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 |
| M 8/27/07 |
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 Monday.
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).
|
| W 8/29/07 |
1.2/ 1, 3-5, 14, 15, 19. |
| F 9/1/07 |
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).
|
| W 9/5/07 |
1.2/18, 23-29.
2.2/1-5, 8, 9, 11, 13, 17, 18, 23, 28-31. For problems in the
7-16 group and the 17-26 group, use the method that I used in
class for the example "dy/dx = xy".
However, remember that "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 that I used in the above example 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. Save your work on this assignment so
that in the next assignment, you can fill in any solutions you missed
the first time through.
|
| Every Friday |
Homework discussion: Starting 9/7/06, I will hold a weekly
session on Friday, 9th period, in Little 201, 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. Attendance is optional;
however I will continue holding this session only as long as at
least 10 students show up (out of the 63 in my two sections put
together, not 10 for each section); I will discontinue it the second
time that fewer than 10 show up. 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.
|
| F 9/7/07 |
Re-examine your work on problems 2.2/8, 9, 11, 13, 17, 18, 23. See
if you really found all solutions; add to your final answers
any solutions that you previously missed.
2.2/27abc, 32-34.
Read Section 2.3.
|
| M 9/10/07 |
2.2/19. (This should really have been part of the last assignment.)
I'm giving you very little HW this weekend, but there will be a lot
due Wednesday and Friday. Budget your time by trying to get ahead in
your other courses over the weekend so that you'll have more time for
DE homework Monday and Tuesday, or try to use what you learned from
reading Section 2.3 to get a head-start on the HW from that section
due Wednesday.
|
| W 9/12/07 |
2.3/1-6, 7-9, 13-15, 17-20, 22, 23 (read Example 2 on p. 52 first),
24, 27a, 28, 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 answers utter garbage. For this reason there is
usually no such thing as a "minor algebra error" in solving
differential equations.
Do non-book problem #3. (This
list of problems was updated 9/10/07, so don't go by what you may have
printed out
earlier.)
|
| F 9/14/07 |
2.2/6, 16, 22. In #22, note that although the differential
equation doesn't specify which variable is (in)dependent, the
initial condition does. Thus your goal in #22 is to produce an
explicit solution "y(x)= ...".
Read Section 2.4 through at least the top of p. 62 (the
sentence that ends "... do not meet the compatibility conditions.").
If you want to get a head-start on the next assignment or get a
preview of what we'll be doing in class Friday, keep reading through
the end of Section 2.4.
2.4/1-8, 27a, 28a. (Use Theorem 2 on p. 61 to decide exactness.)
If you read all of Section 2.4, I encourage you to try some the problems
that are due Monday.
|
| M 9/17/07 |
Read the rest of Section 2.4.
Read the
online handout "A terrible
method for solving exact equations". The parenthetical "we proved
it!" on the handout does not yet apply, since I haven't yet done the
proof in class. However, you did read the proof in the book as part of
your homework.
2.4/11, 12, 14, 16, 17, 19, 20-22, 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).
|
| EXAM-DATE
CHANGE | The first midterm will be given on Fri. Sept. 21.
|
| W 9/19/07 |
No new
homework; start studying for Friday's exam. If you have done
all your homework (and I don't mean "almost all"), you should
be able to do all the review problems on pp. 81-82 except #s 9,
11, 12, 15, 18, 19, 22, 25, 27, 28, 29, 32, 35, 37.
|
| 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
those students' 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.
|
| F 9/21/07 |
First midterm 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 there were topics covered in homework that I did not
discuss in class. Anything that I covered in class or
was covered in the book or in homework is fair game for the exam.
|
| M 9/24/07 |
Read Sections 4.1 and 4.2. |
| W 9/26/07 |
4.1/1-10. Typo correction: In #10a, 2nd line, and in #10d, 2nd line,
the function
written after "B" should be "sin", not "cos".
|
| F 9/28/07 |
Check that all the operators listed on the table in Wednesday's class
are linear except for the squaring operator.
Do
non-book problems 4, 6, 7ab.
|
| Grades scales & exam statistics |
The grade-scales and some statistics for the first exam are now posted
for the 6th-period
and 7th-period
sections. If you want to see how you fared relative to your
classmates, click on the "list of scores" link your section's page
(or the other section's if you want to compare). On the
list-of-scores page, the grouping by first digit effectively
gives a histogram of the scores (with 10-point bins), since most
scores have two digits and therefore take the same horizontal space.
|
| M 10/1/07 |
Do
non-book problems 5, 7c. Note
that there is a paragraph pertaining to problem 7 at the top of
p. 2 of the document.
