Homework Assignments
MAP 2302, Sections 3226 & 3227 -- Elementary Differential Equations
Fall 2005

Exam dates and some miscellaneous items may also appear below.

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.

Read the corresponding section of the book before working the problems. Don't just read the examples, and don't just try the homework problems and refer to the text only if you get stuck.

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Date due	Section # / problem #'s
F 8/26/05	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 8/29/05	1.2/ 1-5, 14, 15, 19.
W 8/31/05	1.2/ 10, 11, 18, 23, 27, 29, 30. Do non-book problem #2. 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 9/2/05	2.2/1-5, 8, 9, 11, 13, 17-18, 23, 29, 31, 32. "Solve the equation" means "find the general solution of the equation" (i.e. find all solutions). Note to 5th-period class: I mis-wrote the last equation on the blackboard on Wednesday. What I should have written is v=g/a -Ce-at.
W 9/7/05	2.2/ 6, 16, 22, 27abc, 33, 34.
F 9/9/05	2.2/30. (I meant this to be part of the previous assignment, but entered it in the wrong place in the html file. I've adjusted the tense from future to past and adjusted some words accordingly.) As illustrated by this problem, and we observed in an example in class on 8/29/05 (revisited Wed. 9/7/05), the brain-off/brain-on method for solving separable equations (the box on p. 41) sometimes misses some solutions, namely "equilibrium solutions". Go back and check whether your general solutions, in the problems from previous Section 2.2 assignments 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). 2.3/1-6, 7, 23 (read Example 2 on p. 52 first), 24, 28. Problems 7, 24, 28 can be solved using the method of the last "Special Case" I covered in Wednesday's class.
M 9/12/05	2.3/8, 13-15, 17-20, 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 solutions utter garbage. For this reason there is usually no such thing as a "minor algebra error" in solving differential equations.
W 9/14/05	2.4/1-8, 27a, 28a. Read all of Section 2.4 in preparation for Wednesday's class. If you think you understand the method of solving exact equations well enough, get started on the problems that are due Friday.
Special note	I have to cancel my office hour on Fri. Sept. 16, and, as mentioned in class, there will not be a 9th-period homework-review session that day. (In fact I am cancelling them for the rest of the semester because of poor attendance.) Therefore my last office hour before the Mon. Sept. 19 exam will be Wed. Sept. 14, 2:50-3:50. Of course, you will also be able to ask me questions on Friday, when the entire class period will be devoted to Q&A.
F 9/16/05	2.4/11, 12, 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). 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. 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	When the sample exam handed out in class on Monday and Wednesday was actually given in 2003, the average score was 65%, a C on the scale for that exam, (I don't work out "+" scores for midterms, but the C range for that exam was 52-71). Many students were unpleasantly surprised by their scores. To help you avoid a similar unpleasant surprise, here is what I told that class after I returned their exams:
	If you had any unpleasant surprises on [this] exam, please re-read the section on pre-requisites 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.
M 9/19/05	First mid-term exam (assignment is to study for it)
W 9/21/05	no homework
F 9/23/05	Read Sections 4.1 and 4.2.
M 9/26/05	Check that all the operators listed on the table in Monday's class are linear except for the squaring operator (for the 5th period section, I wrote down the more general raising-to-nth-power operator; take n=2.)
	Do non-book problems 3-6.
W 9/28/05	4.2/1-10, 13, 14, 17, 18, 20, 21, 22, 26
F 9/30/05	4.2/ 27-33, 39, 40 4.3/1, 4, 6, 7, 9-12, 17, 18
M 10/3/05	4.3/28, 38, 39 Do non-book problem 7. You may currently be wondering why I am giving lectures that seem to have nothing to do with the homework problems in the book. The reason is that the material I've been covering in class the last two lectures, and hope to finish on Monday, is important but is not in this edition of the textbook. The book got dumbed-down between the 3rd and 4th editions, and the material I'm covering now, which appeared early in Chapter 4 in older editions, was deleted. Unfortunately I don't have a large collection of homework problems on this material, just the handful of non-book problems. Were I to wait until I'm done with the "non-book" material before assigning you homework out of 4.2 and 4.3, you'd have too much to do in too little time. However, I think that the book problems I've been assigning from 4.2 and 4.3 are pretty straightforward (with the possible exception of 4.3/38-39), given the formulas for general solutions I told you to use, and the method for solving IVPs illustrated in class today. Once we get to Section 4.4 next week, you'll see me doing many more concrete examples in class.
