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Homework Assignments
MAP 2302 Section 4219 (18286) — Honors Elementary Differential Equations
Spring 2026

Last updated Thu Jan 22 02:16 EST 2026
Note the "last updated" line above. It will always be here to help you tell quickly whether this page has been updated since you last checked it.

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 a few hours after class or later that night. Assignments with due-dates later than the next lecture are estimates. In particular, problems or reading not currently listed for a future assignment may be added by the time that assignment is finalized, and due dates for particular exercises, reading, or entire assignments, may end up being moved either forward or back (but not moved back to an assignment whose due-date has already passed). Note that on any given due-date there may be problems due from more than one section of the book.
It is critical that you keep up with the homework daily. Far too much homework will be assigned for you to catch up after a several-day lapse, even if your past experience makes you think that you'll be able to do this. I cannot stress this strongly enough. Students who do not keep up with the homework frequently receive D's or worse (or drop the class to avoid receiving such a grade). Every time I teach this class, there are students who make the mistake of thinking that this advice does not apply to them. No matter how good a student you are, or what your past experiences have been, this advice applies to YOU. Yes, YOU.
A great many students don't do as well as they'd hoped, for reasons that can be chalked up to not following their instructors' best advice from the start. Much of my advice (and the book's) will require more time, and more consistent effort, than you're used to putting into your classes. It's easy to dig yourself into a hole by thinking, "I've never had to work after every single class, or put in as many hours as following advice like this would take, and I've always done well. And the same goes for my friends. So I'll just continue to approach my math classes the way I've always done." By the time a student realizes that this plan isn't working, and asks his or her professor "What can I do to improve?" it's usually too late to make a big difference.
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 (if posted), which may be longer than average. (Or use the opportunity to get ahead in your other classes, so that you'll have more time available when I do give you a longer assignment.)
Unless otherwise indicated, problems are from our textbook (Nagle, Saff, & Snider) 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.

In the table below, "NSS" stands for our textbook. Exercises are from NSS unless otherwise specified.

Date due Section # / problem #'s

W 1/14/26
Read the class home page and syllabus webpages.
Go to the Miscellaneous Handouts page (linked to the class home page) and read the web handouts "Taking and Using Notes in a College Math Class," "Sets and Functions,", and "What is a solution?"
Never treat any reading portion of any assignment as optional, or as something you're sure you already know, or as something you can postpone (unless I tell you otherwise)! I can pretty much guarantee that every one of my handouts has something in it that you don't know, no matter how low-level the handout may appear to be at first.

Read Section 1.1 and do problems 1.1/ 1–16. Since not everyone may have access to the textbook yet, here is a scan of the first 15 pages (Sections 1.1–1.2, including all the exercises).

Do non-book problem 1. (This link takes you to a page with all the non-book problems that I expect to assign eventually; your current assignment includes only the first of these problems.)
In my notes on first-order ODEs (also linked to the Miscellaneous Handouts page), read the first three paragraphs of the introduction, all of Section 3.1, and Section 3.2.1 through Definition 3.1. In all readings I assign from these notes, you should skip anything labeled "Note(s) to instructors".
   Whenever I update these notes (whether substantively or just to fix typos), I update the version-date line on p. 1. Each time you're going to look at the notes, re-load them to make sure that you're looking at the latest version.

