AMATH 451Introduction to Dynamical Systems
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Applied Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 2 of the last 7 terms. Winter 2027: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.
A unified view of linear and nonlinear systems of ordinary differential equations in Rn. Flow operators and their classification: contractions, expansions, hyperbolic flows. Stable and unstable manifolds. Phase-space analysis. Nonlinear systems, stability of equilibria, and Lyapunov functions. The special case of flows in the plane, Poincare-Bendixson theorem, and limit cycles. Applications to physical problems will be a motivating influence.
Prerequisites
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Winter 2027 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 5579 | 0 / 40 | MW 13:00–14:20 |
| LEC 701 | 2267 | 14 / 9999 | Online or by arrangement |
| TUT 101 | 6416 | 0 / 40 | T 11:30–12:20 |
Reviewed on UW Flow
67% liked it57% easy82% useful
From 9 ratings and 2 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
One of my favourite courses of all time. Really ignited the passion for ODEs in me.
May 2017 · liked it · 1 found this helpfulOn UW FlowRemove this
The content is excellent. It is a continuation of AMATH 351; there is a bit of overlap at the beginning. The content is easy to grasp, the challenging part is the tedious computations sometimes. If you liked AMATH 351, you will like this course a million times more.
Mar 2024 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
14 posts and comments in 10 threads mention AMATH 451, August 2014 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/sheep_herder102: “AMATH 353 and AMATH 451 are probably the most similar to those I’d say. Of course there are many other courses that use differential equations, things like continuum mechanics or quantum theory solve DEs. …”
u/jokerwithnojokes: “AMATH 451 looks fun, any other courses you'd recommend ? (any idea where I can find course notes for 451 because the website by X. Liu is not the most easily accessible in one go)”
Winter 2023
400 level AMATH courses 3 points, 0 comments
u/luizloo: “… I am for sure going to take AMATH 451 and 455, and deciding to take one of AMATH 456, 442, 477, 453. Has anyone taken these 4 courses? Which one is easier than the rest? Could use any advice/suggestion! …”
Fall 2017
[rant] Jun Liu is a terrible, horrible, no good, very bad professor. 17 points, 21 comments
“Let me first off state that Professor Liu certainly understands the Math 137 curriculum very much. Everyone in his class knows that he comprehends this course, and does try to teach it to us. …”
u/Akinohana: “Had him for AMATH 451. He was a pretty good professor in my opinion. He also doesn't have a very strong accent compared to many others in the school. Of course he is not the greatest, but I don't think it can be that bad as OP described. …”
PSA: UWCourseLinker back up, disabled by default, call with [[course code]] 39 points, 31 comments
u/RayDWatson: “Testing all course codes 1/61: [[ACC604]] [[ACC605]] [[ACC606]] [[ACC607]] [[ACC608]] [[ACC609]] [[ACC610]] [[ACC611]] [[ACC620]] [[ACC621]] [[ACC622]] [[ACC623]] [[ACC624]] [[ACC625]] [[ACC626]] …”
u/RayDWatson: “… [[AMATH431]] [[AMATH432]] [[AMATH433]] [[AMATH442]] [[AMATH444]] [[AMATH447]] [[AMATH451]] [[AMATH453]] [[AMATH455]] [[AMATH456]] [[AMATH463]] [[AMATH473]] [[AMATH475]] [[AMATH477]] [[AMATH495]] [[AMATH655]] [[AMATH663]] [[AMATH673]] [[AMATH675]] [[AMATH690]]”
u/UWCourseLinker: “… of Computational Differential Equations AMATH 447 - Introduction to Symbolic Computation AMATH 451 - Introduction to Dynamical Systems AMATH 453 - Partial Differential Equations 2 AMATH 455 - Control Theory AMATH 456 - Calculus of Variations AMATH 463 - Fluid Mechanics AMATH 473 …”
Winter 2017
Best AMATH/Physics Courses? 2 points, 7 comments
“These are two fields I think I might take courses in the next few terms so I was wondering if there were any can't-miss courses in either of these two areas?”
u/Postmodernist_Cancer: “all the good AMATH courses are behind like 2-3 pre-reqs. Like AMATH 451. I don't know about Physics, but probably the same issue.”
Spring 2016
Which 2 courses should I take: CS466, PMATH352/332, STAT444, STAT442, STAT431 0 points, 21 comments
“If I can only choose 2, which should I choose? Or is there some other interesting CO/AMATH/PMATH courses?”
[deleted]: “… As well as AMATH 451, and there is a mathematical biology course also, I forget the course code. CO, meh. There's the history of Math course. Not much else interesting, to me. But I've heard people like graph theory. In STAT I would suggest 433 (pre-req. …”
Is AMATH 455 very engineering-oriented? 5 points, 1 comment
u/ph0tone: “… I enjoyed studying AMATH 451, and I'd like another course of that kind, and I've heard that 455 is related to dynamical systems. …”
Reddit, I have some questions about AMATH 1 point, 6 comments
[deleted]: [deleted]
u/UWGo: “… Like AMATH 451, for example.”
Spring 2015
Questions about AMATH 3 points, 5 comments
“Hey guys, I'm interested in pursuing an AMATH minor. Can you guys recommend amath courses based on content that were more finance related? …”
u/1995_2000_2003_2016: “… I took AMATH250 and took AMATH351, 353, 451 and I did fine (although not great I suppose). There aren't really any directly finance-related courses, but AMATH353 is PDE's which you need for black-scholes. Business people get to take AMATH350 I think which covers it as well. …”
u/1995_2000_2003_2016: “… If you are interested in modelling stuff you could take courses like AMATH451/455 since I found 451 to be pretty fun since you build mathematical models from almost scratch. …”
Spring 2014
200, 300, 400 level math courses 0 points, 20 comments
“Greetings, would anybody be able to tell me the easiest math courses they've taken. I'm doing a non-major math, so I need a couple upper year math courses.”
u/SometimesY: “Are you interested in pure math courses, applied math or what?”
u/8pi: “… If you like those ones, try AMATH 451 Dynamical Systems. …”
u/figgernaggots: “Off topic, do you recommend taking AMATH451 before 342? I know 342 is not a prereq for 451 but now that you mention it it does seem like 342 covers quite a bit of ODE material, so I'm wondering if taking 451 without 342 won't let me "enjoy" the course as much.”
Check it elsewhere for Fall 2026
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