Differential Equations and Matrix Algebra II

MA 222 - Sections 03 and 04

Instructor: Roger Lautzenheiser
Office: G-309
Office Phone: 877-8394
Email: Roger.Lautzenheiser@rose-hulman.edu
Home Phone: 234-7175
Office Hours: See schedule
or call for appointment (ext 8394)

 

Text: Differential Equations and Linear Algebra by C. H. Edwards and D. E. Penney

Class Description

Week 1

Monday

Work During Class: Bring your computer. We will be working with the maple file 2tank.mws from our software directory (look to the left and you will see Software; after pressing software, click on de2). NOTE: When I say to bring your computer, unless I specify that everyone needs to bring a computer, you can work as partners so only one of the pair needs to bring a computer.

Assignment for Tuesday: Nothing to hand in. However, I want you to go through the maple document (2tank.mws) again and carefully read 7.1 (skip the computing project). As you are reading, put question marks beside topics you don't understand. Come to class on Tuesday with questions!!!

Tuesday

Work During Class: No computer. However, bring your text. I want questions from your reading assignment.

Assignment 1 (due Thursday): Read 7.1 again and read 7.2.
Hand in: page 393 - 1,3,7,11,13,17; You need not hand in 24 and 26, but be able to derive the given systems; page 408 - 1,3,5,13,15

Thursday

Work During Class: Today is the day you choose whether or not you want to hand homework in for credit. Quiz 1 (you may use maple and 2tank.mws) - this will be a tank problem in which you will need to be able to set up, solve (using dsolve), and use the solutions to answer questions. After the quiz we will begin 7.3 (we may need to review chapter 6 at this time).

Assignment 2 (due Friday): Read 6.1, 6.2, and start reading 7.3.
Hand in: page 371 - 1,3,13; page 408 - 9, 19, 21, 29, 30 (you need not check the Wronskian in these).

Friday

Work During Class: No computer. Discuss diagonalization and its applications to solving systems of differential equations.

Assignment 3 (due Monday): Read 7.3.
Carefully read the diagonalization handout again. Also look at the syntax for direction fields in desys.mws.
Hand in: page 421 - Do 1 and 3 completely by hand. You can use maple to help find eigenvalues and eigenvectors in 7,9,11,13,17,19,25,27,31

Week 2

Monday

Work During Class: No computer. Please ask questions about the diagonalization handout - notice that there is a quiz over the handout on Tuesday.

Assignment 4 (due Tuesday): Hand in: page 421 - You can use maple to help find eigenvalues and eigenvectors in 15,21,23,35

Tuesday

Work During Class: No computer.. Quiz 2 over the diagonalization handout (especially the theory column) and the structure of the solution of linear systems of DEs. After the quiz, will start looking at some phase plane plots.

Assignment 5 (due Thursday): Read the "Euler Methods for Systems" subsection of 7.6 and ask questions on Thursday. Hand in the two problems on the handout given in class.

Thursday

Work During Class: No computer.. Questions over Euler Method for systems. Questions over the phase plane material. Perhaps start chapter 9.

Assignment 6 (due Friday): Hand in: page 469 - 1,5 (do only Euler's method and the comparison with the actual solution). Also use Euler's method to approximate the solution to x'' +2 x^2 = t, x(0)=1, x'(0) = -2 at t = 0.1, 0.2, and 0.3.

Friday

Work During Class: No computer. Questions and start chapter 9.

Assignment 7 (due Monday): Read 9.1. Hand in page 523 - 1-11.

Week 3

Monday

Work During Class: No computer. Quiz 3 over (1) Euler's Method for a system and (2) Phase portraits. More on chapter 9.

Assignment 8 (due Tuesday): Read 9.2.
Hand in page 523 - 21,25; page 537 - 1,3,5,7,11,13 ,19,21 (Note: discuss stability and only the types (center, spiral pts, saddle point)).

Tuesday

Work During Class: No computer. More discussion of linearization. Hand out quiz 4.

