AMATH 251Introduction to Differential Equations (Advanced Level)
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Applied Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 3 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.
AMATH 251 is an advanced-level version of AMATH 250. Basic techniques for ODEs: integrating factors, undetermined coefficients and variation of parameters. Introduction to existence and uniqueness theorems. Systems of n-dimensional coupled ODEs and high order ODEs. Matrix Exponential. Laplace Transform. Stability and nonlinear ODEs. Phase space analysis and chaos. Introduction to numerical methods. Series solutions and special functions.
Prerequisites
- Complete all of the following
- Must have completed at least 1 of the following:
- Must have completed at least 1 of the following:
Antirequisites
- Not completed nor concurrently enrolled in any of the following:
Leads to
Fall 2026 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 6225 | 20 / 60 | TTh 10:00–11:20 |
| TUT 101 | 6235 | 20 / 60 | M 10:30–11:20 |
Reviewed on UW Flow
56% liked it41% easy93% useful
From 34 ratings and 5 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
A very robust introduction to differential equations. I'm not sure that the advanced section is that different from the regular stream, but either way this course is extremely useful, and covers a lot of content that comes up in later physics courses. This is a pretty intense course; the assignments are long and you'll need to spend a lot of time studying the various techniques of solving ODEs to do well on the midterm and final. Take advantage of any opportunities for bonus marks on assignments, do a lot of practice questions before the exams, and you'll get a good mark.
Jun 2023 · liked itOn UW FlowRemove this
Try to study ahead of time and you will be fine. The materials are interesting although the videos on Mobious can be boring sometimes, but a good course overall, ask on piazza anything you want
Dec 2020 · liked itOn UW FlowRemove this
Very useful stuff that came up in many of my other courses. This course covers so many different topics in the relm of solving ODEs...at times a little too much at once. The material itself is not too difficult but the volume can be a lot at times. There were weekly quizzes PLUS biweekly Maple assignments PLUS two full length projects on top of the midterm and final. I really enjoy linear ODEs but the course could have been structured as to teach it better.
Nov 2017 · didn’t like itOn UW FlowRemove this
Loved the resonance. Resonance is key to this course.
Dec 2015 · liked itOn UW FlowRemove this
One of my favourite courses. Demanding, frequently had to go to TA during his office hours.
Apr 2015 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
102 posts and comments in 81 threads mention AMATH 251, June 2013 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.
Fall 2024
Courses to take if I enjoyed AMATH 250 and AMATH 351 2 points, 5 comments
“title. need to take a few math courses and just wanted to know if any courses would use the material from these courses or build upon it.”
u/surker512: “… There's a small unit on oscillations/springs, just a review of the oscillations/springs unit in AMATH 250/251. The best part is definitely Lagrangian and Hamiltonian mechanics. …”
Is MATH138 physics based better/required for mathphys rather than MATH138 regular 2 points, 4 comments
“If I switch out of MATH138p to regular, how much am I missing out on/will I be burnt by proofs?”
u/cubing_starwars: “… This is good since they are planning on making AMATH 251, the intro ODEs course for amath/math phys majors, a little bit harder next year to compensate for the eventual removal of AMATH 351.”
u/Constant_Reaction_94: “… Last year, the 138p prof skipped some stuff in regular 138 and focused more on DE's, but you will learn that material in amath 250/251 so it really doesn't matter. …”
UW Math Viable 2A Courseload? 14 points, 13 comments
“https://preview.redd.it/sewy50msawyd1.png?width=376&format=png&auto=webp&s=164f19f51cf2407d9f633857108cece82aac7e1c”
u/cubing_starwars: “Quite difficult but very doable. Also, take AMATH 251 over 250, it is not much harder and some quizzes are replaced with assignments.”
Spring 2024
Math 2nd Year (2A) Class Selection 4 points, 6 comments
u/Deriuth: “I am a BMath student entering year 2, and to keep it short I have to choose 2 classes out of the 3: MATH235, STAT230, AMATH251. …”
u/Constant_Reaction_94: “If AMATH 251 is too intensive why not just do AMATH 250? The difference between the courses is not big, and 250 is probably one of the easiest amath courses you can take.”
u/Minute-Wolverine417: “If u wanna do amath251, then take stat230 online”
Easiest non required math courses to get a high mark 6 points, 6 comments
u/goosie2022: “… I have been looking at : math 239, CO 250, Amath 250/ 251, Actsci 231. Please let me know which of these will be a good candidate. …”
Winter 2024
After phys 122 for depth (math faculty) 1 point, 5 comments
“For context, I'm in cs(finished 2A, gonna go into 2B) and I have finished phys 122 (and trying for a depth in physics). …”
u/SU__2__: “PHYS 234 (in my offering) was a pretty great course. Most profs will be willing to let you override into without the AMATH 250/251 course pre-req if you email or ask them to sign an override form after one of their lectures.”
Amath250 textbook 1 point, 2 comments
“Do anyone have am250 textbook pdf for sharing?”
u/EurasianZaltpetre: “I have for amath251”
Fall 2023
Bro.. Why is AMATH 250 so hard 1 point, 4 comments
“I see these reviews on how it's easy, but I took CO 250, and that is much easier than this.”
u/johndoev1: “just take amath251 instead”
I'm an exchange student and I really need some advices 1 point, 5 comments
u/Stunning_Turnip_5515: “… I'm doing ACTSC232, ACTSC372, STAT330 and AMATH251, so anyone has done this course before, can you guys give me some advice for efficient study. Also how can you guys make friends on campus? …”
Amath 251 lec notes 2 points, 0 comments
u/Noob6921: “Im taking amath 251 with kevin this term and was wondering if there are any lec notes from previous terms? doesn't look like he'll post any and dont wanna solely rely on course note book if i miss a class Thank you”
Spring 2023
How is AMATH 251 with Kevin Lamb? 1 point, 1 comment
u/Scary-Being6595: “I'm really interested in learning about the theoretical side of ODE's (and as someone planning to focus more on pure math related things some applications would be neat as well) but I can't find much anything about this course that isn't a decade old on UW flow. …”
u/__scoper__: “I took AMATH 251 with him in Fall of 2021. I think the class was fine. His lectures were dry and boarding but he did taught the content clearly enough. His assignments were stupidly long and tedious sometimes (usually 10+ pages of LaTeX and one even got to 20 for me). …”
How is this courseload for 2A? 0 points, 2 comments
u/Arush242004: “I'm thinking of taking CS135, AMATH251, MATH237, MATH135 + some elective (maybe ECON or in communications).”
Check it elsewhere for Fall 2026
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