Math 220: Differential Equations

Fall 2026

Department of Mathematics, Grinnell College

Books and Resources

We will follow:

Unsolicited advice: The textbook will be your best resource for this semester. I will assign reading for most class meetings and I strongly encourage you to complete it consistently; you can find the reading schedule here. Spending the time to digest the exposition in the textbook (highly non-trivial!) will help you glimpse the themes of calculus. This, in turn, will be your most reliable problem-solving tool. See, also, the Reading and Engagement section below.

Course Goals

We will cover most of the first 9 chapters of the textbook. While covering these, I will expect students to meet the following course objectives

Reading and Engagement

Throughout the semester, you will be assigned reading out of our textbook. Reading this text will better position you to follow, and actively engage with, classroom discussion. The schedule for readings can be found here.

To help you develop a habit of active reading, I will assign (almost) daily worksheets to guide our discussion in class. You will need to have completed the reading to be able to fully engage with these worksheets. You will be asked to upload a random subset of these worksheets to Gradescope and I will use them as a basis for determining the bulk of the "Reading and Engagement" portion of your grade. Besides reading the text regularly and actively, I will expect you to attend class regularly, contribute to class discussions, and ask questions in office hours or via email.

On reading mathematics. There is a wealth of information and advice on how to read mathematics out there. This is something many of the greatest mathematicians have written about; see, for example, the end of this blog post, or point 6. in Tim Gower's blog post.

Homework

Written homework. Homework will be assigned daily and will be due on Fridays at 5 PM; the schedule for assignments can be found here and on our Canvas page.

Labs. There will be a handful of lab assignments where you will explore certain aspects of differential equations using MATLAB. Your scripts and certain outputs will be due on some Fridays at 5 PM; the schedule for labs can be found here and on our Canvas page.

Submission. Homework is to be submitted via Gradescope. Be sure to tag questions correctly to ensure that all your work is evaluated. Instructions on tagging your work can be found here. Late homework will not be accepted unless extenuating circumstances merit an extension. In this case, you will need to bring the emergency to my attention before the due date.

Extensions. You may request a no-penalty extension on any written homework assignment or lab. If I receive your request before the assignment due date, the extension will be granted, and the new due date will be Monday of the following week by class time. Barring extenuating circumstances, no late requests will be granted. To request the extension, send me an email with the assignment name and a brief explanation for why the extension is necessary. Be sure to send your request before the original assignment deadline.

Expectations. Besides originality and related academic honesty matters (see the Academic Honesty section below), I will expect you to submit coherent, neat, and well-written solutions.

On writing mathematics. The notion of well-written mathematics is subjective, but you probably have some sense of what you do and do not like to see in mathematical writing (from, say, reading your textbook). Many mathematicians have written on the subject; see these tips, this advice, or this guide, for example. A great source where many such writings are compiled is Terry Tao's blog post. Of course these sources might sometimes disagree, and that is OK. What you should ultimately focus on is the clarity of your argument and reasoning; not only for the benefit of the reader, but also for your own. The mathematical story in your own mind can be greatly clarified with good writing!

Quizzes

Quizzes will be given in class on Wednesdays and will be based on the previous week's material. There will be no make-up quizzes, but the two lowest quiz grades will be dropped.

Quiz corrections. Immediately after each quiz, a PDF of the quiz will be posted on Canvas (under Files). A week after each quiz, solutions will be posted. In the meantime, you will receive a grade for your quiz on Gradescope. Before solutions are posted, and on questions where you did not get all possible points, you may submit your own hand-written solution and a short reflection on how this new solutions compares to the one you initially presented. I will grade your new solution and you will get back up to 50% of the number of points you lost on the relevant question.

Expectations. Quizzes are closed-notes, closed books. No outside resources are permitted. Quiz corrections are expected to be individual; you may consult your textbook and course notes, but no other outside sources (including the Math Lab and sources listed in the Academic Honesty section below). Because solutions to the quiz will be posted on Canvas at that point, no corrections will be accepted any later than a week after the quiz was administered.