Based on your reading (see the HW due 9/24/07) do the following
problems: 4.2/1-10, 13, 14, 17, 18,
20, 21, 22, 26. Your answer to 21(b) should be the same as what you
would have found by the "integrating factor" method.
|
| W 10/3/07 |
4.2/ 27-33, 39, 40. Typo correction: #39 has a typo in line
5. The function multiplying
c2 should be y3(t).
I know that this material looks nothing like what I've focused on in
class for the last two lectures. As I mentioned, I'm covering
important material that used to occupy two sections of the book that
were deleted in the last revision. By the end of the next lecture, I
should be mostly caught up with what I've assigned from Section 4.2.
Read Section 4.3.
|
| F 10/5/07 |
Based on your reading, do problems 4.3/1, 4, 6, 7, 9-12, 17, 18, 28.
|
| M 10/8/07 |
4.3/ 30, 38, 39.
Do non-book problem 8. This,
and problems 38-39 in the book, fall into the "semi-easy" category I
mentioned in class (DE's for which a clever change-of-variable(s) turns a
nonconstant-coefficient DE into a constant-coefficient DE in the new
variable(s)).
|
| W 10/10/05 |
Complete the steps, started in class, to check that if r
is a complex constant, then d(ert)/dt
= r ert.
Show 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.
|
| F 10/12/07 |
Read Section 4.4.
4.4/9-11, 14.
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 Monday 10/15, so that this material will be
less new to you when you study for the midterm.
|
| EXAM-DATE
CHANGE | The second midterm will be given on Wed. Oct. 17.
|
| (slight) mistake in
textbook | In the colored box on p. 184, insert "and
β is not 0" before the period. Similarly, in the
colored box on p. 191, insert "and β is not 0" before the
last comma. In both cases, "β = 0" puts you in the situation
of the top half the box (with α =
r), in which case it is possible to have s=2.
I don't like the book's separation of the "no sine or cosine
involved" and "sine and/or cosine involved" cases. Both cases are part
of the same master formula. The book's approach obscures this
by putting the "β = 0" case separately, and using a different
letter in the exponent when β = 0 (i.e. using r instead of
α when β = 0).
|
| M 10/15/07 |
4.4/1-8, 12, 13, 15-18, 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 (but see the "(slight) mistake in textbook"
warning above).
|
| W 10/17/07 |
Second midterm exam (assignment is to study for it).
|
| F 10/19/07 |
Read sections 6.1 and 6.2. (We're not done with Chapter 4 yet,
but this material is relevant to Chapter 4.)
|
| Grades scales & exam statistics |
The grade-scales and some statistics for the second exam are now posted
for the 6th-period
and 7th-period
sections.
|
| M 10/22/07 |
6.1/1-6,29
|
| W 10/24/07 |
6.2/15-18.
6.2/1-14. I said in class that the only higher-order operators we'll
be using will come to us in factored form. That's true of the ones
I'll use in class and (probably) on exams, but isn't true in this
group of problems. However, any time you're able find a root
r1 of an nth degree polynomial
Pn(r), the quantity r-r1
is a factor of Pn(r)--
i.e. Pn(r) = (r-r1)
Qn-1(r) for some polynomial
Qn-1 of degree n-1--and you can find the
quotient polynomial Qn-1(r) by long division
of polynomials or by synthetic division, at least one of which you
should have learned in high school. When n=3, you can then
always factor the quadratic polynomial Q2(r),
giving you a complete factorization of P3(r).
The author has made problems 1-14 doable by giving polynomials
that have an easy root to find. In #1, 0 is a
characteristic root. In problems 2-10 and 12, either 1 or
-1 is a characteristic root. In problem 11, you may see the
factorization fourth-degree characteristic polynomial just from your
familiarity with binomial expansions; if not, check whether 1
or -1 is a root (one of them turns out to be), then divide the
fourth-degree polyomial by r-1 if 1 is a root or by
r+1 if -1 is a root, and repeat the process for third-degree
quotient polynomial that you get. In problem 13, you should be able to
figure out what to do because only even powers of r appears in
the characteristic polynomial. In #14, the author's hint gives you a
pair of non-real conjugate roots, hence two linear factors that you
can multiply together to get a real quadratic polynomial. Divide the
characteristic polynomial by this polynomial, yielding another
quadratic polynomial as quotient, and take it from there.
|
| F 10/26/07 | 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've used in class, with α+βi =
r1.
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.
|
| M 10/29/07 |
Read Section 4.6
|
| W 10/31/07 |
BOO!
4.6/1-18, 19 (first sentence only), 21, 25.
|
| M 11/5/07 |
Read sections 7.1 and 7.2.
7.2/21-28.
|
| W 11/7/07 |
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.
|
| EXAM-DATE
CHANGE | The third midterm will be given on Fri. Nov. 16.
I will still return the graded exams on Mon. Nov. 19 (barring serious
illness, etc.), so that students considering dropping the class will
have this information in time to drop.
|
| F 11/9/07 |
7.3/1-8,12,14,19,31
Read Section 7.4. Part of this is a review of partial fractions
(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.
