Syllabus for MA 231 Honors Differential Equations

Syllabus for MA 231 Honors Differential Equations, Fall 2025

Course Information

Lecturer: Ryan Goh

Email: rgoh@bu.edu
Office: CDS 423
Office Hours:
Tuesday 10:30 - 12:30pm
Wednesday 1:30-2:30pm
or by appointment (please provide your availability when requesting an appointment).
Web page: http://math.bu.edu/people/rgoh/

Lectures:

Time: Monday, Wednesday, Friday 12:20pm-1:10pm;
Location: PSY B37

Discussion:

Time: Wednesday 10:10 am-11:00am;
Location: CAS 218

Textbook:

"Differential Equations," by Blanchard, Devaney, Hall, 4th edition; ISBN 978-1133109037. A copy is available on reserve at the BU science & engineering library. It may also be helpful to obtain a copy of the DE tools software that comes with the textbook, this can be downloaded for free on the publishers website . Note you will need Java Runtime 8 to run this software. Amazon Coretto 8 seems to work best. See also this link


  • Additional Reference: "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering," by Steven H. Strogatz, Second Edition. An online copy of the textbook can be found via the BU library here.

    Course Webpage:

    math.bu.edu/people/rgoh/teaching/m231-fs25/course-page.html

    Course Description:

    Differential equations are some of the most popular and powerful tools for understanding the natural world. In its simplest form, a differential equation is an equation which relates the rate of change of a quantity(s), with respect to some other independent variable (most often time), to the quantity itself. In this course we will discuss various methods and techniques to classify, characterize, and understand differential equations and their solutions. The techniques can be broadly organized into three types:
  • 1) Analytical: How can one write down explicit expressions to a given differential equation?
  • 2) Qualitative: Can one understand the general behavior of solutions and how they vary with changes in system parameters?
  • 3) Numerical: How can solutions be approximated using numerical algorithms and a computer?
    • Throughout, emphasis will be made on mathematical modeling with examples drawn from applications in the natural and social sciences.

    Approximate Course Schedule

    Roughly our course schedule, subject to student interests and class pace, will be as follows
  • Week 1: Intro, Sec. 1.1 - 1.3
  • Week 2: Sec. 1.3 - 1.5 also 7.1, 7.2
  • Week 3: Sec. 1.6 - 1.9
  • Week 4: Sec. 2.1 - 2.5
  • Week 5: Sec. 2.6, 3.1, 3.2, Midterm 1
  • Week 6: Sec. 3.3, 3.4, 3.5, 3.7
  • Week 7: Sec. 3.8, higher dimensional linear algebra and linear systems, 4.1 (no class on Monday, class on Tuesday)
  • Week 8: Sec. 4.1 - 4.4, variation of parameters
  • Week 9: Sec. Hill theory/periodic coefficients, 5.1, 5.2
  • Week 10: Sec. 5.2 - 5.4, Midterm 2
  • Week 11: Sec. 5.6/control theory, 6.1, 6.2
  • Week 12: Sec. 6.3, 6.5, 8.1
  • Week 13: Sec 8.2 (no class Wed and Fri),
  • Week 14: Sec. 8.3, 8.4, class presentations
  • Week 15: Class presentations

    Numerical exploration

    We will also utilize computer/numerical simulations to help us explore and analyze differential equations throughout the course. In my examples, I will mainly use MATLAB and Mathematica. The former can be downloaded here for free by any BU student. See this quick tutorial on how to get started with the software if you haven't used it, and here for a tutorial on solving differential equations with it. For the latter download instructions here and a tutorial to get started. You are of course welcome to use another software (such as Python, Julia, etc...) and while I may be familiar with the specific language you are using, I cannot guarentee I will be able to help debug/troubleshoot code written in all languages.

    Course hub

    Links to all facets of the course, Homework assignments, this syllabus, class notes, and gradescope, can be found on the course Blackboard Page .

