Analytic Geometry
Prof. Zeev Rudnick
Fall 20042005, Tel Aviv
Schedule:
Thursday 1315 Melamed auditorium
Recitation session: Mr. Mendy Shoval, Tuesday 1415, Orenstein 103
Syllabus:
The course is an introductory course in the geometry of two and three
dimensions.
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
 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
curvature.
See here for the details of what was taugh this year !.
Bibliography
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
Homework:
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: rudnick@post.tau.ac.il, Office : Schreiber 316, tel: 6407806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/analyticgeom.html