billiards in a rectangle, a circle and an ellipse
- Arc length
- curvature and the differential geometry of curves
- The radius, center and circle of curvature (osculating circle),
the evolute of a curve.
- Frenet's equations, existence and uniqueness of curves with given
As was the situation in previous years with this course, I did not
find any single source that I could use as a
text book. Examples of books part of which are relevant are:
"Introduction to Differential Geometry",
by M. Farber (in Hebrew), mainly the first two chapters.
- "Geometry", by A. Pogorelov
This will be an important part of the course. In order to be eligible
to take the final exam, at least 50% of the assignments have to be
turned in within a week of their due date. 10% of the final grade will be
determined from the homework scores, which will be obtained as the average
grade of a certain number of assignments.
Contact me at: firstname.lastname@example.org, Office : Schreiber 316, tel: 640-7806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/analyticgeom.html