    Homework and practice problems

    In each lecture, I will list a few practice problems from the textbook to go with the day's material. These are for your own practice and to check your understanding of the material. They are not to be handed in and will not be graded. Though I am happy to discuss them in office hours or the discussion section! Graded homework assignments will be posted (every 7 to 10 days) on the course webpage and gradescope. Please neatly write out or type your solutions, turn them into one PDF (scanning if you write them on paper), and submit them through the course Gradescope page. This can also be found on the course blackboard page. Generally, they will be due on Wednesdays at 5pm. No late work will be accepted. Please start problems and get help early! Your lowest two scores will be dropped.

    Doing exercises and problems is the best way to learn mathematics.You are welcome (and encouraged!) to work together, but please make sure to write up solutions by yourself and in your own words. You must understand how to solve the problems yourself. If it is suspected that you copied down your answers from another source of any kind, you may be asked to come to my office and explain your solution(s), without any books or notes.

    In your solution sets, explain your work clearly, concisely, and using complete sentences. Homework should be legible and organized. If you are worried about the legibility of your handwriting, please contact me about using the mathematical typesetting software LaTeX. The homework problems will be graded using the following 6-point system adapted from Prof. Chad Topaz, of Williams College: Solution sets will be posted on blackboard along and your problem sets will be graded on gradescope one to two weeks after the due date.

    Midterms

    There will be two in-class written midterms, tentatively scheduled for Friday, October 3rd and Friday, November 7th during the regular lecture time. It will consist of problems simular to practice problems, homework problems and examples discussed in class. The specific material covered on the exam will be outlined a week or two before the exam.

    Final Exam

    There will be an in-person final exam during finals week. More detail will be forthcoming and please do not schedule your end-of-semester travel until the date and time is confirmed. See the BU final matrix for the tentative time, Wednesday, December 17th, 12:00pm-2pm . The problems will be roughly similar to examples done in class and in homework. The use of the internet or other resources, unless explicitly mentioned, will not be allowed. You must do the exam on your own and will not be allowed to communicate with others about it.

    Project

    You will do a semester long project which focuses on an application and or facet of differential equations. More detail on this will be forthcoming. The project will consist of a 20 page scientific report and a class presentation. The goal is to give you experience in independently learning about and investigating a research topic and composing a coherent scientific document (with an organized bibliography) and presentation which communicates your findings. At the start of the semester you will, in consultation with me, select a ``pet" system of differential equations coming from an application area of interest to you. This ``pet" will come along with you as we traverse the semester (from time-to-time it might even show up in your homework questions), and you will explore and understand it more and more as we go through the semester. Your project report will give a cohesive and comprehensive summary of your journey together, where you will explain the model, what the variables and parameters mean, how the different terms are chosen, and how it is used. You will then use ideas from the course (and also from your own literature study) to describe the qualitative and quantitative properties of its solutions and how they vary with parameters.
    The report should describe and synthesize the topic in you own words, summarizing relevant and related literature, and working out example calculations, exercises, or applications. Wrote copying or paraphrasing of results from a textbook will not be sufficient.
    A rubric for how the report will be graded will be provided later in the semester.
    I encourage you to pick a topic of interest to you or related to what you wish to go on to work on or study after BU. We can then work together to find a pet system of differential equations. A list of some potential areas/systems is listed here . Please do contact me if you need help finding a topic and we can discuss potential ideas!

    Near the end of the semester you will also be required to give a short class presentation on your project. More details and a schedule of talks will be determined later in the semester.

    You are welcome to work by yourself, or with one other classmate on the project. This must be decided when you get your topic approved by me. If working in a pair, the scope of the project will be expected to be proporationally larger (for example: maybe one person describes the theory of a subject, while the other does numerical investigations, and each write half of the report). You will also be required to jointly compose and sign a short statement describing each persons contributions to the project.

    You must meet with me (in office hours or by appointment) at least once to discuss the suitability of your project and get it approved by me. Of course, you are more than welcome to meet with me more than once!

    Project Deadlines

    Missing any of these will result in a 2% grade penalty for the project grade each day you are late.
  • September 17th: Meet with me at least once by this date (ideally earlier), and get a pet equation and project topic approved.
  • December 1st: First draft of report due to me on Gradescope. I will read through and give feedback on the report, so you can make revisions. The draft will not be graded but turning a significant draft (i.e. not just a page or two) on time is required.
  • December 12th: Final draft of project is due to me on Gradescope.

