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
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!!!
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
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).
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
Assignment 4 (due Tuesday): Hand in: page 421 - You can use maple to help find eigenvalues and eigenvectors in 15,21,23,35
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.
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.
Assignment 7 (due Monday): Read 9.1. Hand in page 523 - 1-11.
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)).
Assignment for Thursday: Study for Exam 1. Topics to review include
Assignment for Friday: Read 9.2 again
Assignment for Monday: NONE - Enjoy your holiday break.
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
Assignment 10 (due Thursday): Read 9.4. Hand in Page 551 - 9,10,13,15,17
Assignment 11 (due Friday): Hand in Page 566 - 3,5,13,15
Assignment 12 (due Monday): Hand in Page 581 - 1,4,7,8,9 AND remember that quiz 4 is due.
Assignment 13 (due Tuesday): Hand in Page 581 - 11,15,16,23,27,29,31
Assignment 14 (due Thursday): Hand in page 581 - 33, 39, 40. Page 593 - 1,3.
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
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
Assignment for Tuesday: Start preparing for exam 2 by looking at previous hw and handouts. Please ask questions on Tuesday.
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
Assignment 17 (due Monday): See hw17.mws in our software directory.
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.
Assignment 18 (due Thursday): Hand in: page 614 - 1,2,3,7,8
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).
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.
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).
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.
Assignment 23 (due Friday): Read 9.1. Hand in page 599 of the FS handout - 3,7,9
Assignment 24 (due Monday): Hand in page 599 of the FS handout - 12,13,15,16,23,24,26
Assignment 25 (due Tuesday): Hand in page 607 of the FS handout - 2,9,10,19
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
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
Assignment 27 (due Tuesday): Hand in Page 619 - 3,4,9
Assignment for Thursday: Start preparing for the final
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.
FINAL EXAM - 1 pm on Tuesday, February 25. Period 7 - G315, Period 8 - G313.