F 1/16/26

1.2/ 1, 3–6, 17, 19–22.
Whenever you see the term "explicit solution" in the book, you should (mentally) delete the word "explicit". (Until the third author was added to later editions of the textbook, what NSS now calls an explicit solution is exactly what it had previously called, simply and correctly, a solution.. The authors tried to "improve" the completely standard meaning of "solution of a DE". They did not succeed. See Notes on some book problems for additional corrections to the wording of several of the Section 1.2 problems.
    In #17, don't worry if you're unsure what "one-parameter family of solutions" means; I don't address it till Section 3.2.4 of my notes (and you don't need to know what it means to do the exercise). If you roughly understand the terminology now, great; if not, make a note to yourself to re-read this problem once we've covered that terminology. The book uses the terminology incorrectly in many places, but the usage in 1.2/17 is correct.
Note: The exercise portions of many (probably most) of your homework assignments will be a lot more time-consuming than in the assignments to date; I want to give you fair warning of this before the end of Drop/Add.     However, since my posted notes are only on first-order ODEs, the reading portions of the assignments will become much lighter once we're finished with first-order equations (which will take the first month or so of the semester).
In my notes, read from where you left off in the last assignment through Example 3.11 (p. 15).
Make sure you are keeping up with the reading as I assign it (i.e. if the assignment with due-date X says "Read up through [this item]," then read at least that far by date X), even if it seems to be ahead of, or not connected to, what I've covered in class yet. There isn't enough time to cover everything in my notes in class—among other things, my notes incorporate a lot of material that should have been included in your prerequisite courses, or even in high school, but probably wasn't—and if you wait until you think my class lectures have fully prepared you for a given reading assignment, you'll have far too much to read than you can possible absorb in a few days. Setting aside (only) one day a week as your "differential equations day" will not serve you well in this course.
    You may not understand everything the first time you read it. That's OK. Your brain needs time to process new concepts, and a lot of that processing takes place unconsciously. Ever wake up and suddenly understand something that you didn't understand the day before?
Read the handout "Sets and Functions" posted on the Miscellaneous Handouts page. This part of the assignment is being posted late, so you may not be able to get it done on time. If that's the case, add it to the next assignment.

W 1/21/26
If you did not see the final addition to the previous assignment in time to have done it already, read the handout "Sets and Functions" posted on the Miscellaneous Handouts page.
In the textbook, read the first page of Section 2.2, minus the last sentence. (We will discuss how to solve separable equations after we've finished discussing linear equations, the topic of Section 2.3. The only reason I'm having you read the first page of Section 2.2 now is so that you can do the first few exercises of Section 2.3. But as a "bonus", you'll also be able to do the exercises in Section 2.2 assigned below.)
2.2/ 1–4, 6
2.3/ 1–6
In my notes, read from where you left off in the last assignment through the one-sentence paragraph after Definition 3.19.

F 1/23/26
In Section 2.3 of the book, read up through p. 50, but mentally make some modifications:
Replace the book's transition from equation (6) to equation (7) by the following fact: \(\mu'/\mu =\frac{d}{dx} \ln |\mu|.\) (The book's reference to separable equations is unnecessary, and does not lead directly to equation (7); it leads to a similar equation but with \(|\mu(x)|\) on the left-hand side. In class, I'll go over why we can get rid of the absolute-value symbols in this setting (finding an integrating factor for a linear DE). Equation (7) itself is fine, modulo the meaning of indefinite-integral notation; it's only the book's derivation that has problems.)

Whenever you see an indefinite integral in the book, e.g. \(\int f(x)\, dx,\) the meaning is my "\(\int_{\rm spec} f(x)\, dx\)" (my notation for one specific antiderivative of \(f\)). I'll say more on Friday about about notation for indefinite integrals. For a preview (or, later, a review) of what I'll be saying about that, go to my Spring 2024 homework page, locate the assignment that was due 1/19/24, and in the first bullet-point, read from the beginning of the second sentence ("Remember ...") to the end of the smaller-font green text (in the "sub-bullet" after the word "Note").

In my notes, read from where you left off in the last assignment through the end of Section 3.2.4 (the middle of p. 27). On Fri. 1/23 we'll cover the method you're reading about on pp. 48–50.
If you want to read more examples before next class, it's okay to look at Section 2.3's Examples 1–3, but be warned: Examples 1 and 2 have some extremely poor writing that you probably won't realize is poor, and that reinforces certain bad habits that most students have but that few are aware of. (Example 3 is better written, but shouldn't be read before the other two.) Specific problems with Example 2 (one of which also occurs in Example 1) are discussed in the same Spring 2024 assignment mentioned above. The most pervasive of these is the one in last small-font paragraph in that assignment.
Feel free to get a head-start on the exercises in the next assignment, based on what you've read in Section 2.3; this will help you finish that (much longer) assignment on time.

