Math 231 –
Differential Equations
Fall
Semester 2009
Class 43
Fri Dec 11
Exam 3: A solutions key will be in the tray outside my office at 11:00.
Comprehensive Final Exam: on Monday at 10:30 –
12:30 in STJ-10.
** Click here for solutions to Homework 18 **
Class 42
Wed Dec 9
1. Homework 18 due Thursday (worth
20 points). Deadline is 2:00 p.m.: 14, 15, 22, 24, 29, 42, 50, 52, 58, & 64
on p. 345 ff.
Note. A solutions key to Homework 18 will be in the
tray outside my door at 2:05 tomorrow. However,
if I get these typed up, then I will place a link on this page rather than put
them in my tray.
After I pick up the solutions,
Homework 18 will not be accepted thereafter.
Also:
2. Exam 3 on the topics covered in Chapters 9 & 10 will be Friday. (After the exam on Friday, a solutions key will be in the box outside my office at 11:00).
Study the
practice problems and the problems on the solution keys and the examples in the
book.
Class 41
Mon Dec 7
1. Read
pp. 331-341. (Omit pp. 317-330 & pp.
342-344.)
2. Homework 18 due Thursday (worth
20 points). Deadline is 2:00 p.m.: 14, 15, 22, 24, 29, 42, 50, 52, 58, & 64
on p. 345 ff. (A key will be outside my
door at 2:00).
3. Exam 3 on the topics covered in
Chapters 9 & 10 will be Friday.
(After the exam on Friday, a solutions key will be in the box outside my
office at 11:00).
4. Class evaluations end on Dec 13. Note. An extra 5 points will be added to your homework grades if you email me after filling out the evaluation form.
Class 40
Fri Dec 4
1. Read
pp. 296-315.
2. Have
Table 10.1 on p. 294 memorized for Exam 3 on Friday (and for the Final on
Monday).
3. Homework 17 for
Monday: 1, 3, 6, 8, & 10 on p. 345.
Reminders:
1. Class
evaluations end on Dec 13. Note. An extra 5 points will be added to
your homework grades if you email me after filling out the evaluation form.
2. Exam 3 on the topics covered in
Chapters 9 & 10 will be on Friday, December 11. (After the exam on Friday, a solutions key
will be in the box outside my office at 11:00).
Class 39
Wed Dec 2 For Friday---
1. Read
about
2. Have
Table 10.1 on p. 294 memorized for Exam 3.
3. Homework 16 for this
Friday: 40, 68, & 76 on p. 279 f.
Reminders:
1. Class
evaluations end on Dec 13. Note. An extra 5 points will be added to
your homework grades if you email me after filling out the evaluation form.
2. Exam 3 on the topics covered in
Chapters 9 & 10 will be on Friday, December 11.
Class 38
Mon Nov 30
1. Read
Section 9.5 (Cauchy-Euler equations) & Section 9.9 (Variation of
Parameters)
2. Homework 15 (due
Wednesday): 55, 57, & 58 on p. 280.
Announcements:
1. Class
evaluations start today & end on Dec 13.
Note. An extra 5 points will
be added to your homework grades if you email me after filling out the
evaluation form.
2. Exam 3 on the topics covered in
Chapters 9 & 10 will be on Friday, December 11.
Happy Thanksgiving!
1. Read Section 9.5 (Cauchy-Euler equations).
2. Homework 15 (due Wednesday after Thanksgiving): 55, 57, & 58 on p. 280.
Class 36
Mon Nov 23
1. Read
Section 9.7 and 9.8 (Undetermined Coefficients).
2. Practice
30 & 52 on p. 278 ff.
2. Homework 14 due Wed: 29,
31, 32, 51, & 53 on p. 278 ff. [Tuesday note:
Change the right-hand side of #53 to from exp(2t) to exp(-2t)]
Class 35
Fri Nov 20
1. Read
pp. 238-246.
2. Homework 13 due Monday: 11, 12, 15, 18, & 27 on p. 278.
Class 34
Wed Nov 18
1. Homework 13 due Monday:
11, 12, 15, 18, & 27 on p. 278.
2. Read pp. 238-241.
Class 33
Mon Nov 16
1. Continue
studying pp. 224 - 242.
