MAT 372 - Spring 05 - Spielberg
 Spielberg's homepage


STUDY GUIDE FOR FINAL EXAM

The final exam will be given Monday, May 9, 7:40 -- 9:30 AM.

OFFICE HOURS (after 5/2):  Tu (5/3):  1 - 4
                           W  (5/4):  9 - 11, 1 - 3
                           Th (5/5):  8 - 11, 1 - 4

The following list of topics can guide your study for the exam.  You should
know the definitions of the terms and the statements of the important
theorems.  You should review the exams and homework problems, and come to ask
questions at my office.

(*) topology of R^n:  open and closed sets, limit points, closure,
                      interior, and boundary of a set, compactness.

(*) limits, continuity, and uniform continuity of functions

(*) directional and partial derivatives

(*) differential and derivative:  definition, existence, relation
                                  with directional derivatives.
                       
(*) chain rule, convexity and mean value theorem, equality of mixed partials

(*) operator norm and inequalities

(*) contraction mapping theorem, inverse function theorem, implicit function theorem

(*) content of a set, negligible set, integrable and admissible functions

(*) integrability and step functions, Riemann sums, mesh theorem

(*) Fubini's theorem and iterated integrals