M 1/26/26
2.3/ 7–9, 12–15 (note which variable is which in #13!), 17–20
   When you apply the integrating-factor method don't forget the first step: writing the equation in "standard linear form", equation (15) in the book. (If the original DE had an \(a_1(x)\) multiplying \(\frac{dy}{dx}\) — even a constant function other than 1—you have to divide through by \(a_1(x)\) before you can use the formula for \(\mu(x)\) in the box on p. 50; otherwise the method doesn't work.) Be especially careful to identify the function \(P\) correctly; its sign is very important. For example, in 2.3/17, \(P(x)= -\frac{1}{x}\), not just \(\frac{1}{x}\).

2.3 (continued)/ 22, 23, 25a, 27a, 28, 31, 33, 35
See my Spring 2024 homework page, assignment due 1/22/24, for corrections to some of the Section 2.3 exercises. Also, in that same assignment read the three paragraphs at the bottom of the assignment. (The reason I'm not simply recopying such items into this semester's homework page is that some of my 2023-2024 students said that, although my comments and corrections were intended to be helpful, they made the look of those assignments overwhelming.)
2.2/ 34. Although this exercise is in the section on "Separable Equations" (which we haven't discussed yet), the DE happens to be linear as well as separable, so you're equipped to solve it. For solving this equation, the "linear equations method" is actually simpler than—I would even say better than—the (not yet discussed) "separable equations method". (The same is true of Section 2.1's equation (1), which the book solves by the "separable equations method"—and makes two mistakes in the sentence containing equation (4). This is why I did not assign you to read Section 2.1.)

Do non-book problem 2.

In my notes, read from the beginning of Section 3.2.5 (p. 27) through the end of Definition 3.23 (p. 33), plus the paragraph after that definition. (All of this is needed for a proper understanding of the word "determines" in the book's Definition 2 in its Section 1.2! [I still haven't defined "implicit solution of a DE" yet; the above reading is needed just to understand the single word "determines" in that definition.] This is one of the biggest reasons I didn't assign you to read Section 1.2.) Then do the exercise that's shortly after Definition 3.23 in my notes.