	Exams are graded and will be returned at the end of Monday's class. I will bring your exam to class once and only once. If you are not in class when I return exams, you will have to come to my office to pick up your exam. Any exams not picked up within a week may be thrown out, so if there is some reason you can't pick it up in that time frame, make sure you let me know. Grade scales are posted on the grade-scale pages for the 5th-period section and 6th-period section . Exam-statistics pages are linked to the grade-scale pages. The exams for the two sections were identical.
W 10/5/05	Re-do all exam problems on which you did not get a perfect score.
F 10/7/05	Classes are cancelled for Homecoming, so no homework is due. Since the doors to the math department will be locked after 11:30 a.m, I am also cancelling my Friday Oct. 7 office hour.
M 10/10/05	In class I wrote down a number of things (related to complex exponentials) that I said you should check for homework. Check all of them. 4.3/30 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. Do problems 4.5/1-8.
W 10/12/05	Read section 4.4 and do problems 4.4/1-8. Note: you will not be able to do problems 1-8 until you have read at least as far as the box at the top of p. 184.
	Corrections to previous homework problems : non-book problem 7, equation (2) had two typos in it that have now been fixed. 4.2/39 has a typo in line 5. The function multiplying c2 should be y3(t). 4.2/40: the last statement of the book's hint is wrong; there's no contradiction reached this way. Instead of dividing by exp(r3t), use the "symmetric" linear-dependence relation in Problem 39 (the displayed equation in that problem), then divide by exp(rkt), where rk is the largest of r1 r2, r3, and then take the limit as t goes to infinity. If you do this correctly, you will find that one of the constants Ci is 0. Then repeat this process to show that all the constants are zero.
F 10/14/05	4.4/9-11, 14, 17. Hint for #9 (same idea applies to #10): 9=9e0x Hint for #14: 2=eln(2). If you want to get a head-start on the next assignment, which is much heavier, try to do the problems that are due Monday based on your previously-assigned reading of Section 4.4. (I have not yet covered in class any examples of the types of problems that are due Monday; I will get to these in Friday's lecture.)
M 10/17/05	4.4/12, 13, 15, 16, 18, 20-24, 27-32
	Finish reading Section 4.5. I will be explaining this material more on Monday, but in the meantime I want you to be working problems in order to get the patterns down; you will not be allowed any formula-sheets on the upcoming midterm. 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 Monday's lecture.
Special note on midterm dates	I'm moving the date of your second midterm to Monday, Oct. 24. I intend it to cover through Section 4.6, so you may want to get a head-start reading this section. I will distribute a sample old exam either on Mon. 10/17 or Wed. 10/19. I'm also postponing your third midterm. Tentatively, the new date will be Wed. Nov. 16. I aim to have the exams graded and returned to you on Mon. Nov. 21, which is the last date you can drop a course. (Unfortunately, for the same reason, you're likely to have several other exams the same week as mine, or even the same day--another reason it's important to keep up with the homework in this class and all your others.)
W 10/19/05	4.4/19,25,26 4.5/19,21 read Section 4.6
F 10/21/05	4.6/1-18, 19 (first sentence only), 21, 25
M 10/24/05	Second mid-term exam (assignment is to study for it)
W 10/26/05	No HW.
F 10/28/05	No HW.
M 10/31/05	Read sections 6.2 and 6.3. 6.2/15-18. Read sections 7.1 and 7.2. BOO!
W 11/2/05	7.2/1-8 (note: "Use Definition 1" means "Use Definition 1", NOT a table of Laplace Transforms), 21-23,26-28, 29a-d,f,g,j.
	Exams were returned at the end of Monday's class. I bring graded exams to class once and only once. Any time you are not in class the day I return exams, you can get your exam back only by coming to my office. I do not give out any grade information by email. Any exams not picked up within a week of the day I return them in class may be thrown out, so if there is some reason you can't pick it up in that time frame, make sure you let me know. Grade scales are posted on the grade-scale pages for the 5th-period section and 6th-period section . The broken link to these pages from the class home page has also been fixed.
F 11/4/05	7.2/13-20 Read Section 7.3 and do problems 7.3/1-8,31
M 11/7/05	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 slowing down my presentation with questions about this algebra. Prepare for your next HW assignment by finding the partial-fractions decompositions of all the functions in problems 7.4/1-10, 15, 16, 20, 21-24, 26, 27. (In this HW assignment, I'm not asking you to find the inverse Laplace transforms, which we haven't discussed yet; that will be part of your next assignment. Save your answers for use in the next assignment.)
W 11/9/05	Note: my office hour Wed. 11/9 is cancelled. 7.3/9,10,25 7.4/1-10, 15, 16, 20, 21-24, 26, 27.