Exams

There will be three exams in this course: two midterms and a comprehensive final. The dates/times are on the schedule tab. If you have a conflict with either one, please let me know as soon as possible.

Grading

Grades will be based on:

Your numerical scores will be used to assign you a letter grade based on a scale at least as generous as the following: [90, 100] earns an A- or better, [80, 90) earns a B- or better, [74, 80) earns a C or better.

Passing policy. To pass this course with a letter grade of C or better, aside from attaining the required numerical score, you must pass at least one of the above exams with a score of 70 or better.

Academic Honesty

All students must adhere to Grinnell's academic honesty policy which can be found here.

Collaboration. You are encouraged to work with your classmates and to consult your textbook while brain-storming solutions and strategies to homework problems. That being said, you are expected to independantly write your own solutions in your own words. If you do collaboratively work on a problem, you must indicate this on your solution. There are no formatting requirements for this; a simple "I worked on this problem with Omar" will suffice.

Outside resources. It is not my intention that you will need to use outside books/papers or other resources to be able to complete any given assignment. That being said, I encourage you to consult the supplementary references listed above and other online sources (e.g. video lectures, notes, other textbooks, etc.) to help expand your understanding of material presented in class. You may not do any of the following:

Of course these resources are very useful when conducting independent research or study, but do not serve you (or your classmates) in a structured classroom as ours. David Speyer wrote a reasonable explanation of why this policy is in place, which can be found here

Accommodations and Other Resources

Disabilities. Grinnell College makes reasonable accommodations for students with documented disabilities. Students with disabilities partner with Accessibility and Disability Resources (ADR) to make academic accommodation letters available to faculty via the accommodation portal. If you have not already worked with the Office of Disability Resources and believe you may require academic accommodations for this course, Disability Resources staff can be reached via e-mail at access@grinnell.edu, by making an appointment via the accommodation portal, or by stopping by Steiner Hall. (641-269-3124).

Medical and counseling services. Grinnell offers an array of services to help support students' physical, mental, and social well-being. If you need help, please do not hesitate to reach out to Student Health and Wellness (SHAW). I am happy to work with you in making resonable accommodations to help you engage with our classroom as fully as possible; just let me know when the need arises.

Religious holidays. I encourage students who plan to observe holy days/times that coincide with class meetings or assignment due dates to consult with me in the first three weeks of classes so that we may reach a mutual understanding of how you can meet the terms of your religious observance and also the requirements for this course.

Academic support. If you have other needs not addressed above, please let me know soon so that we can work together for the best possible learning environment. In some cases, I will recommend consulting with the Academic Success Center (ASC). They are an excellent resource for developing strategies for your learning, and they can connect you with other resources. If I notice that you are encountering difficulty, and I have reached out to you and not received a response, or if you have missed multiple class sessions or are not meeting our class objectives repeatedly, I will submit an academic alert via the ASC’s SAL portal. A message notifying you of my concern will get sent to you, along with the ASC staff and your adviser(s), so that they can reach out to you with additional offers of support

Title IX and pregnancy related conditions. Grinnell College is committed to providing learning, living, and working environments free from discrimination and harassment. For this reason, it is important to report if you or someone you know is experiencing any form of sexual harassment. Your professor is responsible to pass reports made to them to the Title IX Coordinator. If you want to make a report to a confidential resource, your professor can direct you to those spaces.

If you are a pregnant student, have pregnancy-related conditions, or are a parenting student who wishes to request reasonable related supportive measures from the College under Title IX, please email the Title IX Coordinator at titleix@grinnell.edu. The Title IX Coordinator will work with Disability Resources and your professors to provide reasonable supportive measures in support of your education while pregnant or as a parent.

“The best thing for being sad," replied Merlin, beginning to puff and blow, "is to learn something. That's the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then — to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn.”

― T.H. White, The Once and Future King