If one day's assignment seems lighter than average, it's a good
idea to read ahead and start doing the next assignment, which may be
longer than average.
Unless otherwise indicated, problems are from our textbook
(Nagle, Saff, & Snider, 4th edition). It is intentional that some of
the problems assigned do not have answers in the back of the book or
solutions in a manual. An important part of learning mathematics is
learning how to figure out by yourself whether your answers are
correct.
| Date due |
Section # / problem #'s |
| F 8/25/06 |
Read the syllabus and the
web handouts
"Taking notes in a college
math class" and "What is a solution?", obtainable from the
Web.
Read Section 1.1 and do problems 1.1/ 1-16.
We did not get to
"order" or "linear vs. non-linear" in class on Wednesday, but you
should have no trouble doing these problems based on pp. 4-5 of the
book, and I will review this material on Friday.
Also, do non-book problem #1.
Note: if you have a problem viewing any of my PDF files, check your
version of Adobe Acrobat at
http://www.adobe.com/products/acrobat/ .
You may need to update (all you need is a recent version of the free
Adobe Reader).
|
| M 8/28/06 |
1.2/ 1, 3-5, 14, 15, 19.
|
| W 8/30/06 |
1.2/ 2, 10, 11, 30.
Do non-book problem #2.
Read pp. 12-14.
Read
sections 2.1 and 2.2. In your reading, make sure you understand the
discussion following Example 3 (bottom of p. 44 to top of p. 45).
|
| F 9/1/06 |
1.2/18, 23-29
2.2/1-5 (you should be able to do these just based on your reading
that was due Wednesday)
I'm about one lecture behind where I'd hoped to be. I would suggest
re-reading Section 2.2 and trying start on the assignment due
Wednesday 9/6/06. You may be able to do them based just on your
reading, and you will then have a smaller assignment over the weekend.
|
| Every Friday |
Homework discussion: Starting 9/1/06, I will hold a weekly
session on Friday, 9th period, in Little 125, for the purposes of
answering homework questions for recently assigned
homework--problems that were due that week, or, if a week was
skipped, since the last homework-discussion. I will continue
holding this session only as long as at least 10 students show up;
I will discontinue it the second time that fewer than 10 show up. (For
the purposes of this two-strikes-and-you're-out policy, today, 9/1/06,
does not count, since I did not get a room and put out this
announcement till today.) I stress again that I expect you to be
doing all your homework by the due-dates, and that these homework
sessions are intended for recent homework problems, not to help
you catch up the week before an exam. If I cancel the sessions because
there's insufficient interest (i.e. fewer than 10 attendees) when an
exam is not imminent, I will not re-institute them the week before an
exam.
|
| W 9/6/06 |
2.2/ 8, 9,
11, 13, 17, 18, 23, 27abc, 29-34. "Solve the equation" means "find
the general solution of the equation" (i.e. find all
solutions). For some of the problems in the "7-16" group, the method
I presented in class is not sufficient to find all the
solutions, so you may not be able to finish these problems completely
yet. Problem 30 of this assignment illustrates the relevant issue, but
on Wednesday we will see how to find systematically the solutions that
are missed by separating variables (these correspond to "Case (ii)" of
the analysis I started on Friday but did not complete). Save your work
on this assignment so that in the next assignment, you can fill in any
solutions you missed on this assignment.
|
| F 9/8/06 |
Go back and check whether
your general solutions, in the problems from the previous
assignment that asked for them, omitted any equilibrium solutions. In
any future problems involving separable equations, when you're asked
to find the general solution, make sure that you have indeed included
all solutions (both non-equilibrium and equilibrium).
2.2/6, 16, 22
Read Section 2.3.
2.3/1-6. If you feel comfortable with the method, try
some of the problems due Monday. The ones I would start with are numbers 7,
23 (read Example 2 on p. 52 first), 24, and 28.
|
| M 9/11/06 |
2.3/7, 8, 13-15, 17-20, 23 (read Example 2 on p. 52 first),
24, 27a, 28.
|
| Special note about Friday's problem-session |
For those of you who attended the problem-session on Friday 9/8/06:
I incorrectly wrote a formula (part of the general solution to some DE)
as 1/(Cet+1). What I should have written was
1/(Ce-t+1).
|
| W 9/13/06 |
2.3/30-33, 35. In #33, note that what you might think is
only a minor difference between the DE's in parts (a) and (b)--a
sign-change in just one term--drastically changes the nature of
the solutions. When solving differential equations, a tiny algebra
slip can make your solutions utter garbage. For this reason there is
usually no such thing as a "minor algebra error" in solving
differential equations.
