### 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

**Textbook:**

[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

**R**

^{p}: 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.

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