2. Homework 12
due Wed: 6, 10, 15, 20, & 24 on p. 278. Note (Tuesday morning note): #15 has complex
roots; so skip it for tomorrow’s homework.
Graded exams will be returned
Wednesday.
Class 32
Fri Nov 13
1. Read
pp. 224 - 242.
2. Practice 1, 2, 3, 4, 6, 7, 10, 16, & 21 on p. 278.
Graded exams will not be returned until
next Wednesday.
Class 31
Wed Nov 11
1. For
Friday, read in Chapter 10, read pp. 213 - 222.
2. Exam 2
today.
Class 30
Mon Nov 9
1. Exam 2 covering
Chapters 1-8 on Wednesday. (No
calculators)
One part of the exam will require
determining whether a differential equation is (1) separable, (2) linear, (3)
exact, or (4) none of these types
For example, see Problems 20 - 34 on
p. 211 f.
The
worksheet Classification
of ODEs & Suggested Solution Methods can help you with such problems.
·
Exam 2 Fall
2008 (Caveat. The exam on
Wednesday will not necessarily look like this.
For example, Wednesday’s exam will include Chapter 7 whereas last year’s
did not.)
2. For
Friday, read in Chapter 10, read pp. 213 - 222.
(Quadratic formula )
Class 29
Fri Nov 6
1. In Chapter 10, read pp. 213 - 222.
Reminders:
· Homework 11 due
Monday: 16 & 18 on p. 189.
· Exam 2 covering
Chapters 1-8 will be Wednesday, Nov. 11.
One part of the exam will require
determining whether a differential equation is (1) separable, (2) linear, (3)
exact, or (4) none of these types. See
Problems 20 - 34 on p. 211 f.
The
worksheet Classification
of ODEs & Suggested Solution Methods can help you with such problems.
·
Exam 2 Fall
2008 (Caveat. The exam on
Wednesday will not necessarily look like this.
For example, Wednesday’s exam will include Chapter 7 whereas last year’s
did not.)
Class 28
Wed Nov 4
1. Homework 11
due next Monday: 16 & 18 on
p. 189.
Reminder:
2. Exam 2 covering Chapters 1-8 will be
Wednesday, Nov. 11.
One part of the exam will require
determining whether a differential equation is (1) separable, (2) linear, (3)
exact, or (4) none of these types. See
Problems 20 - 34 on p. 211 f.
The
worksheet Classification
of ODEs & Suggested Solution Methods can help you with such problems.
Class 27
Mon Nov 2
1. Change in date: Exam 2
covering Chapters 1-8 will be Wednesday, Nov. 11.
2. Turn
in “Homework 10” on
Wednesday.
3. Read
about Dirac delta functions: pp. 169-180.
4. Practice 16 on p. 189 f.
Class 26
Fri Oct 30
1. As you read pp. 159-168, you may wish to use the Maple worksheet
Modeling
Abrupt Changes.
2. Homework 10 due Monday: 14, 18, 22 on p. 155 f. Also, 2, 6, 10 on p. 186 f.
Class 25
Wed Oct 28
Announcement:
1.
Turn in today’s
homework on Friday.
Three of the problems were graded on
Homework 6. Check the others yourself
using the Homework Key.
However points are deducted if a problem is
not done or where no serious attempt is made.
One paper had no name on it.
Assignment for Friday:
1. In Chapter 7, read pp. 159-168.
2. Practice
16, 20, 21 on p. 156. Also, 1, 3, 5, 7,
9 on p. 186.
3. Homework 10 is
due Monday: 14, 18, 22 on p. 155.
Also, 2, 6, 10 on p. 186.
Reminders:
Exam 2 will cover Chapters 1-8 and will be on Friday, Nov. 6.
Class 24
Mon Oct 26
1. Read pp. 135-141.
2. Links
for today’s class: Periodic table & E.
coli bacteria.
Announcements:
1. Midterm
Grades were calculated as follows: .60*[Exam 1] + .40*[ Average of Homeworks
& Quizzes]. (Homeworks 6, 7,
& 8 were not included.)
2.
Two of the problems were graded on Homework 8.
Check the other three yourself with the Homework Key.
Reminders:
1. Homework 9 is due Wednesday: 3, 4,
& 9 on p. 153 f.