    • Course Grade

    Your course grade will assigned as follows
  • Homework scores (25% - two lowest scores dropped)
  • Semester Project (20%)
  • Midterms (15% each )
  • Final Exam (25%)
    • Records for assignment grades will be kept on the course blackboard website.

    Classroom policies

  • Questions are always welcome during lecture. Please raise your hand or interupt me if I'm facing the board. Sometimes, due to time restraints or flow of the lecture, I may have to delay a question till another section, or after class.
  • The use of cellphones, laptops, or the internet, when not part of class activities (i.e. to take notes, or share the result of a computer simulation), is forbidden. Such activities can be very disruptive, distracting, and disrespectful to those around you and are not conducive to a productive learning environment.
  • Please be at lecture on time. I understand that things come up once in a while, but if you are late please do not walk in front of me while I'm lecturing. It can be very distracting.
  • Attendance Policy : Students are expected to attend each class. We will follow the BU attendance policy . The class periods will be a key component of the course. While math is mostly learned by doing, I view lectures as a guide which helps one more efficiently and effectively learn a topic.

    Communication

    The course will use the we are going to try the Blackboard Ultra messaging platform . There you will be able to post, answer, and follow questions about course materials, problems, etc... I will try to answer questions on this board regularly. We also strongly encourage you to discuss and answer questions with your fellow classmates. We hope this will be helpful as asking questions, as well as seeing and answering those of others, can be very beneficial to your learning! Please be respectful, encouraging, and supportive. If you have a more private matter to discuss about the course, feel free to only message me in blackboard or email myself. Please do keep mind that this is a forum meant for this course. Extraneous, disrepectful, or erroneous posts will not be allowed. If you email me a question about course content, I most likely will post and answer it on blackboard (unless of course it is of a personal/confidential nature), so it might be quicker to just post on blackboard!

    Announcements

    Course announcements will be posted on Blackboard. Occasionally I may also email out something to the class. Please try to check both Blackboard and your BU email at least daily. Email response policy : During the work week, I aim to answer any emails/messages received within 24 hours (most of the time sooner). During the weekend, I may not answer until Sunday evening. Finally, late night emails may not be replied to until the next day.

    Excused absenses and make-up exams

    Please let me know about all religious observances at the beginning of the semester. As mentioned above, there will be no make-ups for homeworks. In extreme circumstances (religious observance, death in the family, emergency) there can be make-ups for exams. Please tell me during the first week of school if you will need a make-up exam.

    Students with disabilities

    Please contact me as soon as possible. I am happy to work with you and the BU office of Dissability and Access Services.

    Academic code of conduct

    Please do not cheat. Furthermore, copying of answers from a friend, solution manual, or online solution set is detrimental to your learning. You will be held to the BU academic code of conduct.

    How to be successful in this class

  • Attend and be an active participant in lectures and discussion sections.
  • Read the corresponding sections of the textbook (it's very readable!) before class and try to work through some of the examples. This will help you follow along in lecture!
  • Do all the of the homework problems (assigned and suggested) and discuss them with classmates, and myself!
  • Get help as soon as possible when you don't understand a concept (see below), the concepts of this course build on each other as we go through the semester
  • I view this course as partial bridge between 100-level calculus courses and more advanced mathematics. Cookie-cutter/"Plug-and-chug" type methods and problems will only be a part of this course. It will require a more conceptual and qualitative understanding of the material. This can sometimes be difficult to adjust to for some students used to more "reguritory" type courses. I will do my best to help you all adapt and grow!
  • If it has been a while since you have taken a math course, please review basic calculus (differentiation rules/concepts, integration concepts/techniques), and standard functions (trigonometric, exponential, logarithmic, etc.) as soon as possible.

    Extra Help

    If you feel you are falling behind in the course please do not hesitate to contact me! It is always easier to address misunderstandings sooner than later. In addition to working with me, I can also put you in touch with TAs in the     tutoring room who are knowledgeable in differential equations.



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