Read Section 2.4. If you think you understand the method of
solving exact equations well enough, get started on the problems that
are due Friday. The best ones to start with are numbers 1-8, 27a, and 28a.
|
| F 9/15/06 |
2.4/1-8.
Based on your reading (especially the Test for Exactness on
p. 61, the Method for Solving Exact Equations on p. 63, and Examples 2
and 3), try to solve
2.4/11, 12, 16, 17, 19, 20-22, 27a, 28a, 32 (note that #22 is
the same DE as #16, so you don't have to solve a new DE, you just have
to incorporate the initial condition into your old solution). I will
be carefully going over this method in class, with examples, on
Friday, so it's okay to wait until Friday after class to start these
problems; they're really due Monday. But the more you're able to get
done by Friday, the more time you'll have to familiarize yourself with
this method and to review other material before Wednesday's exam.
Note: sometimes the simple algebraic operation of clearing fractions
can turn a non-exact equation into an exact one (cf. Example 1, p. 59).
You are responsible for being able to solve such equations.
|
| Special note |
Exam-date change: first midterm is postponed until Wednesday, Sept. 20.
This may result in other exam-dates being postponed. I'll
update you when we get closer to the originally-estimated dates.
|
| M 9/18/06 |
Complete all the problems from Section 2.4 listed above that you
haven't completed yet.
Read the online handout "A terrible
method for solving exact equations". This year, the parenthetical
"we proved it!" on the handout does not apply, since I didn't get to the
proof in class. However, you did read the proof in the book as part of
your homework.
|
| Special note |
Here is what I told a 2003 Differential Equations class after they
performed less well than they'd hoped on their first midterm. I'm
hoping that this advance warning will help you to avoid the flaws in
their study habits, exam prep, etc.
|
|
If you had any unpleasant surprises on [this] exam, please re-read
the section on prerequisites on the
class home page, and the sections on homework, workload, attendance,
and miscellany on the syllabus.
You may also want to re-read the handout "Taking notes in a college
math class".
Never try to figure out the minimum amount of work you need to do
to get the grade you want. Your goal should be to put yourself in a
position to get 100% on every exam, regardless of what subset of
fair-game material ends up being represented on the exam, and
regardless of what form the questions take. If you make this your
goal, you will learn and retain far more material, and get far better
grades.
|
| W 9/20/06 |
First mid-term exam (assignment is to study for
it). The relevant book-sections for the exam are 1.1-1.2 and 2.1-2.4.
However, bear in mind that I went into greater depth than the book on
certain topics, and anything that I covered in class or was
covered in the book or in homework is fair game for the exam.
|
| F 9/22/06 |
Read Sections 4.1 and 4.2.
|
| M 9/25/06 |
4.1/1-10. Typo correction: In #10a, 2nd line, the function
written after "B" should be "sin", not "cos".
|
| W 9/27/06 |
Review your notes.
Catch up and/or get ahead in your homework
for other classes, so that you'll have time for MAP2302 problems
once I start assigning them again next lecture.
|
| F 9/29/06 |
Check that all the operators listed on the table in Monday's class
are linear except for the squaring operator.
Do
non-book problems 3-6.
|
| M 10/2/06 |
Re-read section 4.2 and do problems 4.2/1-10, 13, 14, 17, 18,
20, 21, 22, 26.
|
|
Exam 1 is now graded! For the grade-scale, click on your
section: 6th period (12:50 -
1:40)
or
8th period (3:00 -
3:50). The linked page "list of scores" has some grade-related
statistics.
Exams will be returned at the end of
class on Monday (or, if you want to get yours earlier, you may come to
my Monday 10:30-11:30 office hour). This is the only day I will
bring your exam to class. If you are absent Monday, you will have to
see me in office hours to get your exam back. Any exams not picked up
after one week may be thrown out. I will give no grade-related
information by email, and will not respond to email asking for such
information or attempting to engage me in a grade-related
discussion. I will discuss grades, grading, and grade policy
only in person.
|
| W 10/4/06 |
4.2/ 27-33, 39, 40. Typo correction: #39 has a typo in line
5. The function multiplying
c2 should be y3(t).
