Math 240C (Driver, Spring 2002) Real Analysis
Driver, APM 7414, 534-2648.
Meeting times: MWF 11:15 --
12:05 PM in
Textbook: Gerald B. Folland, "Real
Analysis, "Modern Techniques and Their Applications," 2nd
I will also make lecture notes available
from this site.
Students are assumed to have completed last
quarters Math 240B.
Homework: There will be weekly homework
assignments, which I will grade.
Test times: The final is scheduled for
Office Hours: To be determined.
Grading: The course grade will be computed
|Quick review of limit operations including
sums on arbitrary sets|
|Basics of Metric spaces, Normed spaces
(including dual spaces), Hilbert spaces and Topological spaces|
|Introduction to sigma - algebras, measurable
functions, and measures|
|Construction of the integral from a measure on
a sigma - algebra|
|General properties of the integral (Fatou's
lemma, monotone convergence, Lebesgue dominated convergence, Tchebychev
inequality, Jensen's inequality)|
|Product measures and the Fubini-Tonelli
spaces, Holder inequality, the dual of dual of Lp spaces.|
Possible further topics
|A little complex analysis|
|Distribution theory and elliptic regularity|
|Unbounded operators and the Spectral Theorem for self-adjoint
|Properties of ordinary differential equations|
|Implicit and Inverse function theorems|