Time and Place: MWF 12:30pm–01:20pm in UNIV 201

Instructor: Arshak Petrosyan

Office Hours: MWF 11:30am-12:30pm, or by appointment, in MATH 610

Course Description: Credit Hours: 3.00. Real analysis in one and n-dimensional Euclidean spaces. Topics include the completeness property of real numbers, topology of Euclidean spaces, Heine-Borel theorem, convergence of sequences and series in Euclidean spaces, limit superior and limit inferior, Bolzano-Weierstrass theorem, continuity, uniform continuity, limits and uniform convergence of functions, Riemann or Riemann-Stieltjes integrals.

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 Rp. (5 hrs.)
  • Sequences in Rp. 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 Taylor’s 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.)

Homework will be collected weekly on Wednesdays (with some exceptions), at the beginning of class. No late homeworks will be accepted, however, the lowest homework score will be dropped. The assignments will be posted here at least one week prior to the due date.

Exams: There will be two midterm exams (evening exams) and a comprehensive final exam (covering all material). The exact times and place will be specified due course.

Grading: Your final grade will be computed by the scheme

Final Score = (1/3)FE + (7/30)ME1 + (7/30)ME2 + (1/5)HW,

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

Note: If you perform better than average on both midterm exams, you will be given an option of not taking the final exam and your score will be computed by an alternative scheme (to be specified towards the end of the course).

Academic Integrity: As a reminder, all students must comply with Purdue’s policy for academic integrity:

https://www.purdue.edu/odos/osrr/academic-integrity/

Students with Disabilities: In this mathematics course accommodations are managed between the instructor, student, and DRC Testing Center.

Students should see instructors outside class hours ­– before or after class or during office hours – to share their Accommodation Memorandum for the current semester and discuss their accommodations as soon as possible.

Emergencies: In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor’s control. Relevant changes to this course will be posted onto the course website or can be obtained by contacting the instructor via email or phone. You are expected to read your @purdue.edu email on a frequent basis.