W 1/28/26

F 1/30/26

M 2/2/26

W 2/4/26

F 2/6/26

M 2/9/26

W 2/11/26

F 2/13/26

M 2/16/26

W 2/18/26

F 2/20/26

M 2/23/26

W 2/25/26

F 2/27/26

M 3/2/26

W 3/4/26

M 3/6/26

M 3/9/26

W 3/11/26

F 3/13/26

M 3/23/26

W 3/25/26

F 3/27/26

F 3/29/26

W 4/1/26

F 4/3/26

M 4/6/26

W 4/8/26

F 4/10/26

M 4/13/26

W 4/15/26

F 4/17/26

M 4/20/26

W 4/22/26

Date due	Section # / problem #'s
W 1/14/26	Read the class home page and syllabus webpages. Go to the Miscellaneous Handouts page (linked to the class home page) and read the web handouts "Taking and Using Notes in a College Math Class," "Sets and Functions,", and "What is a solution?" *Never treat any reading* portion of any assignment as optional, or as something you're sure you already know, or as something you can postpone (unless I tell you otherwise)! I can pretty much guarantee that every one of my handouts has something in it that you don't know, no matter how low-level the handout may appear to be at first. Read Section 1.1 and do problems 1.1/ 1–16. Since not everyone may have access to the textbook yet, here is a scan of the first 15 pages (Sections 1.1–1.2, including all the exercises). Do non-book problem 1. (This link takes you to a page with all the non-book problems that I expect to assign eventually; your current assignment includes only the first of these problems.) In my notes on first-order ODEs (also linked to the Miscellaneous Handouts page), read the first three paragraphs of the introduction, all of Section 3.1, and Section 3.2.1 through Definition 3.1. In all readings I assign from these notes, you should skip anything labeled "Note(s) to instructors".** Whenever I update these notes (whether substantively or just to fix typos), I update the version-date line on p. 1. Each time you're going to look at the notes, re-load them to make sure that you're looking at the latest version.
F 1/16/26	1.2/ 1, 3–6, 17, 19–22. Whenever you see the term "explicit solution" in the book, you should (mentally) delete the word "explicit". (Until the third author was added to later editions of the textbook, what NSS now calls an explicit solution is exactly what it had previously called, simply and correctly, a solution.. The authors tried to "improve" the completely standard meaning of "solution of a DE". They did not succeed. See Notes on some book problems for additional corrections to the wording of several of the Section 1.2 problems. In #17, don't worry if you're unsure what "one-parameter family of solutions" means; I don't address it till Section 3.2.4 of my notes (and you don't need to know what it means to do the exercise). If you roughly understand the terminology now, great; if not, make a note to yourself to re-read this problem once we've covered that terminology. The book uses the terminology incorrectly in many places, but the usage in 1.2/17 is correct. Note: The exercise portions of many (probably most) of your homework assignments will be a lot more time-consuming than in the assignments to date; I want to give you fair warning of this before the end of Drop/Add. However, since my posted notes are only on first-order ODEs, the reading portions of the assignments will become much lighter once we're finished with first-order equations (which will take the first month or so of the semester). In my notes, read from where you left off in the last assignment through Example 3.11 (p. 15). Make sure you are keeping up with the reading as I assign it (i.e. if the assignment with due-date X says "Read up through [this item]," then read at least that far by date X), even if it seems to be ahead of, or not connected to, what I've covered in class yet. There isn't enough time to cover everything in my notes in class—among other things, my notes incorporate a lot of material that should have been included in your prerequisite courses, or even in high school, but probably wasn't—and if you wait until you think my class lectures have fully prepared you for a given reading assignment, you'll have far too much to read than you can possible absorb in a few days. Setting aside (only) one day a week as your "differential equations day" will not serve you well in this course. You may not understand everything the first time you read it. That's OK. Your brain needs time to process new concepts, and a lot of that processing takes place unconsciously. Ever wake up and suddenly understand something that you didn't understand the day before? Read the handout "Sets and Functions" posted on the Miscellaneous Handouts page. This part of the assignment is being posted late, so you may not be able to get it done on time. If that's the case, add it to the next assignment.
W 1/21/26	If you did not see the final addition to the previous assignment in time to have done it already, read the handout "Sets and Functions" posted on the Miscellaneous Handouts page. In the textbook, read the first page of Section 2.2, minus the last sentence. (We will discuss how to solve separable equations after we've finished discussing linear equations, the topic of Section 2.3. The only reason I'm having you read the first page of Section 2.2 now is so that you can do the first few exercises of Section 2.3. But as a "bonus", you'll also be able to do the exercises in Section 2.2 assigned below.) 2.2/ 1–4, 6 2.3/ 1–6 In my notes, read from where you left off in the last assignment through the one-sentence paragraph after Definition 3.19.
