Homework Assignments
MAP 2302, Section 3151-- Elementary Differential Equations
Spring 2009

Homework problems and due dates (not the dates the problems are assigned) are listed below. This list, especially the due dates, will be updated frequently, usually in the late afternoon or evening the day of class or the next morning. Due dates and assignments more than one lecture ahead are estimates; in particular, due dates may be moved either forward or back, and problems not currently on the list from a given may be added later (but prior to their due dates, of course). On a given day there may be problems due from more than one section of the book.

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, Fundamentals of Differential Equations and Boundary Value Prolems, 5th 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.

Date due	Section # / problem #'s
F 1/9/09	Read the syllabus and the web handouts "Taking notes in a college math class" and "What is a solution?". Read Section 1.1 and do problems 1.1/ 1-16. 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 the Adobe Acrobat website. All you need is a recent version of the free Adobe Reader.
M 1/12/09	1.2/ 1, 3-5, 14, 15, 19. "Explicit solution" is synonymous with "solution". I will say more about the terminology "explicit solution" and "implicit solution" (which we have not used yet in class) at a later time. Note: Many of the homework assignments I give will be a lot longer than the ones I've given so far. I don't want anyone to feel after Drop/Add that he/she wasn't warned. Often, most of the book problems in a section aren't doable until we've finished covering practically the entire section, at which time I may give you a large batch to do all at once. Heed the suggestion above the assignment-chart: "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."
Correction to time of final exam	Ack! I blew it again. The final exam will be given pm Tuesday Apr. 28, but starting at 3:00 p.m., not the previously-announced time. This has now been corrected in the syllabus. (The syllabus I handed out in class has the correct date, but wrong day of the week, and wrong time of day.) Thank you, my sharp-eyed students.
W 1/14/09	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).
F 1/16/09	1.2/18, 23-29. 2.2/1-5. Class ended just before I would have gotten to define "separable", but you should be able to do these problems based just on your reading (assigned previously).
W 1/21/09	2.2/8, 9, 11, 13, 17-19, 23, 27abc, 28-31, 33, 34. "Solve the equation" means "Find the general solution of the equation".
F 1/23/09	Read Section 2.3 and do exercises 1-6.
M 1/26/09	2.3/7-9, 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. Note added 1/27/09: there was a typo (a plus-sign instead of a minus-sign) in part (b) of this problem that has now been corrected. The comment above about #33 applies here as well. Remember when I said "There's no such thing as a small algebra error in solving differential equations"? The same thing goes for typos, and I apologize and have slapped myself accordingly for this mistake (well, mentally).
W 1/28/09	In case you didn't finish the assignment that was due Monday, finish it now. See "Noted added 1/27/09". 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, keep reading through the end of Section 2.4.
F 1/30/09	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)= ...". Based on your reading (especially Theorem 2 on p. 61), do the following problems: 2.4/1-8, 27a, 28a. We did not get this far in class on Wednesday, but I want you to start practicing on this material. If you read all of Section 2.4, I encourage you to try some the problems that are due Monday.
EXAM-DATE CHANGE	Your first midterm will be on Fri. Feb. 6.
M 2/2/09	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).
W 2/4/09	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, and the last part of 41. Read The Math Commandments.
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 2/6/09	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 2/9/09	No new HW.
W 2/11/09	Read Sections 4.1 and 4.2. 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".
Grades scales & exam statistics	The grade-scales and some statistics for the first exam are now posted. If you want to see how you fared relative to your classmates, click on the "list of scores" link. 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. Of the six problems on your exam, I've given five of them before. On each of these five, your class did better than the last class that I gave the problem to. This was a very pleasant finding for me when I compared the statistics, and it's the first time I can remember it happening. Michael Phelps, Barack Obama, and now this! What a year!
F 2/13/09	Do non-book problems 4, 6, 7ab. I actually did 7ab in class, but you should re-do these for yourself.
M 2/16/09	Do non-book problem 7c. Note that there is a paragraph pertaining to problem 7 at the top of p. 2 of the document. Some of the material I'm doing now is in Chapter 6. Read pp. 342-344 through equation (14). Based on your reading (see the HW due 2/11/09) 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 2/18/09	4.2/ 27-33, 35,36. Note: for problems 27 and 35a, the answers in the back of the book are wrong.
