MTH436 
Introduction to Mathematical Analysis II

(Page Under Construction!!)
 
MW 3:00-4:15 PM
Lippitt Hall 204

Instructor    Araceli Bonifant  
Office: Lippitt Hall 200 B
Phone: 874-4394
Email: bonifant@math.uri.edu

Office Hours: Monday 4:30 PM, Tuesday 2:00PM.

Final-436.pdf
Hints-F436.pdf

Book: Introduction to Real Analysis, 3rd Edition by Robert G. Bartle and Donald R. Sherbert.

Course Description. This course is the follow up to Introduction to Real Analysis I. As in MTH435 we will look more deeply at the 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. MTH435


Tentative List of Topics:

  • Differentiation: The Derivative, The Mean Value Theorem, L'Hospital's Rule, Taylor's Theorem.

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

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

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

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

  • A Glimpse Into Topology: Open and Closed Sets in ${\mathbb R}$, Compact Sets, Continuous Functions, Metric Spaces.


    • Homework Chapters VI
    Sec 6.1, Page 166, 167: # 1c, 2, 4, 7, 11b, 11d, 14
    Sec 6.2, Page 175, 176: # 1c, 6, 9, 10, 13, 15, 20
    Sec 6.3, Page 182, 183: # 3, 5, 8(c,d), 9(b,c), 10(c,d), 11
    Sec 6.4, Page 191, 192: # 2, 6, 10, 12, 15, 16, 22, 23
    Sec.7.1, Page 201, 202: # 7, 9, 11, 12, 14, 16, 15, 18
    Sec.7.2, Page 209, 210: # 1, 5, 7, 8, 9, 15, 16, 22
    Sec.7.3, Page 217, 218: # 3, 9, 10, 11, 14, 16, 17, 18, 20, 21
    Sec.8.1, Page 232, 233: # 4, 6, 14, 16. 22. 23, 24
    Sec.8.2, Page 238, 239: # 5, 6, 8, 11, 12, 13, 17
    Sec.9.1, Page 256, 257: # 1, 2, 3, 6, 7, 11, 13
    Sec.9.2, Page 262, 263: # 5, 6, 7, 8, 14, 16, 17
    Sec.9.3, Page 265, 266: # 1, 5, 6, 11, 14, 15
    Sec.9.4, Page 272, 273: # 2, 6, 8, 11, 14, 15, 18, 19
    Sec.11.1, Page 318, 319: # 9, 10, 13, 14, 15, 16, 17, 23, 24
    Sec.11.2, Page 322, 323: # 3, 4, 5, 6, 8, 12, 14

    Evaluation Policy:

  • Weekly Quiz                   20%
  • Exam I                            25 %    March 3rd.
  • Exam II                           25 %    April 26th.
  • Final Exam                     30 %    May 6 (3:00 PM - 6:00 PM)       

    • You are expected to abide by the University's civility policy:

    "The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class."

    Cell phones, IPods, beepers and any electronic device must be turned off in class!!

    You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. Use of unauthorized aids such as cheat sheets or information stored in calculator memories, will be considered cheating. The Mathematics Department and the University strongly promote academic integrity.

    Illness Due to Flu: The H1N1 Flu Pandemic may impact classes this semester. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify me at 874-4394 or email me at bonifant@math.uri.edu of your status, and we will communicate by email or by phone. We will work together to ensure that course instruction and work is completed for the semester.

    The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view
    http://www.cdc.gov/flu/protect/habits.htm

    URI information on the H1N1 will be posted on the URI website at
    http://www.uri.edu/news/h1n1, with links to the
    http://www.cdc.gov site.

    Special Accommodations: Students who need special accommodations and who have documentation from Disability Services should make arrangements with their instructor as soon as possible. Students should contact Disability Services for Students, Office of Student Life, 330 Memorial Union, 874-2098.