COURSE PREFIX/NUMBER: MAT 473

TITLE OF COURSE: Intermediate Real Analysis II

INSTRUCTOR: John Quigg

TIME: 12-1:15 TTH

LOCATION: LL 103

LINE #: 18604

COURSE DESCRIPTION:
This is the continuation of MAT 472. The sequence 472-473 forms the
basis for our Graduate Qualifying Exam in Real Analysis, and is good
preparation for graduate real analysis at any university. The sequence
is typically taken by (very) well-prepared undergraduate students, as
well as beginning graduate students who have not seen the material in
their undergraduate studies.

MAT 473 covers analysis in n-dimensional Euclidean space, including
differentiation and Lebesgue integration. The highlights are the
Implicit Function Theorem, giving general conditions under which a
system of nonlinear equations can be solved differentiably for some
variables in terms of the others, convergence theorems for Lebesgue
integrals, and the Change of Variables Theorem, giving a general
process for transforming multiple integrals.

PREREQUISITES: MAT 472 or instructor approval.

TEXTBOOK: No required text - instead, lecture notes will be available.
But suggested references include:

W. Rudin, "Principles of mathematical analysis", 3rd ed., McGraw-Hill, 1976.
F. Jones, "Lebesgue integration on Euclidean space", Jones and Bartlett, 1993.
G. Folland, "Real analysis", 2nd ed., Wiley, 1999 (particularly Section 2.6).