Final Exam

Scheduled 7:00-9:00pm, Monday, December 11, in REC 113

Covers all material.

Additional office hours: 11:00-2:00pm Fri, Dec 8 in MATH610
Review: 11:00-12:15pm Mon, Dec 11 in REC316

Homework

All problems are from [B]
#10 Due Thur, Dec 7: 34.K, 35.D (d,e,f), 37.B, 37.G, 37.H(c,e,f)
#9 Due Thur, Nov 9: 29.S, 30.A, 30.D, 30.F
#8 Due Thur, Nov 2: 25.V, 27.D, 28.B, 28.K, 28.O
#7 Due Thur, Oct 26: 23.G, 23.I, 24.C, 24.D, 24.E (a,d,e)
#6 Due Thur, Oct 19 : 20.G, 20.P, 22.E, 22.F, 22.R
#5 Due Thur, Sep 28: 15.N, 16.A, 16.G, 18.B, 18.F
#4 Due Thur, Sep 21: 12.C, 12.F, 14.D, 14.M, 14.N, 14.O
#3 Due Thur, Sep 14: 10.C, 10.F, 10.G, 11.A, 11.C, 11.K
#2 Due Thur, Sep 7: 7.J, 8.F, 8.G, 8.Q, 9.G, 9.L
#1 Due Thur, Aug 31: 4.H, 5.C, 5.O, 6.D, 6.G, 6.H, 7.G

Midterm Exam 2

Thursday, November 16, in class

Covers the material from Oct 12 -- Nov 9 (see Course log)

[Practice Problems]

[Exam Solutions]

Course Log

Covered
Nov 9: § 29 Integration by Parts, § 30 Change of Variables, § 31 Convergence and Integral, Integral form of the Remainder
Nov 7: § 30 Mean Value Theorem, Differentiation Theorem, Fundamental Theorem of Calculus
Nov 2: § 29 Riemann Integral (see project 29.alpha), Properties of Integral, § 30 Riemann Criterion of Integrability
Oct 31: § 28 Taylor's Theorem, § 29 Riemann Integral
Oct 26: § 27 Differentiation, Mean Value Theorem, Rolle's Theorem, Cauchy Mean Value Theorem
Oct 24: § 25 Limit of the function at a point, upper and lower limits
Oct 19: § Uniform continuity, § 24 Pointwise and Uniform Convergence of Functions (see also § 17), Weierstrass Approximation Theorem
Oct 17: § 22 Global continuity theorem, preservation of compactness, connectedness
Oct 12: § 20 Local properties of continuous functions
Sep 30: § 18 limsup, liminf, Examples (number e)
Sep 28: § 16 Monotone convergence, § 18 limsup, liminf
Sep 21: § 15 Subsequences, § 16 Bolzano-Weierstrass, Cauchy sequences
Sep 19: § 14 Convergent sequences, examples, § 15 Combinations
Sep 14: §12 Connected sets, connected sets in R
Sep 12: §11 Compactness and Heine-Borel theorem
Sep 7: §10 Nested Cells and Bolzano-Weierstrass
Sep 5: §9 Open and closed sets; Open sets in R
Aug 31: §8 Vector spaces, inner products, norms, distance, §9 Open Sets
Aug 29: §7 Nested Intervals, Cantor Set, §3 Finite and Countable sets
Aug 24: §6 Completeness property of R
Aug 22: §4 Algebraic properties of R, §5 Order properties of R

Midterm Exam 1

Thursday, October 5, in class

Covers §§ 4-18 from [B], except §13 and §17 (see Course log)

[Practice Problems]

[Exam Solutions]

Course Information

Schedule: TTh 12:00-1:15pm in REC 113

Instructor: Arshak Petrosyan
Office Hours: TTh 9:30 -10:30am, or by appointment, in MATH 610

Course Description: Basic real analysis, limits, continuity, differentiation, and integration.
Prerequisite: MA350 or MA351

Textbook:
[B] R. Bartle, The Elements of Real Analysis, Second Edition, John Wiley & Sons, New York, 1975.

Course Outline:

• The algebraic, ordering, and completeness properties of the real numbers. (3 hrs.)
• Topology of R^p. (5 hrs.)
• Sequences in R^p. Convergence and Uniform convergence. Lim Sup and Lim Inf. (5 hrs.)
• Continuous and uniformly continuous functions. sequences of continuous functions. Approximation Theorems. (7 hrs.)
• Differentiation. Mean Value and Taylors Theorem. (3 hrs.)
• The Riemann (Riemann-Stieltjes) Integral. Improper Integrals. (6 hrs.)
• Infinite Series of constant and functions. Absolute and Uniform Convergence. Weierstrass M-Test; Dirichlet and Abel Test. Power Series. Double Series and the Cauchy Product. (8 hrs.)
• Selected Applications of Basic Material (8 hrs.)
  • a) Fourier Series
  • b) Stone-Weierstrass Theorem
  • c) Existence and Uniqueness Theory of Ordinary Differential Equations
  (Time should permit to do two of the above applications).

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