MTH436
Introduction to Mathematical Analysis II

MW 3:00-4:45 PM
Ballentine Hall 102

Instructor    Araceli Bonifant
Office: Lippitt Hall 202 G
Phone: 874-4394
Email: bonifant@uri.edu

Office Hours:

Book: Introduction to Real Analysis by Robert G. Bartle and Donald R. Sherbert, 4th. Edition

Course Description. This is the second of two courses providing a rigorous introduction to Mathematical Analysis and Metric Space Topology as a basis for advanced work in mathematics. In this course we will look more deeply at concepts you learned in your Calculus classes. We will discuss how to prove many of the facts you have used in the past. You will learn precise definitions of notions, get a deeper understanding of concepts, and make your reasoning more rigorous. A very important component of this course is to expose you to proofs. The goal is for you to learn how to write proofs.

Prerequisites. MTH 435 or permission of instructor.

Tentative List of Topics:

• Differentiation: The derivative, The Mean Value Theorem, L'Hospital's Rules, Taylor's Theorem.

• The Riemann Integral: Riemann Integral, Riemann Integrable Functions, The Fundamental Theorem, The Darboux Integral, Approximate Integration.

• Sequences of Functions: Pointwise and Uniform Convergence, Interchange Limits, The Exponential and Logarithmic Functions, The Trigonometric Functions.

• Infinite Series: Absolute Convergence, Tests for Absolute Convergence, Tests for Nonabsolute Convergence, Series of Functions.

• The Generalized Riemann Integral: Definition and Main Properties, Improper and Lebesgue Integrals, Infinite Intervals, Convergence Theorems.

• Evaluation Policy:

• Homeworks and Quizzes             25%
• Exam I                                         20 %    Wednesday March 2
• Exam II                                         20 %    Wednesday April 6
• Final Exam                                   35 %    Wednesday May 11,        3:00 PM - 6:00 PM
• Standards of behaviour: Students are responsible for being familiar with and adhering to the published "Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook. If you must come in late, please do not disrupt the class. Please turn off all cell phones, pagers, or any electronic devices.

Special Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.