Time and Place: TTh 12:00-01:15pm UNIV 119
Instructor: Arshak Petrosyan
Office Hours: TTh 11:00-12:00noon, or by appointment, in MATH 610
Course Description: MA44200 covers the foundations of real analysis in several variables, assuming the single variable notions of these concepts. Prerequisite: MA44000
[B] R. Bartle, The Elements of Real Analysis, Second Edition, John Wiley & Sons, New York, 1975.
[R] W. Rudin, Principles of mathematical analysis, Third edition, McGraw-Hill, New York, 1976
[M] J. Munkres, Analysis on Manifolds, Addison-Wesley, 1991.
- [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 additional topics, such as integration on manifolds.
Homework will be collected weekly on Thursdays. The assignments will be posted on this website at least one week prior the due date.
Exams: There well be two midterm exams (in-class or evening) and a final project. The exact times and places will be specified due course.