Time and Place: MWF 12:30pm–01:20pm REC 313

Instructor: Arshak Petrosyan

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

Course Description: Credit Hours: 3.00. Basic real analysis, limits, continuity, differentiation, and integration. Typically offered Fall.

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 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.)
• Fourier Series
• Stone-Weierstrass Theorem
• Existence and Uniqueness Theory of Ordinary Differential Equations

(Time should permit to do two of the above applications).

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.

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: