MA442 Multivariate Analysis I (Honors)

Purdue University Spring 2006

Wednesday, March 01, 2006

Course Information (Updated)

Schedule: MWF 11:30am-12:20pm in REC 117

Instructor: Arshak Petrosyan
Office Hours: MWF 10:30 -11:30am, or by appointment, in MATH 610

Course Description: MA442 covers the foundations of real analysis in several variables, assuming the single variable notions of these concepts.
Prerequisite: MA440

[B] R. Bartle, The Elements of Real Analysis, Second Edition, John Wiley & Sons, New York, 1975.
Additional text:
[R] W. Rudin, Principles of mathematical analysis, Third edition, McGraw-Hill, New York, 1976

Course Outline:
[B], Ch. II, (2 wks.): Topology of Rp: Heine-Borel, connectedness, etc.
[B], Ch. III, §§14-17 (1 wk): Sequences, Bolzano-Weierstrass thm., Cauchy criterion.
[B], Ch. IV, §§20-22 (1 wks): Continuity (with emphasis on the equivalence of different definitions).
[B], Ch. VII, §§39-41 (5 wks.): Differentiation, mapping theorems.
[B], Ch. VIII (4 wks.): Riemann integration, including "content", Lebesgue's criterion for integrability, and careful treatment of change of variables.

The final two weeks will be spent on [R], Ch. 10: Differential forms and Stoke's Theorem.

Homework will be collected weekly on Wednesdays. The assignments will be posted on this website at least one week prior the due date.

Exams: There well be two midterm exams (evening exams) and a comprehensive final exam (covering all topics). The exact time and place will be specified as the time approaches.