Math 5320, Basic Real Analysis 2
Semester 2, 2002-03
Course Lecturer
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
Email: packer@euclid.colorado.edu
URL: http://spot.colorado.edu/~packer
Course Information:
This course is meant to continue the study of analysis of real-valued functions of one or several variables,
with an emphasis on Lebesgue measure
and Lebesgue integration on the real line and R^n.
Topics to be covered include:
convex functions,L^p - spaces, definitions and examples; Minkowski's inequality, Holder's inequality;
Signed measures, definitions and basic properties, Hahn decomposition Theorem,
Jordan decompostion, mutually singular measures, Jordan decomposition Theorem,
comparison of measures, absolutely continuous measures, Radon-Nikodym Theorem,
Lebesgue decomposition theorem; product measures: Fubini's Theorem, Tonelli's Theorem, applications of Fubini Theorem to integral operators;
multivariable differential calculus: inverse function theorem, implicit function theorem, smooth manifolds in R^n, derivatives, tangent spaces.
Prerequisite:
Math 5310, or Math 6310, or instructor consent.
Course Text:
We will use as a primary text the book
"Real Analysis", by H.L. Royden, covering most of Chapters 6,11, and 12,
and will use as a secondary text for the multivariable analysis
the book "Primer of Modern Analysis" by K.T. Smith, Spinger Verlag, 1983, covering parts of Chapters 11 and 12.
Assessment:
- Homework Assignments (every two weeks or so): 30 %
- In-class mid-term test - Wednesday, March 5, 10 - 11: 30 %
(click here to see the test)
- Final exam, Wednesday, May 7, 10:30 a.m. - 1 p.m. : 40 % .
Lecture Hours and Venue:
MWF 10 a.m.-11 a.m. Duane G1B27
Office Hours:
Wed., Fri. 11 a.m.-12 noon, 4 p.m. -5 p.m., and by appointment.
Homework:
Some Important Names associated with Real Analysis :
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Last modified January 22, 2003.