Assignment for Thursday: Study for Exam 1. Topics to review include

Thursday

Work During Class: No computer. Exam 1

Assignment for Friday: Read 9.2 again

Friday

Work During Class: No computer. Hand back exam. Questions over linearization of non-linear systems. Questions over the table in Figure 9.2.12. Discussion of predator/prey systems.

Assignment for Monday: NONE - Enjoy your holiday break.

Week 4

Monday

Work During Class: No computer. Discussion of applications in 9.3.

Assignment 9 (due Tuesday): Read 9.3. Hand in Page 551 - 1 (i.e linearize about (b/q,a/p) and show you get a center for the linearized system), 2,4,5,6,7

Tuesday

Work During Class: No computer. Questions over linearization. Perhaps start Laplace Transform.

Assignment 10 (due Thursday): Read 9.4. Hand in Page 551 - 9,10,13,15,17

Thursday

Work During Class: No computer. (Note that quiz 4 is now due Monday.) More on the Laplace Transform.

Assignment 11 (due Friday): Hand in Page 566 - 3,5,13,15

Friday

Work During Class: No computer. More on the Laplace Transform. Start discussion of the Heaviside function.

Assignment 12 (due Monday): Hand in Page 581 - 1,4,7,8,9 AND remember that quiz 4 is due.

Week 5

Monday

Work During Class: No computer. Take home group quiz 4 due. More on the Heaviside function and properties of the Laplace transform.

Assignment 13 (due Tuesday): Hand in Page 581 - 11,15,16,23,27,29,31

Tuesday

Work During Class: Quiz today - will cover (linearization, defn of Laplace transform, Heaviside function, properties of Laplace transform). After the quiz, will continue discussion of Laplace transform.

Assignment 14 (due Thursday): Hand in page 581 - 33, 39, 40. Page 593 - 1,3.

Thursday

Work During Class: More on properties of the Laplace transform. Look at ws5.mws in our software directory.

Assignment 15 (due Friday): If you haven't been reading the text, start. Also look at ws5.mws again. Hand in: Page 593 - 5,7,9,11,13

Friday

Work During Class: More on properties of the Laplace transform.

Assignment 16 (due Monday): Hand in: Page 593 - 17,19,25; page 603 - 1,3 6,7,11,13,15,27; page 624 - 1,3,5

Week 6

Monday

Work During Class: Questions over WS 6. Questions over properties of the Laplace transform.

Assignment for Tuesday: Start preparing for exam 2 by looking at previous hw and handouts. Please ask questions on Tuesday.

Tuesday

Work During Class: Questions and then intro to Dirac function.

Assignment for Thursday: Study for Exam 2. You will be allowed to use a calculator and the Laplace table, but not Maple. Topics will include

Thursday

Work During Class: Exam 2

Friday

Work During Class: Start discussion of the Dirac function.

Assignment 17 (due Monday): See hw17.mws in our software directory.

Week 7

Monday

Work During Class: Hand back exam 2. More on the Dirac function.

NOTE: I put a copy of my grade sheet without names (Grades.xls) in our software directory.
You should be able to find your line using your grades from the exams. Lines 3 through 28 are from period 7 and lines 29 - 50 are from period 8. If you can't find your line, send me an email.
The formula for your numerical grade is functional, so you may enter grades for exam 3 and the final
exam to see what your final grade will be based on what you enter. Please look over the exam, hw, and
quiz grades so far; if you see any errors, please let me know immediately.

Assignment for Tuesday: Go over exam 2. Prepare for quiz 6.

Tuesday

Work During Class: Quiz 6 - Exam # 6. After the quiz, a little more on the Dirac function and start convolution (10.4).

Assignment 18 (due Thursday): Hand in: page 614 - 1,2,3,7,8

Thursday

Work During Class: More on the convolution. Discussion of periodic functions.

Assignment 19 (due Friday): Hand in: page 614 - 9,11,13, 26(see page 609 for an explanation and an example of this type of problem).

