Syllabus for MA 226 -A1 and C1, Differential Equations

Syllabus for MA 226 - A1 and C1, Differential Equations, Spring 2025

Course Information

Lecturer: Ryan Goh

Email: rgoh@bu.edu
Office: CDS 423
Office Hours: W 12:30pm-2pm, Th 9am-10:30am

or by appointment, please provide your availability when requesting an appointment.
Web page: http://math.bu.edu/people/rgoh/

Lectures:

Time:
 A1: Monday, Wednesday, Friday, 10:10 - 11:00 am, CAS 224
C1: Monday, Wednesday, Friday, 9:05-9:55am; CAS 224
Location (both sections): CAS 224
Lecture Notes: I will use notes with gaps for lectures. PDFs for the weeks lectures will be posted on the Blackboard website the Monday before. These notes will have gaps in them. The idea is that you will download these notes, either write them out in your notebook, print them out, or load onto a tablet, and bring them to class to fill in the spaces as we go through the material. This will also allow you to see what we will be covering during the week. I highly recommend preparing by reading through the corresponding textbook sections and working out examples. This generally helps absorb the material when you come to lecture!

Teaching Fellows:

Kate Finnerty

Email: ksfinn@bu.edu
Office: CDS 536
Office Hours: T 10-11am, Th 1-2pm
Tutoring room hours: Th 4-5pm

Robert Jencks

Email: jencksr@bu.edu
Office: CDS 528
Office Hours: M 2:30-3:30pm, F 12-1:00pm
Tutoring room hours: F 1-2pm

Office Hours

Office hours will be held in-person, in my office. If I'm not in my office, check one of the collaboration spaces on the 4th floor of CDS, as I might have moved office hours there due to capcity issues (I will try to leave a note on my door if this is the case).

Discussion Sections

Note: If you are registered in the A1 lecture section of the class, you must be registered in one, and only one, of the A discussion sections listed below. Similarly for A1 and the A discussion sections In these sessions you will be able to work through problems, and ask questions of your classmates and teaching fellow. Math is learned by doing, and this is a great place to do more of it and get help on problems!
Section Place Time
A2 CAS 229 M 12:20-1:10pm
A3 CAS 229 M 2:30-3:20pm
A4 PSY B47 M 3:35-4:25pm
A5 CAS 320 T 8-8:50am
A6 CAS 320 T 11:15am-12:05pm
C2 CAS 320 M 10:10-11am
C3 CSOC B59 M 1:25-2:15pm
C4 CAS 320 R 8:00AM - 8:50AM
C5 CAS 320 R 11:15am-12:05pm
C6 CAS 320 R 3:35-4:25pm

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.

    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

    Approximate Course Schedule

  • Week 1: Intro and Sec. 1.1 (Monday discussions will not meet))
  • Week 2: Sec. 1.2 - 1.4
  • Week 3: Sec. 1.5-1.7
  • Week 4: Sec. 1.8, review, exam 1
  • Week 5: Sec. 1.9, 2.1, 2.2 (no class Mon. 2/17, Monday schedule on Tuesday 2/18, Tuesday discussions will not meet)
  • Week 6: Sec. 2.3-2.6
  • Week 7: Sec. 2.7 and Review, Exam 2, Lorenze system and Chaos theory
  • Week 8: Sec. 3.1 - 3.3
  • Week 9: Sec. 3.4 - 3.6
  • Week 10: Sec. 4.1-4.3
  • Week 11: Sec. 4.4, review, Exam 3
  • Week 12: Sec. 5.1 - 5.3
  • Week 13: Sec 6.1,6.2 (no class 4/21, Patriot's day 4/23 is a monday class),
  • Week 14: Sec. 6.3 - 6.5, Review (last day of class)

    Course hub

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

    Homework

    Weekly homework and associated readings will be posted on the course webpage. You are required to write out, scan, and submit homework via Gradscope (details below) each Friday at 5:00pm. The homework will cover material covered in last weeks lecture. Due time-constraints with our TF and grader(s) no late work will be accepted . To accomodate unforseen happenings, illness, etc. your lowest two scores will be dropped. The first homework assignment, due on Friday Jan 24th, is graded on completion only, and is meant to get you acquainted with Gradescope. If you submit this assignment on time you will get full credit. Homework will consist of two components, assigned problems which must be written up and turned in, as well as suggested problems which are meant to give you extra practice in understanding the concepts for the week and are not to be turned in. See this link for guidelines on the homework (including some links on how to use Gradescope) and an example of a homework solution.

