Math 441: Differential Equations

Spring 2008

Instructor: Andrea Barreiro (abarreir (at) math (dot) uiuc (dot) edu)
Office: 337 Illini Hall, Office hours T 9-10am, W 1-2pm, or by appointment.
Class Location and Time: MWF 9-9:50 am, 154 Henry Bldg.
Text: Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, 8th Edition.
This website will contain most logistical information for the course. Please check frequently to get homework assignments and announcements.

Announcements

4/29/08

The final exam will be on May 2, 7-10 pm, in our usual classroom. It will be CLOSED BOOK. The problems will be distributed roughly 30% Exam 1, 30% Exam 2, 30% Exam 3, 10% covered material from Chapter 7. I will have extra office hours Thursday and Friday 11 am - 12 noon.
We have departed slightly from the syllabus: we have covered 7.1,7.5 and 7.6. On April 30 we will cover 9.3.
SECTION COVERED ON FINAL EXAM: 2.1-2.6, 2.8, 3.1-3.8, 4.1-4.2, 5.1-5.7, 7.1, 7.5, 7.6. You will not have to execute Picard iteration on the exam (question was asked in class on April 30)

4/16/08

There are practice exams on Profs. Stimac's and Henson's websites (see below). We will go over the solutions to Prof. Henson's exam in class on Friday. Also, we will go over homework problems from 3.8 and 3.9, as those sections are covered on the exam.

4/14/08

The third exam will be in class on 4/21 (I announced this in class last week). I will have extra office hours Thursday (4/17) 11 am-12 pm.

3/31/08

Because I have a visitor on 4/1 I need to cancel my usual office hour that day. Instead I will be in Thursday (4/3) 9-10 am.

3/7/08

Practice exams: see W. Henson's website as well as those referred to earlier (J. Tyson and S. Stimac). The exam will cover 3.1-3.7 and 4.1-4.4 (so any questions about "resonance" should be considered out of scope for this exam).

2/29/08

The second exam will be in class on 3/14. It will be closed book and cover most of Chapters 3 and 4 (those parts we have covered up until then).

2/18/08

I will be travelling Tuesday and Wednesday, so my office hours will be cancelled. Instead, I will be available 2/21 9-11 am in my office to answer questions. Prof. Deville will lecture on 2/20.

2/6/08

The first exam will take place in class on 2/15. It will be a CLOSED BOOK exam. It will cover Chapter 2. To prepare, I particularly suggest going over the homework assignment questions. Also, exams from previous semesters can be found at J. Tyson's website and S. Stimac's website.

Syllabus

This course provides a rigorous introduction to the subject of ordinary differential equations. We will concentrate on the theoretical foundations of the subject, and give detailed discussions and/or proofs of the fundamental theorems. We will also discuss applications in science, engineering, and occasionally business and finance.
The topics we will cover, along with approximately how many class periods we will use to cover them, are:

Chapter 1.1-1.3: Introduction (1 lecture)
Chapter 2.1-2.6, 2.9: First-order differential equations (14 lectures)
Chapter 3, 4: n-th order equations (12 lectures)
Chapter 5: Series solutions (9 lectures)
Chapter 7: Systems of equations (2 lectures)
Chapter 9: Stability of solutions (3 lectures)

A more detailed syllabus is here. Please note that dates are approximate.

Course Requirements

There will be three exams given during the semester, and one final exam. Homework will be assigned every week and must be turned in by 4 pm on the day it is due. The distribution of the final grade will be 20% HW, 50% Exams (16.66% each) and 30% Final.

Grading and Guidelines for Exams

The approximate dates of the exams are 2/13,3/14,4/18
Each exam will be curved individually, so that you receive a GPA score for each exam in addition to your raw score.
Alternate times for the in-class exams may be arranged only for a very good reason, and only by prior arrangement. You must take the final at the scheduled time.
Exams will take places during your normal class time. No cell phones or ear phones/buds of any kind are permitted.
The final exam will take place at a time scheduled by the University. The University requires me to give you a failing grade for the course if you fail to take this exam.

Grading and Guidelines for the Homeworks

Homework must be turned in by 4 pm on its due date.
Detailed correct solutions with complete explanations are required. Handwriting should be understandable; the grader will not grade a problem if it is unreadable.
For each assignment, I may select a subset of problems that will be graded, so it is to your advantage to do every problem. If you happen to have skipped the problems that are graded that week, you will receive a 0, even if you did all the other problems!
No late homeworks are accepted. However, your two lowest grades will be dropped to allow for illness or emergency situations.
You are encouraged to work together to solve problems; however everyone should turn in their own set of solutions.

Homework Assignments

Homework number	Date due	Problems assigned	Notes
HW 1	1/25/08	1.1 (15-20), 1.2 (3,7,13), 1.3 (29,30), 2.1 (14,20,30)
HW 2	2/1/08	2.2 (4,6,21,23), 2.6 (4,10,16,24), 2.4 (4,10,22,25)
HW 3	2/8/08	2.3 (8,12,16,19), 2.5 (2,4,10,14,22,23)
HW 4	2/15/08	2.8 (1,2,4abc,6abc,13,14)	For (4) and (6), you can do (b) by hand.
HW 5	2/29/08	3.1 (6,14,18,20), 3.2 (3,6,12,18,27), 3.3 (2,4,10,17,22)
HW 6	3/7/08	4.1 (6,8,12,20abc), 3.4 (4,10,18,22), 3.5 (8,12,16,24)
HW 7	3/14/08	3.6 (10,18), 3.7 (4,16,21), 4.3 (6,13,15), 4.4 (2,7)
HW 8	4/4/08	3.8 (13,14,26), 3.9(6,8,12), 5.2(8,14,20)
HW 9	4/11/08	5.3 (6,8,10,15), 5.4 (4,6,16,20), 5.5 (6,8,21)	For 5.3 (15), you must explain fully - it is not sufficient to repeat the statement in the back of the text
HW 10	4/18/07	5.6 (8,16), 5.7 (8,14,20), 5.8 (9abc)
Chapter 7	Practice only	7.1 (2,12), 7.5 (2,4,16,24,25), 7.6 (2,6,28)	For more pictures of phase planes, see Section 9.1 (Cases 1,2,4)

Other Resources

Additional Tutoring

Websites, etc

Mathworld is an online encyclopedia of mathematics which I have found very helpful over the years. You can often get formulas and definitions in an accessible way here.