2. Exam 2 will cover Chapters 1-8
and will be on Friday, Nov. 6.
** Fall Break Oct. 17 – Oct 25 **
Class 23
Fri Oct 16
1. Practice: 1, 3, 4, 7, 10 & 12 on p. 153 f.
2. Homework 9 is
due Wednesday, October 28: 3, 4, & 9
on p. 153 f.
Announcement.
1. Extra Credit (not required) is due at class time Monday, Oct. 26:
(a) Poiseuille’s law (medium difficulty): 71 on p. 47.
(b) Zyzzyvas problem (difficult) 35 on p. 212.
2. Exam 2 will cover Chapters 1-8
and will be held on Friday,
Nov. 6.
Class 22
Wed Oct 14
1. In Chapter 6, continue reading pp. 129-139.
2. Practice: 1, 3, 4, & 7 on p. 153 f.
Reminder
Homework
8 (due Friday): 22, 24, 27,
30, & 31 on p. 211 f.
Class 21
Mon Oct 12
1. In Chapter 6, read pp. 129-139.
2. Homework 8 (due
Friday): 22, 24, 27,
30, & 31 on p. 211 f.
Class 20
Fri Oct 9
1. In Chapter 8, read pp. 199-209.
2. Practice problems starting on p. 210: 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, & 19. (blue = worked in class)
Reminders:
1. Homework 7 (due Monday):
Work the 3 problems at the end of
“Total
Derivatives & Differentials”.
Staple
the Maple solutions to your pencil-and-paper solutions.
2. Graded exams will be returned Monday.
Class 19
Wed Oct 7
1. In Chapter 8, read pp. 191-198.
2. Homework 7 (due Monday):
Work all of the problems at the end of the Maple worksheet “Total
Derivatives & Differentials”.
Staple
the Maple solutions to your pencil-and-paper solutions.
3. Graded exams probably won’t be completed
until Monday.
Class 18
Mon Oct 5
Exam
1 covering Chapters 1, 2, 3, & 4.
Homework 6
is due Wednesday! See below.
Class 17
Fri Oct 2
1. Exam 1 on Monday covers Chapters 1, 2, 3, & 4.
The
following link is the first exam in the Fall Semester of 2007: Exam 1
Fall 2007. And here is last year’s
first test: Exam 1
Fall 2008.
2. Practice p. 126: 30, 31, 32, & 34.
3. Homework 6 (due next Wed): 6, 13, 21, 24, 27, 33, & 43 on
pp. 126-127.
Class 16
Wed Sept 30
1. Read pp. 103-122 in Chapter 5.
2. Practice p. 126: 1-9 (odd); 10, 12, 14, 16,
18, 23, 26, 27, & 28.
Reminder: Exam 1 will be on Monday and will cover
Chapters 1, 2, 3, & 4.
Class 15
Mon Sept 28
1. Begin reading Chapter 5.
2. Quiz 4 on Wed will be over Problems 1-7 on p. 100.
Note. You can check answers that are not in the
back of the book with the Maple worksheet Euler’s Method .
Announcement:
Pick up Homework 5 Solution Key. Your graded work will be returned Wed.
Class 14
Fri Sept 25
1. Study Chapter 4.
2. As you read Chapter 4, go through the
Maple worksheets Euler Polygonal Curves & Euler’s Method .
3. Quiz 4 on Wed will be over Problems 1-7 on p. 100.
Announcement:
Your
graded Homework 4 will be returned today.
Class 13
Wed Sept 23
1. Read Chapter 4 for Friday.
2. Homework 5 (due Friday):
Problems 10, 11, 14, & 15 on p. 87.
Announcements:
1. Pick up your graded Quiz 3.
2. Your graded Homework 4 will be returned
Friday.
Class 12
Mon Sept 21
1. Begin reading Chapter 4.
2. Practice 8 & 9 on p. 87.
3. Homework 5 (due Friday):
Problems 10 & 11 on pp. 86-87. (More will be assigned on Wed).
Announcements:
1. Pick up your graded Homework 3. Everyone began with 10 points. You lost points if you did not work #10 and
#25 correctly.
Moreover,
points were deducted if the “homework rules” were not heeded---also, if you did
not attempt a problem.
