Elementary Analysis II

Winter, 2019

Lecture: MWF 9:00-9:50, 195 Anstett Hall

Instructor: Yuan Xu, Office: Deady 101, Telephone: 346-5619, e-mail: yuan@uoregon.edu .

Webpage: http://uoregon.edu/~yuan/Teaching/M317.html

Office Hours: MWF 10:00-10:50 or by appointment.

Textbook

K. Ross: Elementary Analysis: The Theorey of Calculus, 2nd ed.

Prerequisite

Math 316 or Math 315.

Course description

This is the second part of a two-courses sequence. In the first part (click the link), M316, we discussed the fundamental concepts on the limit of seqeunces, infinite series and continuuity, and emphasized on rigorous definition and proof. In the second part, we will continue the discussion on continuous functions, starting from a review of Sect. 17-18, and convering Sect. 19 ad 20; then continue to cover sequences and series of functions (Sect. 223-26), differentiation (Sect. 28-31) and integration (Sect. 32-34).

Students should be familiar with the mechanics of calculus. What this course will stress are the rigorous foundations of the subject.

Learning Outcomes

Students must be able to demonstrate an understanding of the nature of mathematical proof by proving various assertions. They should be able to not only calculate but also prove their answer for various limits. They are expected to be able to give proofs related to limit of functions, especially those related to continuity and differentiability of functions. They should be able to understand rigorous definitions of derivatives and integrals. They are expected to understand the limit of sequence of functions and convergence of infinite series of functions, and be able to use and prove uniformly convergence for sequences and series of functions. They should be able to understand the concept of integrability, understand and appreciate the Fundamental Theorem of Calculus.

Homework

There will be a homework assignment for each week. You can check the ASSIGNMENTS here. Homework will be collected each Wednesday in class on the material of the previous week. Late homework will not be accepted. Your lowest homework score will be dropped. It is very important to keep up with your homework. Start it early, do not wait until the night before you have to turn it in.

Quizzes

There will be two quizzes of 25-minutes in week 3 (Friday, Jan. 25) and week 8 (Friday, March 1).

Exams

There will be one midterm exam in Week 6 (Monday, Feb. 11). If you must miss an exam due to extraordinary circumstances, you must get my permission and schedule a make-up exam in advance. The final exam is scheduled on 10:15 Friday, March 22 at 195 Anstett Hall.

Grade

Your course grade will be based on your homework, quizzes, midterm and final.

Homework:	20%
Quiz 1:	10%
Quiz 2:	10%
Midterm Exam :	20%
Final Exam:	40%

Incomplete

Incomplete are only awarded in the Mathematics Department when two criteria have been satisfied: first, a student must have a passing grade at the time the I is assigned; secondly, some work could not be completed due to extenuating circumstances (illness, auto accident, etc.). Under no circumstances will an I be awarded as a substitute for a W, D or F/N . If you find yourself in trouble, drop the course!

Disability Service

If you are a student with a documented disability please meet with me soon to discuss your needs. If you have not already requested a notification letter from Disability Services outlining recommended accommodations, please do so as soon as possible.

Academic Misconduct

The University Student Conduct Code (available at http://dos.uoregon.edu/conduct) defines academic misconduct. Students are prohibited from committing or attempting to commit any act that constitutes academic misconduct. By way of example, students should not give or receive (or attempt to give or receive) unauthorized help on assignments or examinations without express permission from the instructor. Students should properly acknowledge and document all sources of information (e.g. quotations, paraphrases, ideas) and use only the sources and resources authorized by the instructor. If there is any question about whether an act constitutes academic misconduct, it is the students' obligation to clarify the question with the instructor before committing or attempting to commit the act.