    Quizzes

    Weekly quizzes will be given online in Blackboard. They will be on the lecture material of the week are meant to be quick little checks to see how well you recall and synthesize course materials in a timed, "on-the-fly" environment. Once you begin the quiz, you will have 60 minutes to enter your answers and submit them. Each quiz will be released on Friday at noon, and must be completed by Monday at midnight, 11:59pm. To emphasize that these are only quick checks, you will be allowed multiple times to enter the correct answer and will be able to see when your answer is incorrect. Hence, these are meant to give you a little bit of practice in a timed-enviornment. No quiz make ups will be allowed but the two lowest quiz scores will be dropped.

    Exams

    There will be three exams during the semester. They will be held on Friday, February 14th and Wednesday, March 5th and Friday, April 11th at the regular lecture time and location. Logistics of each exam will be discussed during class.

    Final Exam

    The date for the final exam is TBD, in a location TBA. No early finals will be given and please do not plan your end-of-semester travel until the precise date and time are set.

    Grades

    Your course grade will be assigned as follows
  • In-semester Exams (40%)
    • 40% total, %20 each exam, lowest exam score dropped, cannot receive an A or A- grade if an exam is missed for an unexcused absence)
  • Final exam (30%)
  • Homework (20% - two lowest scores dropped)
  • Quizzes (5% - graded on completion only, can miss two quizzes without penalty),
  • Participation (5%): Participating in in-class, discussion section activities and work, online campuswire discussions (asking/answering questions)

    • Classroom policies

  • Questions are always welcome during lecture. Please raise your hand. 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 in class, when not part of class activities (i.e. to take notes, read the textbook, take a campuswire question etc...), is forbidden. Such activities can be very disruptive, distracting, and disrespectful to those around you and are not conducive to a productive learning environment. Furthermore, there are many people in this course, so small disturbances (such as whispering to your neighbor, listening to music with headphones, browsing the internet, etc...) can add up and become disruptive to the lecture.
  • 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.
  • I will project my lecture notes, written on my iPad, onto a projector screen in the lecture room. I will take a brief pause after each page of notes before moving to the next one. Please let me know if you need more time to write something down or my handwriting is unclear. My notes will be synced to dropbox (nearly-live), with link accessible on blackboard. Lecture notes will be posted to blackboard.

    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, the T.F., 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.

    Getting Help

  • Post and answer questions on the course campuswire page. Both myself and the TF will keep an eye on these pages. Someone might have the same question as you!
  • Feel free to come to office hours, or make an appointment to get help with course work and materials.
  • If you start to feel that you are falling behind, be proactive and take steps to catch up. The concepts of the course build on each other so if you wait it will only become more difficult to catch up!
  • If you need more help feel free to visit the math department tutoring room for more help.
  • See also the Math Help Night for another option.

    Communication

    The course will use the Campuswire platform. I will email out a registration link to this course messaging/question/posting software. There you will be able to post, answer, like, and follow questions about course materials, problems, etc... The TFs and 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 use the "direct message" feature in CampusWire or email myself or the TFs. 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 campuswire (unless of course it is of a personal/confidential nature), so it might be quicker to just post on campuswire!

    Announcements

    Course announcements will be posted on Campuswire. Occasionally I may also email out something to the class. Please try to check both campuswire and your BU email at least daily. Email response policy : During the work week, I aim to answer any emails received within 24 hours (most of the time sooner). I will answer campuswire questions once during the day, and once in the evening. 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. I am happy to work with you about such an observance with sufficient notice. As mentioned above, there will be no make-ups for quizzes or homeworks. In extreme circumstances (religious observance, death in the family, emergency, illness) there can be make-ups for exams. If possible, please tell me during the first week of school if you will need a make-up exam.

    Students with accomodations

    Please contact me as soon as possible. I am happy to work with you and the BU office of disability and access services.

    Academic code of conduct

    Please do not cheat. Furthermore, copying of answers from a friend, solution manual, online solution, or online help platform (such as Chegg) is detrimental to your learning and is not allowed. Submitting work that is not yours is not allowed. You will be held to the BU academic code of conduct.




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