Check
the other 3 problems yourself with the Solution Key that I handed out Friday.
2. 1st Announcement: Exam 1 will be
on Monday, Oct. 5.
Class 11
Fri Sept 18
1. Read pp. 73-84. As
you read, continue to work through the worksheet: Direction Fields and Solution Curves.
2. Quiz 3 Monday on Problems 1, 2, 3, 4, & 5 on pp. 85-86.
Note. I do not have Homework 3 graded yet but
please pick up a Solution Key today.
Class 10
Wed Sept 16
1. Read pp. 67-73. As
you read, go through the worksheet: Direction Fields and Solution Curves.
Reminder:
Homework 4 (due Friday):
51, 52, 55, & 58 on p. 64. (The
solution of #55 is on p. 473, but find the differential equation from whence
the solution is derived
and
use the method of separating variables to solve the differential equation.
Also,
attach a Maple worksheet showing the solutions of 51 and 55 (with the problems
typed up as usual.)
Extra
Credit. Problem 57 (the snowplow
problem) on p. 65. (I will give no help
on an “extra credit problem” other than to clarify it.)
Class 9
Mon Sept 14
1. Practice p. 64: 46, 47, 48, 49, 53, & 56.
2. Homework 4 (due Friday): 51, 52, 55, & 58 on p.
64. (The solution of #55 is on p. 473,
but find the differential equation from whence the solution is derived and use
the method of separating variables to solve the differential equation.
Also,
attach a Maple worksheet showing the solutions of 51 and 55 (with the problems
typed up as usual.)
Extra
Credit. Problem 57 (the snowplow
problem) on p. 65. (I will give no help
on an “extra credit problem” other than to clarify it.)
Class 8
Fri Sept 11
1. Read pp. 60-62.
2. Practice
p. 63: 18, 22, 28, 31, 37, 43, 44, &
47.
3. Homework 3 (due Monday): 10, 13, 25, 35, & 36 on p. 63.
Class 7
Wed Sept 9
1. Maple Assignment #1 (10 points) is due Friday: Submit
a short Maple worksheet with a title, your name and the name of the course and
section, such as M231B, the problems typed up, and the Maple commands with the
Maple solutions of Problems 1, 2, & 3 at the end of the “acquaint2”
worksheet.
2. Read
pp. 49-60.
3. Practice p. 63: 1-9 (odd); 11, 14, 16, & 17.
Monday, September 7 (Labor Day
Class 6
Fri Sept 4
1. Go over the Maple worksheet called
“acquaint2.” Right-click on the
following hyperlink acquaint2
and “Save Target As acquaint2.mw” on the Desktop.
2. Maple Assignment #1 (10 points)
is due next Friday
(September 11):
Create
a new Maple worksheet to work the 3 exercises at the end of “acquaint.”
3. Quiz 2 next Wednesday on
Problems 49-65 on p. 44.
Class 5
Wed Sept 2
1. Practice p. 44: 49-65 (all).
2. Quiz 2 Wednesday, Sept. 9
will cover the above practice problems.
Class 4
Mon Aug 31
1. Practice problems starting on p. 44: 9, 11, 39-42
(all), 43-48 (all).
2. Quiz 1 on Wednesday
will cover Table 1.4 and the above practice problems.
Class 3
Fri Aug 28
1. Read pp. 35-42.
2.
To read an article explaining tabular integration by parts, click here.
3.
Practice p. 44: 43 & 45.
4.
Homework 2 (due
Monday): p. 43: 22, 28, 34, 38, and 47.
Class 2
Wed Aug 26
1. Read pp. 19-34.
2. Memorize
the standard integral formulas in Table 1.4 (which are the standard ones in
Calculus I & II).
3. Practice
p. 43: 1-35 (odd)
4. Homework 2 (due Monday):
p. 43: 22, 28, 34, 38, + [more to come on Friday].
Reminder:
Homework 1 (due Friday) is to turn in starting on p. 43: 6, 14, & 16.
Class 1
Mon Aug 24
1. Read the handout: Information about M231.
2. Read
the Preface and pp. 1–19.
3. Practice
p. 43: 1-7 (odd), 13, 15, 17.
4. Homework 1 (due Friday) is to turn in starting on p. 43: 6, 14, & 16.
