Syllabus
Math 309 D Autumn 2009
Instructor: Michael Goff
Office: Padelford
C-406
e-mail address: mgoff@math.washington.edu
Website: www.math.washington.edu/~mgoff/m309
Office hours: Monday, 2-3, Friday 10-12
Textbook: Elementary Differential Equations and Boundary Value Problems, by
Boyce and DiPrima, Ninth Edition.
Available at the University Bookstore.
Structure: I plan to cover Chapters 7 and 10, and also a
bit of Chapter 9 if we have time.
Chapter 7 is about systems of differential equations. The first two sections of Chapter 9, if we
get there, look at some of the qualitative and geometric aspects of solutions
to differential equations. Chapter 10
covers partial differential equations, Fourier series, and boundary problems.
Math 309 is the culmination of the 307-308-309
sequence. This course pulls together
concepts from both 307 and 308, and it is part of a large field of study known
as linear analysis. This material is
used in almost all of the sciences and in different kinds of engineering. The emphasis of the course will be on
techniques for solving problems, although we will also discuss some of the
theory. We will generally avoid proofs.
Prerequisites: Math 307 and Math 308.
How to succeed in this
class:
Math 309 is a tough course, significantly harder than even Math 307 and
308. The problems tend to be long and
involved, and the class may require more time than you have spent on previous
classes. Here are the best ways to do
well.
1)
On most days, I will say which material we will cover in the following
class. Read the section ahead of
time. In lecture, I will cover the
textbook fairly closely, and I will presume that you have read it already.
2)
If you find something confusing, ask me about it as soon as you can. If you fall behind, it is much harder to
catch back up.
3)
Keep your Math 308 book and review it as necessary. We will do some review of linear algebra in
class, but you may need to review some more on your own.
4)
Make sure you review for homework and exams when solutions are available, and
if you make a mistake, work out the problem again to make sure you have it
right. You need lots of practice to
master the material.
Homework and Exams: On most weeks, there
will be a homework assignment. Homework
is due on Friday unless otherwise stated.
Exam
1 is on Friday, October 23, and I plan for it to cover Chapter 7.
Exam
2 is on Friday, November 20, and I plan for it to cover Chapter 9 (if we do any
of it) and some of Chapter 10.
The
final exam is comprehensive, but the emphasis will be on the material we cover
after the second exam.
Grading: 20% each
midterm
35% final exam
25% homework
Missing class: I will give make-up exams
only if there is a good reason for missing the scheduled class. I may ask for a note under some
circumstances. If you know in advance
that you will miss class, please let me know and we can try to make
accommodations. Homework is due at the
beginning of class on the due date. If
you are not in class that day, you can put the homework in my mailbox, which is
on the first floor of Padelford in the C Wing.
It is due by whenever I get to my mailbox after class.
List of homework: Week 1: Due Friday,
October 9
7.1:
4
7.2:
2, 4, 8, 12, 21, 24, 25
7.3:
14, 16, 19, 22, 25
7.4:
6
A
hint for 7.4, 6: Note that we are looking for a system of homogeneous linear
equations, so the form of the solution should be
x1’
= p11(t)x1 + p12(t)x2
x2’
= p21(t)x1 + p22(t)x2
The
general solution to the system of equations is 
. As a first step,
differentiate and solve for c1 and c2.
Week
2: Due Friday, October 16
7.5:
9, 14, 16, 17, 20
7.6:
7, 9, 21 (For #21, use the equation tu = eln t u)
7.7:
3, 6, 11
Week
3: Not collected
7.8:
9a, 17
7.9:
1, 4
Week
4: Due Friday, October 30
9.1:
1abc, 4abc, 7abc, 13
10.1:
2, 7
Week
5: Due Friday, November 6
10.1:
14, 18
10.2:
15, 21
Do
#15 by hand. You may do #21 by hand or
by a computer algebra system (the latter is recommended). If you use a computer, make sure you state
which program you use.
Week
7: Due Monday, November 16
10.3:
2
10.4:
15, 23
10.5:
3, 8, 10
Week
10: Due Friday, December 5
10:7:
1a, 3a, 4a, 5a, 7a, 8a
For
3 and 7, you are encouraged to use a computer for evaluating the integrals.
October
7: 7.4
October 9: 7.5 and 7.6
October 12: 7.7
October 16: 7.8
October 19: 7.9
October 26: 9.1
October 28: 10.1
October 30: 10.2
November 6: 10.3
November 9: 10.4, 10.5