Read Section 4.3.
|
| M 10/9/06 |
4.3/1, 4, 6, 7, 9-12, 17, 18, 28, 30, 38, 39
Do non-book problem 7.
|
| W 10/11/05 |
Perform the check that I assigned in class for homework: that if
c is a complex constant and h is a complex-valued
function, then (ch)'=ch'.
Read section 4.5 pp. 186-189 through the end of Example 2, excluding
Example 1. We will cover section 4.4 after we have done most or all of
section 4.5 , but most of the examples in 4.5 assume (naturally) that
you've already read 4.4; except for Example 2 they will not make
sense to you yet.
4.5/1-8.
I discovered some typographical errors in the book
problems. See the assignments for 9/25/06 and 10/4/06 for the
corrections.
|
| F 10/13/06 |
Read Section 4.4. If possible, get started on the next assignment,
which is pretty long.
I've broken it into pieces in the order in which you should attempt
it; depending on how far I get Friday, I may spread it across more than
one
assignment.
|
| M 10/16/06 |
4.4/1-8, 9-11, 14, 17.
Hint for #9: 9=9e0x
(same idea applies to #10). Hint for #14: 2=eln(2).
Based on your reading, try to do as many problems as possible
from the assignment due Wednesday 10/18, so that this material will be
less new to you when you study for the midterm.
|
| Special note |
Date for 2nd midterm: Friday, Oct. 20. Fair game for the exam
is anything in sections 4.1-4.5, plus material covered in class since
the last exam that's not in the book.
|
| W 10/18/06 |
4.4/12, 13, 15, 16, 18, 20-24, 27-32
Finish reading Section 4.5.
4.5/9-16, 17, 18, 20, 22, 23-30, 31-36.
(READ INSTRUCTIONS--problems 9-16
require no significant computation!) The box on p. 191, "Method of
Undetermined Coefficients (Revisited)" covers all the different types
of functions g for which L[y]=g can be
solved by this method; from your reading and from this box, you
should be able to do most or all of the problems from Section 4.5
even before Wednesday's lecture.
|
| F 9/20/06 |
Second mid-term exam (assignment is to study for
it).
|
| M 10/23/06 |
No homework.
|
| W 10/25/06 |
Read Sections 6.1 and 6.2.
6.2/15-18.
|
| F 10/27/06 |
Read Section 6.3. Note that the book's operator
(D-α)2 +β2 is the same as the
operator
(D-(α+βi))(D-(α-βi))
that I used in class (check this).
6.3/1-4, 11-20, 21-29. Although the
book says to use the method of undetermined coefficients for problems
1-4 and the annihilator method for problems 21-29, they are really
the same method, so it's OK to use the method of undetermined
coefficients for all these problems. The DE in #29 is third-order,
but you should have no problem factoring the characteristic
polynomial.
|
|
Exam 2 is now graded. For the grade-scale, click on your
section: 6th period (12:50 -
1:40)
or
8th period (3:00 -
3:50).
|
| M 10/30/06 |
4.6/1-18, 19 (first sentence only), 21, 25
|
| Special Notice |
Exam-date change. The third midterm will not be given on
the originally-planned date of Nov. 8. It will be given either on
Wed. Nov. 15 or Fri. Nov. 17. I will announce the exact date when
I'm sure of it. In either case, my intention is to return the graded
exams to you by Mon. Nov. 20, the last date to drop a class.
|
| W 11/1/06 |
Read sections 7.1 and 7.2.
7.2/21-28.
BOO!
|
| F 11/3/06 |
7.2/1-8, 10, 12 (note: "Use Definition 1" means "Use Definition 1", NOT the
box on p. 358 or any other
table of Laplace Transforms), 13-20, 29a-d,f,g,j.
|
| M 11/6/06 |
7.3/1-8,12,14,19,31
|
| W 11/8/06 |
7.3/9,10,25
Read the review of partial fractions in Section 7.4
(pp. 370--373). I will not have time to review this prerequisite
Calc 2 material in class, so it is important that you come to class prepared
to follow any problem I present that uses partial fractions
without asking the sort of
questions one would expect from students who have never seen (or have
completely forgotten) partial fractions.
7.4/1-10, 15, 16, 20.
|
| M 11/13/06 |
7.4/21-24, 26, 27.
Read the web handout
"Partial fractions and Laplace Transform problems"
(pdf file).
7.5/1-8,10, 15,21,22,29.