Friday

Work During Class: Bring your computer - you will need it on Quiz 7 - Dirac and Convolution. The quiz has one by-hand DE with the Dirac function, one find-the-convolution-by hand, one salt tank with Dirac (you will need Maple here), and one spring mass with Dirac (you will need Maple here). After the quiz, I will talk a little about transfer functions.

NOTE: Take Home Quiz 8 (due Tuesday) is in our software directory. Monday, during class, is the only time that I will answer questions about quiz 8. Also if you think that you had trouble on quiz 7, I put a copy (quiz7.pdf) of the quiz along with the solutions (quiz7sol.mws) in our software directory. If you are having trouble with some of the Maple commands, please look at my solutions.

Assignment 20 (due Monday): Hand in: page 624 - 13, 19,21,25,26,27,31

NOTE: I dropped #36 from assignment 20. I also sent students an email giving some suggestions for working the problems.

Week 8

Monday

Work During Class: Questions over quiz 8 (this is the only time I will answer questions about this quiz). Just a few more minutes on the Laplace transform. Begin discussion of series - 11.1.

Assignment 21 (due Tuesday): Read 11.1. Hand in page 640 - 1,3,5 (in these problems, you need not check the radius of convergence; simply do the problems as in eg 1, page 633).

Tuesday

Work During Class: Take Home Quiz 8 is due. More on Power Series.

Assignment 22 (due Thursday): Hand in page 640 - 7 (y(0)=1), 11 (y(0)=1, y'(0)=1), 13 (y(0)=1, y'(0)=1), 21. Notice that I gave you an initial condition(s) with each of these problems (thus you will not be finding the general solution). Also don't worry about the radius of convergence or finding the recurrence relation. Start with the initial condition(s) and find a few (4 or 5) of the a's.

Thursday

Work During Class: Begin discussing handout on Fourier series.

Assignment 23 (due Friday): Read 9.1. Hand in page 599 of the FS handout - 3,7,9

Friday

Work During Class: More on FS

Assignment 24 (due Monday): Hand in page 599 of the FS handout - 12,13,15,16,23,24,26

Week 9

Monday

Work During Class: More on FS.

Assignment 25 (due Tuesday): Hand in page 607 of the FS handout - 2,9,10,19

Tuesday

Work During Class: More on FS.

Assignment for Thursday: Study for Exam 3. You will be allowed to use a calculator, the Laplace table, and one clean Maple worksheet in Maple. Topics will include

Thursday

Work During Class: Exam 3 You will be allowed to use a calculator, the Laplace table, and one clean Maple worksheet in Maple.

Friday

Work During Class: Discuss Example 2 on page 605. Start discussion of sine and cosine series.

Also hand back exam 3 (mu=79, sigma=15, 90's - 14, 80's - 12, 70 's - 10, < 70 - 12) . I put a copy of the solutions in our software directory. I also put a current copy of my grade sheet in the software directory. Note that I entered 80% for the final exam so you would see what your numerical score would be with an 80% on the final. You can change 80 to other numbers to determine what you need in order to get the grade you would like.

Assignment 26 (due Monday): Read pages 609-614 (through the end of example 1) of 9.3. Hand in page 607 - 17 (note that in (a), the period is 2, so L=1), 24 (definitely use maple to show that the coefficients agree with those given); page 619 - 2

Week 10

Monday

Work During Class: More on Sine and Cosine series.

Assignment 27 (due Tuesday): Hand in Page 619 - 3,4,9

Tuesday

Work During Class: Discussion of an application of FS to DEs.

Assignment for Thursday: Start preparing for the final

Thursday

Work During Class: Review

NOTE: I updated the grade sheet. I believe that all the hw, quiz, and exam scores, as well as the corrections that people gave me, have been entered. Please take one more look to make sure that your grades are correct.

 

Friday

Work During Class: No class. I have a conflict Friday afternoon and rather than having a substitute on the last day of class, I am canceling class. To make up for missing Friday's class, I will be in my office 5-7 pm, Monday in case you have questions.
 
 
 

FINAL EXAM  - 1 pm on Tuesday, February 25. Period 7 - G315, Period 8 - G313.