F 1/23/26	In Section 2.3 of the book, read up through p. 50, but mentally make some modifications: Replace the book's transition from equation (6) to equation (7) by the following fact: \(\mu'/\mu =\frac{d}{dx} \ln \|\mu\|.\) (The book's reference to separable equations is unnecessary, and does not lead directly to equation (7); it leads to a similar equation but with \(\|\mu(x)\|\) on the left-hand side. In class, I'll go over why we can get rid of the absolute-value symbols in this setting (finding an integrating factor for a linear DE). Equation (7) itself is fine, modulo the meaning of indefinite-integral notation; it's only the book's derivation that has problems.) Whenever you see an indefinite integral in the book, e.g. \(\int f(x)\, dx,\) the meaning is my "\(\int_{\rm spec} f(x)\, dx\)" (my notation for one specific antiderivative of \(f\)). I'll say more on Friday about about notation for indefinite integrals. For a preview (or, later, a review) of what I'll be saying about that, go to my Spring 2024 homework page, locate the assignment that was due 1/19/24, and in the first bullet-point, read from the beginning of the second sentence ("Remember ...") to the end of the smaller-font green text (in the "sub-bullet" after the word "Note"). In my notes, read from where you left off in the last assignment through the end of Section 3.2.4 (the middle of p. 27). On Fri. 1/23 we'll cover the method you're reading about on pp. 48–50. If you want to read more examples before next class, it's okay to look at Section 2.3's Examples 1–3, but be warned: Examples 1 and 2 have some extremely poor writing that you probably won't realize is poor, and that reinforces certain bad habits that most students have but that few are aware of. (Example 3 is better written, but shouldn't be read before the other two.) Specific problems with Example 2 (one of which also occurs in Example 1) are discussed in the same Spring 2024 assignment mentioned above. The most pervasive of these is the one in last small-font paragraph in that assignment. Feel free to get a head-start on the exercises in the next assignment, based on what you've read in Section 2.3; this will help you finish that (much longer) assignment on time.
M 1/26/26	2.3/ 7–9, 12–15 (note which variable is which in #13!), 17–20 When you apply the integrating-factor method don't forget the first step: writing the equation in "standard linear form", equation (15) in the book. (If the original DE had an \(a_1(x)\) multiplying \(\frac{dy}{dx}\) — even a constant function other than 1—you have to divide through by \(a_1(x)\) before you can use the formula for \(\mu(x)\) in the box on p. 50; otherwise the method doesn't work.) Be especially careful to identify the function \(P\) correctly; its sign is very important. For example, in 2.3/17, \(P(x)= -\frac{1}{x}\), not just \(\frac{1}{x}\). 2.3 (continued)/ 22, 23, 25a, 27a, 28, 31, 33, 35 See my Spring 2024 homework page, assignment due 1/22/24, for corrections to some of the Section 2.3 exercises. Also, in that same assignment read the three paragraphs at the bottom of the assignment. (The reason I'm not simply recopying such items into this semester's homework page is that some of my 2023-2024 students said that, although my comments and corrections were intended to be helpful, they made the look of those assignments overwhelming.) 2.2/ 34. Although this exercise is in the section on "Separable Equations" (which we haven't discussed yet), the DE happens to be linear as well as separable, so you're equipped to solve it. For solving this equation, the "linear equations method" is actually simpler than—I would even say better than—the (not yet discussed) "separable equations method". (The same is true of Section 2.1's equation (1), which the book solves by the "separable equations method"—and makes two mistakes in the sentence containing equation (4). This is why I did not assign you to read Section 2.1.) Do non-book problem 2. In my notes, read from the beginning of Section 3.2.5 (p. 27) through the end of Definition 3.23 (p. 33), plus the paragraph after that definition. (All of this is needed for a proper understanding of the word "determines" in the book's Definition 2 in its Section 1.2! [I still haven't defined "implicit solution of a DE" yet; the above reading is needed just to understand the single word "determines" in that definition.] This is one of the biggest reasons I didn't assign you to read Section 1.2.) Then do the exercise that's shortly after Definition 3.23 in my notes.
W 1/28/26
F 1/30/26
M 2/2/26
W 2/4/26
F 2/6/26
M 2/9/26
W 2/11/26
F 2/13/26
M 2/16/26
W 2/18/26
F 2/20/26
M 2/23/26
W 2/25/26
F 2/27/26
M 3/2/26
W 3/4/26
M 3/6/26
M 3/9/26
W 3/11/26
F 3/13/26
M 3/23/26
W 3/25/26
F 3/27/26
F 3/29/26
W 4/1/26
F 4/3/26
M 4/6/26
W 4/8/26
F 4/10/26
M 4/13/26
W 4/15/26
F 4/17/26
M 4/20/26
W 4/22/26

Class home page

Homework Assignments MAP 2302 Section 4219 (18286) — Honors Elementary Differential Equations Spring 2026

Homework Assignments
MAP 2302 Section 4219 (18286) — Honors Elementary Differential Equations
Spring 2026