# Math 414 Analysis II

## Spring 2004

Instructor: David Marker
Call Number: 65733
Class Meets: 1200 MWF 317 BH
Office: 411 SEO
Office Hours: M 1:30--3:00, W 9:30--11:30
phone: (312) 996-3069
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/math414

#### Text

• S. Abbott, Understanding Analysis, Springer.
• M. Rosenlicht, Introduction to Analysis Dover.
• Quick Tour of the topology of R, Supplementary notes on the topology of the reals for Math 413-414 (pdf file).

#### Prerequisites

Grade of C or better in Math 413 Analysis I, or consent of instructor.

#### Description

A continuation of Math 413 rigorously revisiting many of the ideas and results from Calculus I and II, including:
• Integration
• Sequences of Functions
• Series and Power Series
As time permits, additional topics may include metric spaces, differential equations and Fourier series.

Here is a detailed week-to-week syllabus.

#### Problem Sets

As in all advanced mathematics courses, homework problem sets are an essential part of the course. There will be roughly 12 homework assignement. The lowest 2 problem sets will be dropped.
You may discuss homework problems with other students, but you must write up your solution independently. All proofs should be written neatly with complete gramatical sentences. Problem sets should be writen so that there is room for comments on each problem. Late homework will be accepted only in exceptional circumstances.

• There will be two midterm exams. The best of your two scores will count for 30% of your final grade. The midterm exams will be on Friday March 5 and Friday April 23
• The final exam will count for 40% of your final grade. Part of the final may be a take home exam. The final exam will be Friday May 7 at 8:00 am.
• Homework will count for 30% of your final grade. The 2 lowest homework scores will be dropped.

#### Homework Assignments

• Problem Set 1: (Due Friday 1/23) Exercises 7.2.2, 7.2.6, 7.3.4
• Problem Set 2: (Due Friday 1/30)
• Problem Set 3: (Due Friday 2/6)
• Problem Set 4: (Due Friday 2/13) [typo corrected]
• Problem Set 5: (Due Friday 2/20)
• Problem Set 6: (Due Friday 2/27)
• Problem Set 7: (Due Friday 3/12) Exercises: 2.7.5, 2.7.12, 2.7.13, 2.7.14
• Problem Set 8: (Due Friday 3/19) Exercises: 6.2.1, 6.2.4, 6.2.5, 6.2.8
• Problem Set 9: (Due Friday 4/2) Exercises: 6.2.7, 6.3.3, 6.3.4, 7.4.6 a)-c)
• Problem Set 10: (Due Friday 4/9) Exercises: 6.4.3, 6.4.7, 6.4.8, 6.5.2, 6.5.4 (NOTE: There is a typo in 6.5.4b) it should read (-R,R]).
• Problem Set 11: (Due Friday 4/16)
• Problem Set 12: (Due Friday 4/30) [revised 4/19]

#### Bonus Problems

• Bonus Problem 1: Exercise 7.5..8 (Turn in by Friday 2/13)
• Bonus Problem 2 (Turn in by Friday 2/27)
• Bonus Problem 3 (Turn in by Wednesday 3/3)
• Bonus Problem 4 Exercise 6.2.13 (Turn in by Friday 4/2)
• Bonus Problem 5 Exercises 6.2.14-6.2.16 (Turn in by Friday 4/2)