************************************** * The final exam is at 10:00 a.m. on * * Sunday, January 19. * * I shall announce the location * * here and on my office door. * ************************************** This directory is for Math 271, year 2002/3, fall semester. We meet on Mondays and Wednesdays at 17.40 in M-204. In-term exams will be on: Monday, October 28 (or 30, if the other day is a holiday) and Monday, December 9. These exams are during our regular class time. Therefore there are no "make-up" exams because of a conflict with another course. The main reference for the course is the lectures---and therefore your own notes. In preparing the lectures, I write my own notes, which are in the files . One cannot assume that these notes contain everything important from the lectures. Here is a rough outline of the content of the course: 1. The real numbers, as composing a complete ordered field. 2. Metric spaces: Euclidean spaces Bolzano--Weierstrass Theorem Cantor Intersection Theorem Compactness (Heine--Borel Theorem) Metric spaces as such 3. Sequences: Convergence-preservation theorems Monotone convergence theorem Complete metric spaces (Cauchy Convergence Criterion) 4. Continuous functions Effect on open and closed sets Extrema on compact sets Bolzano's Theorem Connectedness Uniform continuity of functions Uniform convergence of sequences of functions Fixed-point theorem for contractions 5. Differentiation [not covered: 6. Bounded variation] --------------------- The following books may be useful: Robert G. Bartle, The Elements of Real Analysis Tom M. Apostol, Mathematical Analysis Michael Spivak, Calculus The catalogue-description of the course-content is: "Real numbers. Metric spaces. Completeness, compactness and connectedness. Uniform limits and uniform continuity. Real functions on a compact metric space. Contraction mapping theorem. Functions of bounded variation. Differentiability of functions of several variables." ~