Read Section 7.5.
|
| W 11/14/07 |
7.3/9,10,25
7.4/1-10, 15, 16, 20, 21-24, 26, 27.
7.5/1-8,10, 15,21,22,29. To learn some shortcuts, you may want
first to read the web handout "Partial fractions and Laplace
Transform problems"
(pdf file), but I'm not officially assigning this till after the
exam.
|
| minor corrections to syllabus |
The syllabus that I originally handed out had two minor errors
relating to the 7th-period (1:55-2:45) section: (1) near the top of
the syllabus, I wrote "8th period" instead of "7th period"; and (2) in
the paragraph about the final exam, I wrote the wrong section number
(3615) instead of the correct 5010. None of this affects anyone in any
material way; the date and time of the final exam are the same as
originally written. But if you printed out a copy of the syllabus you
may want to fix these mistakes, or view/print the corrected syllabus.
|
| office hours Thurs. Nov. 15 |
I'll have office hours, just for my MAP 2302 students, Thursday
Nov. 15, 2:00-3:30. I'm making this one-time exception to my
no-Thursday-office-hours rule in view of the compressed week and
Friday's exam.
|
| F 11/16/07 |
Third midterm exam (assignment is to study for it).
|
| M 11/19/07 |
Read the web handout
"Partial fractions and Laplace Transform problems"
(pdf file).
Read Section 7.6.
|
| Grades scales & exam statistics |
The grade-scales and some statistics for the third exam are now posted
for the 6th-period
and 7th-period
sections.
|
| W 11/21/07 |
There will be class this day. The day before a holiday is
not a holiday.
7.6/1-4,6,8,10,11,12,14-18
|
| M 11/26/07 | Re-read
the material in Section 7.6 on periodic functions (bottom of p. 390
through Example 6 on p. 392). I did not get to go over this in class,
but the book's coverage is straightforward, and you will be
responsible for this material. However, you will not be responsible
for the portion of Section 7.6 beyond Example 6.
7.6/5,7,9,13,21-28, 29-31, 33, 35-37, 39. For all the problems in
which you solve an IVP, write the final answer in "tabular form". (For
those of you who missed class, by "tabular form" I mean an expression
like the one given in Example 1, equation (3), for the function
f. I.e. do not leave your final answer in the form
that's at the end of Example 1, after you've inverse-transformed
Y(s). The unit step-functions should be viewed as convenient
gadgets to use in intermediate steps to work through a problem
efficiently.)
Read Section 8.1.
|
| W 11/28/07 |
Read Section 8.2. This is related to what I covered in class on
Monday (all of which was review of material from Calculus
2). Although I've already had you read Section 8.1, in class it will
be more efficient for me to cover 8.2 first.
8.2/1-6,7,8. Note: "convergence set" in the book is what I
initially called "domain of convergence" and, later, "interval of
convergence". In problems 1-6, find only the open interval of
convergence; don't worry about the endpoints.
|
| F 11/30/07 |
8.2/9,10,11-14,17,19,20,21,22,23,24,27. In all these problems, treat
the power series as formal power series; on Friday I will state a
theorem that justifies this.
8.1/1,2,4,8-12. (I have not covered this material in class yet, but you
should be able to do these problems based on your reading. I will
cover some of this material briefly in class on Friday.)
Read Sections 8.3 and 8.4.
|
| M 12/3/07 |
8.2/31,34,37,38
(better hint: integrate the
series for 1/(1+x) and figure out what to do next).
8.3/1,3,5,7-10,11-14,18, 20-22,24,25,33. I realize these will be
challenging for you to do before I've done a single example in class,
but I still want you to get started on these right away so you can get
as much practice as possible before the final. I will do
examples (and hardly any theoretical stuff) on Monday.
|
| W 12/5/07 |
8.3/32,34. In #34 note that n is not a summation index; it
has a different meaning in this problem. This problem can be done
without using "Σ-notation"; you shouldn't need a summation index.
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). Note:
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.
|
| 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, 7.1-7.6 (minus the
portion of 7.6 from Example 7 to the end of the section), 8.1-8.3, and
the material from 8.4 indicated 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 | I
will hold a question-and-answer review session (6th- and 7th-period
sections combined) Sunday starting at 2:30 p.m. in the location I
announced in class (if you were not there, ask a classmate for
directions).
|
|
Viewing and/or picking
up graded exam |
The final exams are now graded.
Please remember that I will not communicate any
grade-related information by email; email that asks grade-related
questions will not receive a response. Students wishing to know their
final-exam scores and/or wanting to see their graded finals should see
me in my office in January.
Once I know my January office hours, I will post them on my
schedule
page.
|
|