Read Section 7.6 through Example 6.
|
| Special note |
Date for 3rd midterm: Friday, Nov. 17.
|
| W 11/15/06 |
7.6/1-18
|
| F 11/17/06 |
Third mid-term exam (assignment is to study for
it). Although I've already had you read through Example 6 in Section
7.6, the exam will not cover any material beyond Example 4. You will
be tested on transforms and inverse-transforms involving
piecewise-continuous functions that are
discontinuous and/or "piecewise-defined", but you will not be
required to solve any DE's where the right-hand side is such a
function (such as in Example 5 of Section 7.6). As usual, everything
else is fair game: anything in Section 4.6, anything in Chapter 7
through Example 4 of Section 7.6, anything covered in homework, and
anything covered in class. Every problem on the Laplace-transform
sample exam is of fair-game type except for 5b.
|
| M 11/20/06 |
Read Section 7.8. We will cover Section 7.7 after Section 7.8.
|
| W 11/22/06 |
There will be class this day. The day before a holiday is
not a holiday.
7.6/21-28, 29-31, 33, 35-37, 39
|
| M 11/27/06 |
Read Sections 8.1 and 8.2. These are a review of Calc 2 material; I will
only discuss them briefly, if at all, in class, but I will expect you
to have this material at your fingertips.
Eat.
Have fun and think a lot about differential equations. Oh, excuse me,
I'm being redundant.
|
| W 11/29/06 |
7.8/1-12, 13-15, 17-19, 21-23, 30
7.7/6,9,13, 15, 20
|
| F 12/1/06 |
7.7/1-4
8.1/1,2,4,8-12. I will not spend time in class to cover Section
8.1; you should be able to do all these problems based on the
previously-assigned reading. On Friday I will rapidly review
Section 8.2 and begin to discuss Section 8.3.
Note: This week my Friday morning office-hour is cancelled so
that I may attend a UF Board of Trustees meeting. However, I
will hold our Friday 9th-period problem-discussion session (in Little
125, as usual).
|
| M 12/4/06 |
8.2/1-6 (find only the open interval of convergence; don't worry about
the endpoints),7-10,17,19,21,22,23,24,27, 31,34,37,38
(better hint: integrate the
series for 1/(1+x) and figure out what to do next).
Read Sections 8.3 and 8.4. When I test you on Section 8.4, I will
be more concerned with your knowing how to find power-series solutions
than with knowing what Theorem 5 says about their radii of
convergence.
8.3/1,3,5,7-10.
|
| W 12/6/06 |
8.3/11-14,18, 20-22,24,25,32-34
8.4/15, 20,21,23,25, 29
(in #29 be careful not to use the letter n as a
summation index since it already has an assigned, different meaning
in this problem).
|
| Material for final exam |
The final will be cumulative, with a disproportionate emphasis on
material covered since the last midterm (probably more than 25% but
less than 50%).
Sections 1.1-1.2, 2.1-2.4, 4.1-4.6, 6.2-6.3, 7.1-7.8 (minus the
portion of 7.6 from Example 7 to the end of the section), 8.1-8.3, and
the material from 8.4indicated below.
Section 8.4: you are not responsible
for the material in this section on radius of
convergence. Basically this means that what you are responsible
for in this section is the first two sentences of Theorem 5
and everything from Example 4 to the
end of the section. For exam-problems related to this section, I would
only ask you to deal with power series centered at 0 (i.e. with
x0 = 0).
Anything covered in homework, both book- and non-book problems.
Anything I said in class, whether or not it was covered in the
book or in homework.
|
Review session
and
remaining office hours |
I
will hold a question-and-answer review session (6th- and 8th-period
sections combined) on Friday Dec. 8, starting at 12:50, in our usual
classroom. I may be a few minutes late. I'm expecting the session
to last an hour, but it could be longer or shorter depending on the
questions asked.
|
|
My office hour on Friday Dec. 8 is cancelled.
For students who have been attending class regularly, I will
hold the office hours listed below. For students who have not been
attending class regularly, I have no more office hours for the rest of
the semester. The hours on Tues., Wed., and Thurs. of next week are
only for students who have their exam on Friday, and are
tentative until Monday 12/11 (they may change if students tell me they
can't make those hours, but I won't change them after Monday, and I
won't make exceptions for students who haven't told me by Monday that
they have conflicts with all the hours listed below).
Please remember that I will not communicate any
grade-related information by email; email that asks grade-related
questions will not receive responses.
Students wishing to know their final-exam scores and/or wanting
to see their graded finals should see me in my office in January.
|