Final Project

Due: Fri, May 4, 12:20pm

[Final Project]

Submission: From around noon on Mon, Apr 30, an envelope will be affixed at the door of my office MATH 610. Place the completed project into the envelope before 12:20pm on Fri, May 4.

Final Score

Two schemes for calculating your final score will be used: with or without final project.

Scheme I = (3/10)ME1 + (3/10)ME2 + (1/5)FP + (1/5)HW
Scheme II = (3/8)ME1 + (3/8)ME2 + (1/4)HW

where FP, MEi, HW are the scores (in %) for Final Project, Midterm Exam i, Homework

You will have to contact me (by email) by Fri, Apr 27 (last day of classes) to tell whether you will be completing the Final Project (Scheme I will be used) or not (Scheme II will be used). If you do not contact me by then, your score will be calculated according to Scheme I.

Homework Assignments

(All problems are from [B] unless stated otherwise)

#10 Due Tue, Apr 24: from Munkres [M], §24 #2, 4, §25 #4,8
#9 Due Thur, Apr 5: from Munkres [M], §21 #2, §22 #2,4, §23 #3
#8 Due Thur, Mar 29: 45.G, 45.K, 45.M, 45.O, 45.P
[Partial Solutions]
#7 Due Thur, Mar 22: 44.O, 44.R, 45.B, 45.C, 45.D
[Partial Solutions]
#6 Due Tue, Mar 6: 43.R, 43.S, 44.G, 44.H (a), 44.J (Use 43.R), 44.K
[Partial Solutions]
#5 Due Tue, Feb 28: 42.R, 42.S(a,c), 42.U, 43.B, 43.D, 43.Q
[Partial Solutions]
#4 Due Tue, Feb 14: 42.A(a-c), 42.B, 42.D, 42.F(d,e), 42.O, 42.Q
[Partial Solutions]
#3 Due Tue, Feb 7: 41.J, 41.K, 41.L, 41.R, 41.U, 41.V
[Partial Solutions]
#2 Due Tue, Jan 31: 40.E, 40.L, 40.R, 40.S, 40.T, 40.U
[Partial Solutions]
#1 Due Thur, Jan 19: 21.M, 39.E, 39.J, 39.T, 39.V, 39.W
[Partial Solutions]

Midterm Exam 2

Scheduled Thur, Apr 12 8:00-10:00pm in HAAS G066

The exam will cover §§43-45 of Bartle [B] and §§21-23 of Munkres [M].

[Practice Problems]

Extra Material

Extra material from [M] Munkres, Analysis on Manifolds

[Partition of Unity] [Manifolds]

Course Log

Covered
Tue, Feb 28: §44 Content and Integral, Sets with Content
Thur, Feb 23: §43 Properties of Integral, Existence of Integral
Tue, Feb 21: Review for Midterm 1
Thur, Feb 16: §43 Content zero, Definition of Integral
Tue, Feb 14: §42 Inequality Constraints
Thur, Feb 9: §42 Extremum Problems with Constraints, Lagrange's Theorem.
Tue, Feb 7: §42 §42 Local Extrema, Second Derivative Test.
Thur, Feb 2: §41 Inversion Theorem (cont), Implicit Functions
Tue, Jan 31: §41 Surjective Mapping Theorem, Open Mapping Theorem, Inversion Theorem.
Thur, Jan 26: no class
Tue, Jan 24: §41 Class C1, Approximation Lemma, Injective Mapping Theorem
Thur, Jan 19: §40 Interchange of Order of Differentiation, Taylor's Theorem
Tue, Jan 17: §40 Chain Rule and Mean Value Theorems.
Thur, Jan 12: §39 Partial derivatives, differentiation (cont)
Tue, Jan 10: §21 Linear functions, §39 Partial derivatives, differentiation

Planned
Thur, Mar 1: §44 Characterization of Content Function, Further Properties of Integral.

Midterm Exam 1

Scheduled Wed, Feb 22, 8:00-10:00pm in REC 121

The exam will cover §§39-42.
We will have a review session on Tue, Feb 21.

New! [Practice Problems]

Course Information

Schedule: TTh 1:30-2:45pm in MATH 211

Instructor: Arshak Petrosyan
Office Hours: TTh 11:00-12:00 noon, 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

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

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 in-class midterm exams and a comprehensive final exam (covering all topics). The exact time and place will be specified as the time approaches.