# MA442 Multivariate Analysis I (Honors)

Purdue University Spring 2006

## Thursday, May 04, 2006

### Final Exam

Scheduled Thu, May 4, 2006 10:20-12:20pm in REC 117

Exam statisfics
Average: 66.4%, St.Dev: 15.1%, Max Score: 88%, Min Score: 46%, Median: 69%

[Final Exam Solutions]

## Wednesday, April 26, 2006

### Homework

#11 (Due on Wed, Apr 26):   45.G, 45.K, 45.M, 45.O, 45.P
[Solutions]
#10 (Due on Wed, Apr 12):   44.K, 44.O, 44.P, 44.R, 45.B, 45.C, 45.D
[Solutions]
#9 (Due on Wed, Apr 5):   43.B, 43.M, 43.Q, 43.R, 44.H, 44.J
[Solutions]
#8 (Due on Mon, Mar 27):  42.A(a-c), 42.D, 42.F(d,e), 42.P, 42.Q, 42.R, 42.S(c), 42.U
[Solutions]
#7 (Due on Mon, Mar 6):  41.K, 41.N(a-b), 41.O, 41.R, 41.U, 41.V, 41.W
[Solutions]
#6(Due on Wed, Feb 22):  40.K, 40.R, 40.S, 40.T, 40.U, 41.D, 41.J
[Solutions]
#5(Due on Wed, Feb 15):  39.D, 39.G, 39.J, 39.T, 39.V, 39.W, 40.E, 40.L
[Solutions]
#4(Due on Wed, Feb 8):  20.K, 20.P, 21.L, 21.M, 22.F, 22.G, 22.H, 22.S
[Solutions]
#3(Due on Wed, Feb 1):  14.D, 15.I, 15.N, 15.O, 16.Q, 17.D, 17.I, 17.S
[Solutions]
#2(Due on Wed, Jan 25):  11.C, 11.G, 11.N, 12.C, 12.E, 12.I
[Solutions]
#1(Due on Wed, Jan 18:  8.Q, 8.beta(a-c), 9.G, 9.H, 9.I, 9.L, 10.C, 10.F
[Solutions]

## Monday, April 24, 2006

### Midterm Exam 2

Scheduled at 7:00-9:00pm on Thu. Apr 20, 2006 in REC 121

We will have review on Wed, Apr 19, in class, possibly on Mon, Apr 17 as well.

Practice Problems

Exam statisfics
Average: 66.1%, St.Dev: 11.4%, Max Score: 83%, Min Score:48%, Median: 68%

[Midterm Exam 2 Solutions]

## Friday, April 21, 2006

### Couse Log

Planned
Apr 24-28 Review for Final Exam
What was covered
Apr 17-19: Review for Midterm 2
Apr 14: § Problems on Change of Variables
Apr 12: § Jacobian Theorem, Change of Variables
Apr 10: § 45 Linear Change of Variables, Transformations Close to Linear
Apr 7: §45 Transformation of Sets, Content and Linear Mappings
Apr 5: §44 Integral as Iterated Integral; §45 Transformations of Sets of Content Zero
Apr 3: §44 Further Properties of Integral, Mean Value Theorem
Mar 31: §44 Content and Integral
Mar 29: §43 Properties of Integral, Existence of Integral
Mar 27: §43 Definition of Integral, Riemman, Upper and Lower Sums
Mar 24: §42 Inequality Constraints, §43 Content Zero
Mar 22: §42 Extremum Problems with Constraints: Problems
Mar 20: §42 Extremum Problems with Constraints
Mar 10: Class cancelled (because of evening exam)
Mar 8: §42 Extremum Problems, Second Derivative Test
Mar 6: §41 Implicit Function Theorem, §42 Extremum Problems.
Mar 3: §41 Implicit Function Theorem
Mar 1: Overview of Midterm Exam
Feb 27: Review for Midterm Exam
Feb 24: §41 Inverse Mapping Theorem
Feb 22: §41 Surjective Mapping Theorem, Open Mapping Theorem
Feb 20: §41 Injective Mapping Theorem, Surjective Mapping Theorem (started)
Feb 17: §41 C1 functions, Injective Mapping Theorem (started)
Feb 15: §40 Mixed derivatives (finished), higher derivatives, Taylor's theorem
Feb 13: §40 Mean Value Theorem, mixed derivatives (stared)
Feb 10: §39 Tangent planes, §40 Combinations of Diff. Functions, the Chain Rule
Feb 8: §39 Examples, Existence of the derivative
Feb 6: §39 Partial derivatives, differentiability
Feb 3: §22 Global continuity theorem, preservation of compacteness, connectedness
Feb 1: §21 Linear functions, §22 Relative topology, global continuity
Jan 30: §20 Continuity at a point (different definitions)
Jan 27: §17 Sequences of functions, pointwise and uniform convergence
Jan 25: §§15-16 Bolzano-Weierstrass (revisited), Cauchy sequences
Jan 23: Finish §12; §§14-15 Convergence of sequences
Jan 20: §12 Connected sets
Jan 18: §11 Compactness, Heine-Borel, Cantor Intersection Theorem
Jan 16: MLK day, no class
Jan 13: §10 Cluster points, Bolzano-Weierstrass, Nested Cells; started §11
Jan 11: §9 Open and closed sets, interior, boundary, closure
Jan 9: §8 Cartesian spaces, inner products, norms

## Wednesday, March 01, 2006

### Midterm Exam 1

Scheduled at 7:00-9:00pm on Tue, Feb 28, 2006 in MATH 211

The exam will cover material from Jan 9 to Feb 17 inclusive (see the Course Log)

We will have review on Mon, Feb 27, in class.

[Practice problems]

Exam statisfics
Average: 46%, St.Dev: 17.5%, Max Score: 75%, Min Score:14%

[Midterm Exam Solutions]

### 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.
[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.