F 2/20/09	Read Section 4.3 and do problems 4.3/1, 4, 6, 7, 9-12, 17, 18, 28. For purposes of doing these problems, the most important part of Section 4.3 is the box "Complex Conjugate Roots" on p. 181. I don't expect you to fully understand this material before I cover it in class, but in the meantime you can at least get familiar with the mechanical technique, which is all you'll need to do these assigned problems.
M 2/23/09	No new homework.
W 2/25/09	Read Sect. 4.7, pp. 207-211, up to but not including "Variation of Parameters". Do problems 4.7/23, 24ab, 25,30. Also do the first part of 24cd: use the indicated method to transform the DE with independent variable t into a constant-coefficient DE with independent variable x. (You do not have the tools yet to solve the resulting DEs for 24cd.) Do non-book problem 8. This problem was revised 2/24/09 to bring page- and exercise-numbers from the previous edition of the textbook up to date with the current edition, so if you printed the non-book problems prior to this date, you'll need to re-print (or at least re-read) problem 8.
EXAM-DATE CHANGE	Your second midterm will be on Fri. Mar. 6.
F 2/27/09	Read Section 4.4.
M 3/2/09	Read Section 4.5 through Example 2.
(slight) mistake in textbook	In the colored box on p. 193, the sentence that includes equation (15) should start "If β is not 0, then to find a particular solution ...". Similarly, in the colored box on p. 200, insert "where β is not 0", at the start of the line that's two lines above equation (14). 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).
W 3/4/09	4.4/1-8, 9 (note that -9=-9e0t), 10, 11, 13, 14, 17, 18, 25, 30 4.5/1-8, 9-16, 19-21, 25-29
F 3/6/09	Second midterm exam. (Assignment is to study for it.)
M 3/16/09	Enjoy your spring break! Grade-scale for 2nd midterm is now posted.
W 3/18/09	4.4/12, 15, 16, 19-24, 26, 27-29, 31-32 4.5/17, 18, 22, 24, 30, 31-36 ("form" of a particular solution means the sort of thing you see in the box on p. 200; in problems phrased this way you are not being asked to solve for the actual values of the undetermined coefficients) Write down a short paragraph (1-3 sentences) stating clearly the difference between an "undetermined coefficient" and an "arbitrary constant". Catch a leprechaun.
F 3/20/09	Free that leprechaun. What were you thinking? Read sections 6.1 - 6.3. (We're not done with Chapter 4 yet, but this material is relevant to what I did in class Wed.)
M 3/23/09	4.6/1, 3-18, 19 (first sentence only) 4.7/24cd, 37-44. (In all of these, assume the domain interval is {t > 0}.) Note: to apply Variation of Parameters as presented in class, you must first put the DE in "standard form", with the coefficient of the second-derivative term being 1 (so divide by the coefficient of this term, if the coefficient isn't 1 to begin with). Note that it is possible to solve all the DEs in 24cd and 37-43 either by the Cauchy-Euler substitution applied to the inhomogeneous DE, or by using Cauchy-Euler just to find a FSS for the associated homogeneous equation, and then using Variation of Parameters for the inhomogeneous DE. Both methods work. I've deliberately assigned exercises that have you solving some of these equations by one method and some by the other, so that you get used to both approaches.
W 3/25/09	Read sections 7.1 and 7.2.
F 3/27/09	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), 21-28, 29a-d,f,g,j.
M 3/30/09	7.2/13-20 Read Sections 7.3 and 7.4. When we get to 7.4 in class, I will not have time to review the method of partial fractions; I will assume you know the method when I do examples.
W 4/1/09	7.3/1-10,12,14,19,25,31
F 4/3/09	7.4/1-10,11,13,15,16,20,21-24,26,27,31 7.5/15,21,22
M 4/6/09	Third midterm exam. (Assignment is to study for it.)
W 4/8/09	Read Section 7.5. 7.5/1-8,10. To learn some shortcuts, you may want first to read the web handout "Partial fractions and Laplace Transform problems" (pdf file). Read Section 7.6 through Example 5.