IMPORTANT NOTE	The date of the third midterm is contingent upon how fast I am able to get through sections 7.4, 7.5, and ideally part of 7.6. If I can't get through all of Section 7.5, and possibly if I can't get through certain material in Section 7.6, by the end of the lecture on Wed. 11/9/05, the midterm will be postponed till Fri. 11/18/05. (In this case we would cover new material on Mon. 11/14 [11/11 is a holiday] and have a review on Wed. 11/16.) Even if I give the exam on Friday, 11/18, I plan to return it to you on Mon. 11/21 since that's the last drop-day.
How to do worse and how to do better	Attendance has dropped off since the second midterm was returned, especially among students who haven't been doing well. Of course, if you're certain that you're going to drop this class, there's no point attending it, but so far nobody has actually dropped since the exam was returned.
	It's not uncommon for students to think "Hey, coming to class isn't doing me any good, so I'll just stop coming." This is a Bad Idea. In over 20 years of teaching I have not seen a single student improve his or her grade while decreasing his or her attendance. In fact, except for students who were already earning E's, the vast majority of students who decrease the frequency of their attendance haven't even maintained their grades--they've turned C's into D's, and D's into E's. Don't delude yourself! The way to improve your grade is to work more, not less. Most of this work represents time you have to put in outside of class, but part of it is learning how to get more out of your time in class. To help you with that, as part your very first homework assignment I assigned you a handout to read, "Taking notes in a college math class" (scroll up and you'll see the link). There really is some very good advice there, and I recommend you re-read it. I also remind you what I warned you about in the syllabus: keep up with homework. Doing anything less than all of the assigned homework, or not doing it on time, is another way of virtually ensuring that the grade you receive will be less than the grade you're capable of. Over the years I've also seen many students--a minority, but cumulatively a pretty good number--improve their study habits (which invariably necessitates a greater time commitment) after doing poorly on an exam or two, and pull their grades up. If you're not getting the grade you want, it's up to you which group you'll belong to: the self-deluders who say "To heck with this; I know what it takes to do well; I've never had to work that hard before and I'm not going to work that hard now; and I'll still get at least the grade I'm getting now", or the students who learn from their mistakes and say "Yes, I can do better if I try a lot harder, and I am willing to try."
M 11/14/05	Read 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.
W 11/16/05	Note: In class I mis-remembered the number of the section we are currently studying and said "7.5", when I should have said "7.6", in response to a question concerning the content of the upcoming exam. Fair game for the exam is anything in Chapter 7 through Section 7.6 Example 5 (most but not all of which I covered in Monday's lecture; the most important thing that I didn't do an example of is the method used in Example 1). This includes all material represented by the homework below. 7.6/1-10, 11-18, 29-31, 33, 35-37, 39.
F 11/18/05	Third mid-term exam. Assignment is to study for exam. Exam will cover through the portion of Section 7.6 up to and including Example 5 (this includes all of the homework from Section 7.6 assigned above).
M 11/21/05	No new homework. The midterm is now graded and will be returned Monday. The grade scales have been posted on the grade-scale pages for the 5th-period section and 6th-period section .
W 11/23/05	There will be class this day. The day before a holiday is not a holiday. 7.6/21-28 Read Section 7.8
M 11/28/05	7.8/7-12, 13-15, 17-19, 21-23, 30 Read Section 7.7. 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 11/30/05	7.8/1-6 8.1/9, 10 8.2/1-6 (find only the open interval of convergence; don't worry about the endpoints), 7,8
F 12/2/05	7.7/6,9,13, 15, 20 8.2/9,10,17,19,21,22,23,24,27, 31,34,37,38 (better hint: integrate the series for 1/(1+x) and figure out what to do next).
M 12/5/05	7.7/1-4 8.2/11-14,16
W 12/7/05	8.1/1,2,4,8,11,12 Read Section 8.3 and do problems 8.3/1,3,5,7-10,11-14,18.
due date: your final exam date	8.3/20-22,24,25,32-34 8.4/15, 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, 7.1-7.8 (minus material on the gamma function in 7.6), 8.1-8.3.
	Section 8.4, minus the material on radius of convergence. Basically this means the first two sentences of Theorem 5 (this is the theorem I stated in class on Wednesday, worded differently) 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 (5th- and 6th- period sections combined) on Friday Dec. 9, 2:00-3:00, in Little 125.
	I will hold my usual office hours through Wed. Dec. 14 (except that on Fri. 12/9 the time will be 3:15-4:15, so as not to conflict with the review session) but will have no office hours after that for the remainder of the semester. If you want to see me Mon., Tues., or Wed. of exam week but your exams conflict with my hours, let me know. 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.