Text and syllabus
Jerrold E. Marsden and Michael J. Hoffman, Elementary Classical Analysis. W. H. Freeman and Company, second edition,
1993
The course is a continuation of Math 360, and explores advanced topics in calculus. Unlike the basic freshmen and sophomore calculus courses that focus on the skill of calculation, MATH-360/361 emphasizes the theoretical aspects of the subject. Rather than teaching you how to calculate, the purpose of this course is to give you both a logical understanding and an intuitive appreciation of some key concepts, theorems, and proofs.
Possible topics include: Integrability (the Riemann Integral and its limitations); Lebesgue measure and Lebesgue integral; convergence of functions in various function spaces (Banach and Hilbert spaces); the application of function spaces in Fourier theory.
Class Meetings
Lectures: TR 10:30-12noon, DRL 4C4.
Recitations: M 6:30-8:30 PM, DRL 4C6.
Office hours
Erik van Erp (instructor): DRL 4E3, Wednesday 11 AM - 1 PM.
Pilar Herreros (TA): DRL 4C15, time to be announced
Exams
There will be two take-home exams, one during the semester,
and one "final exam". However, the "final exam" is not comprehensive: it covers the material of the second half of the course.
Both tests have equal weight in determining your final grade.
Half of your course grade is determined by your performance on homework.
Grade
Course grade = 50% Homework + 25% for each of two take-home exams.
Homework
Homework will be assigned once a week, on Wednesday or Thursday, and is due a week from Friday (eight days later).
The details of the homework policy (how, when, where to turn it in; exceptions) is set by the TA.
Final Exam
The final exam (or second mid-term) is your last assignment for this semester. Please leave your work in my mailbox in the math office no later than Wednesday December 12, 12noon.
Wed Nov 21
No homework assigments this time. Enjoy the holidays!
Thu Nov 15
Read from chapter 10 in the text book, pp.543-563.
Turn in Homework Assignment 8.
This assignment is due on Monday Nov 26, at the start of recitations.
Thu Nov 8
Read from chapter 10 in the text book, pp.543-555.
The exercises on p.551 are recommended for practice, but do not hand them in.
Turn in Homework Assignment 7.
This assignment is due on Monday Nov 19, at the start of recitations.
Thu Nov 1
No homework this week.
Thu Oct 25
The homework for this week will count as the first take-home exam.
Turn in your solutions to the problems on this Midterm Exam at the start of class on Tuesday November 6. While discussion of the problems in the test with others is allowed, the solutions you hand in should be your own work.
Thu Oct 18
Finish reading section 2.2 in the updated Lecture Notes.
Some proofs have been simplified and corrected thanks to suggestions of Tom, Christine, and Chinawat.
Turn in Homework Assignment 5.
Thu Oct 11
Read sections 1.5, 1.6, 2.1, and 2.2 in these Lecture Notes.
Turn in Homework Assignment 4.
This assignment is due on Monday Oct 22, at the start of recitations.
Thu Oct 4
Read sections 3 and 4 in these Lecture Notes.
There is a one week extension for last week's homework assignment.
In addition, do Exercise 1 from the Lecture Notes.
Thu Sep 27
Read these Lecture Notes on cellular sets.
Turn in Homework Assignment 3.
Thu Sep 20
Read sections 8.3 and 8.4. Study the proof of Lebesgue's Theorem 8.3.1 (p. 476ff).
Turn in Homework Assignment 2.
Thu Sep 13
Read sections 8.1 and 8.2. Study step 1 and step 4 in the proof of Thm 8.1.2 Darboux's Theorem and Thm 8.1.3 Riemann's Condition (p. 472ff).
Turn in Homework Assignment 1. (Note: corrected on 9/13/07, 12noon)