F 4/10/09	7.5/29
M 4/13/09	7.6/1-10,11,12,14-18
W 4/15/09	7.6/13,29-32, 33-40. 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.
F 4/17/09	Read Section 8.2. This is related to what I covered in class on Wednesday (all of which was review of material from Calculus 2). 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". Any time the book's problems tell you to find the convergence set, find only the open interval of convergence; I don't want you to spend time trying to decide whether the series converges at the endpoints. For this class, 100% of the way we'll apply power-series ideas to solving DEs involves only the open interval of convergence; what happens at the endpoints will be irrelevant to us (unlike in MAC 2312).
Note about next week	Because of the amount of material left to cover (through at least section 8.4, possibly with some omissions), I estimate that I'm going to need to cover new material on Wed. Apr. 22, the last day of class. I'll then hold an attendance-optional review session (Q&A format, as always), on Friday Apr. 24 at our usual class time. This does have a side-benefit of putting the review two days closer to the final exam, which will take place on Tues. Apr. 28, starting at 3:00 p.m.
M 4/20/09	8.2/9,10,11-14,17-20,23,24,27,28,37. In 9-14, determine the open interval of convergence on which your formal manipulations are valid. Read sections 8.3 and 8.4.
W 4/22/09	8.3/1,3,5-10,11-14,18, 20-22,24,25, 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 ("Equation (16)" is the first un-numbered equation after Equation (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).
Review session	I'll hold a Q&A session Friday 4/24 at our usual class time in our usual room. I will not hold my morning office hour that day (I have to attend a graduate student's exam). However, I'll be in my office and available to you the period before the review. Monday I will have office hours at times posted below.
Note on sample exam	Ignore problem-part 5c. I did not cover Laplace transforms of periodic functions this year, and you're not responsible for knowing that material. You should be able to do all the other problems.
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%). You're responsible for everything in Sections 1.1-1.2, 2.1-2.4, 4.1-4.6, 7.1-7.6 (minus the portion of 7.6 from Definition 6 to the end of the section), 8.2-8.3, and the material from 8.4 indicated below. You're also responsible for 6.2 to the extent that I covered that material in class. 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). You're responsible for anything covered in homework, both book- and non-book problems. You're responsible for anything I said in class, whether or not it was covered in the book or in homework. You'll be given the same Laplace Transform table that you were given on the last midterm.
Reminder: Final exam day, time, room	Tuesday, April 28, starting at 3:00 p.m., in our usual classroom.
Office hours Mon. 4/27 and Tues. 4/28	I'll have office hours Monday 11:00 a.m.-12:00 noon and 3:00-4:00 p.m., and Tuesday 11:00 a.m.-12:00 noon. If you have exams that conflict with all these times but want to see me Monday or Tuesday, email me (groisser@math.ufl.edu) by the following times so that we can work something out: If you want to see me Monday morning, email me by Sun. 6:00 p.m. If you want to see me Monday afternoon, Tuesday morning, or early Tuesday afternoon (I will not see anyone after 1:00 p.m.) email me by Monday 11:00 a.m. No last-minute math questions at the exam!
Post-exam info	Please remember that I will not communicate any grade-related information by email; email that asks grade-related questions will not receive a response. I will get the exams scored, and your final grades computed, as quickly as I can without sacrificing carefulness. After the exams are scored, I have to set the grade-scales, enter the info into my grade-spreadsheets, check each student's grade, and send the final grades to the registrar. I know you are anxious, but all this takes time. The only way you will know that I've finished grading the finals is to see whether your course-grade has posted yet on ISIS. Any questions sent to me before then ("Are you done grading yet?", "Do you know when you'll be done grading?", etc.) will just slow down the process. Once grades have posted, students wishing to know their final-exam scores and/or wanting to see their graded finals should see me in my office. For this purpose I'll have office hours Monday 5/11/09 2:13-3:45. If can't make it to my office at that time, you may phone me during those office hours, or email me to make an in-person or telephone appointment. I will not send or discuss grades or any exam-related information by email, and will delete, without responding, any email requesting a response related to grades or exam-scores. After Monday 5/11/09, I'll have no regular office hours until the fall semester.

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