AMATH 453Partial Differential Equations 2
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Applied Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 1 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.
A thorough discussion of the class of second order linear partial differential equations with constant coefficients, in two independent variables. Laplace's equation, the wave equation and the heat equation in higher dimensions. Theoretical/qualitative aspects: well-posed problems, maximum principles for elliptic and parabolic equations, continuous dependence results, uniqueness results (including consideration of unbounded domains), domain of dependence for hyperbolic equations. Solution procedures: elliptic equations -- Green functions, conformal mapping; hyperbolic equations -- generalized d'Alembert solution, spherical means, method of descent; transform methods -- Fourier, multiple Fourier, Laplace, Hankel (for all three types of partial differential equations); Duhamel's method for inhomogeneous hyperbolic and parabolic equations.
Prerequisites
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Reviewed on UW Flow
83% liked it0% easy90% useful
From 6 ratings and 4 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Ignore the course description; much of that is now in PDEs 1. We used part II of Evans. We started with the weak derivative, spent a month on measure theory and functional analysis, and then studied approximations and inequalities on the Sobolev space. Next, we covered E&U of weak sols to 2nd order elliptic eqns, interior and boundary regularity. We finished the course with E&U of weak sol to 2nd order parabolic eqns. Overall, this course was very much a PMATH course since we did nothing but proofs; it was difficult due to the sheer amount of content, but foundational for both modern PDE theory and numerical analysis. Realistically, you should have taken a previous course in real or…
Dec 2025 · liked itOn UW FlowRemove this
I really liked this course. A lot of the content was super interesting, but relied a lot on different analysis courses (functional, real, measure theory, etc). Not very sure if this course is super useful later on, but goes very in-depth into the discussion of existence and uniqueness of second-order linear PDEs, with emphasis on elliptic and parabolic PDEs. Definitely not easy, but the course being full assignments made things a lot better. Also the professor was great. This will eat up a lot of your time if you don't start early.
Nov 2025 · liked itOn UW FlowRemove this
Definitely one of the hardest undergraduate courses offered by the AMATH faculty. The assignments (taught by Dr. Siegel) were very lengthy, and there was a large number of topics covered. If you take this course, get ready to work very hard.
Jan 2018 · liked itOn UW FlowRemove this
This is a very interesting and useful course! Even if you didn't like PDE's 1 that much, you'll like this one a lot better. You learn a lot of cool theoretical results for PDE's and solution techniques. Some of the material in this course is tricky though.
Dec 2017 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
10 posts and comments in 9 threads mention AMATH 453, January 2016 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.
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 2020
I'm leaving UW after 19 school terms in a row, AMA. 590 points, 142 comments
u/ram8g: “What courses you took? And can I ask for some pointers. I'm trying to study a bit of pure math on my own”
u/ram8g: “What is a good book for advance real and complex analysis? I actually took 331 and 332 but I wanted to learn more. Also did you take the PDE2(amath 453) course by any chance?”
Spring 2020
Hardest math courses at Waterloo? 16 points, 16 comments
u/Laeriana: “… really, but CO 250 has a bias as it's a course frequently taken PMATH 331, 333, 352, 354 AMATH 350, 453 My own most personal challenging math courses include.... …”
Fall 2017
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: “… [[AMATH432]] [[AMATH433]] [[AMATH442]] [[AMATH444]] [[AMATH447]] [[AMATH451]] [[AMATH453]] [[AMATH455]] [[AMATH456]] [[AMATH463]] [[AMATH473]] [[AMATH475]] [[AMATH477]] [[AMATH495]] [[AMATH655]] [[AMATH663]] [[AMATH673]] [[AMATH675]] [[AMATH690]]”
u/UWCourseLinker: “… 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 - Quantum Theory 2 AMATH 475 - Introduction …”
Any way to disable UWCourseLinker from posting? 16 points, 26 comments
“posting a reply to my comment I find the bot annoying.”
u/Jackhofmann: “PSYCH 483 PSYCH 484 PSYCH 485 PSYCH 486 PSYCH 490R PSYCH 499A PSYCH 499B PSYCH 499C PSYCH 621 PSYCH 630 PSYCH 677A PSYCH 704A PSYCH 704B PSYCH 707 PSYCH 710 PSYCH 714 PSYCH 717 PSYCH 720A PSYCH 721A …”
u/Jackhofmann: “… AMATH 250 AMATH 251 AMATH 271 AMATH 331 AMATH 342 AMATH 350 AMATH 351 AMATH 391 AMATH 442 AMATH 453 AMATH 456 AMATH 463 AMATH 473 AMATH 495 AMATH 663 AMATH 673 AMATH 731 AMATH 732 AMATH 740 AMATH 751 AMATH 871 AMATH 875 AMATH 900 ANTH 100 ANTH 100W ANTH 201 ANTH 202 ANTH 204 …”
Spring 2017
What courses are you taking this fall? 28 points, 129 comments
“With course selection and add/drop happening this week I figured this would be a cool discussion post. …”
u/Kakateo: “ENGL 108D - Digital Lives STAT 231 - Statistics PHYS 475 - Cosmology AMATH 453 - PDEs 2 AMATH 456 - Calculus of Variations PMATH 347 - Groups and Rings We'll see how this goes...”
Spring 2016
Do AMATH courses get better? 2 points, 3 comments
u/amaththrowaway96: “… I'm considering taking AMATH 231, AMATH 271, AMATH 351, AMATH 353, AMATH 373, AMATH 453. Are these courses better than AMATH 250? …”
Winter 2016
Math/BBA vs CS/BBA 3 points, 13 comments
“Can someone tell me the pros/cons of either. I know they start to split of in 2nd year and I'd like an opinion of both especially in form of industry. …”
u/Huex3: “… PMATH351 and AMATH350/442/453 should be a core elective if it is not. Quantitative skills are infinitely more important than your degree. Master degree in a quantitative field almost absolutely required. PhD typically required for research level. …”
CS 246 and C++? 1 point, 33 comments
“So as my name says, I am interested in Quantitative Finance. I am currently enrolled in CS 116 (I'm not a first year student, though), because I wanted to learn Python. …”
u/anatomyofafart: “Take CS 476 no matter what. I'm currently taking this class, and it's everything a prospective quant would want out of a course. …”
u/UWquant: “… AMath 342, 442, 351, 353, 453? I.e: Computational Math for DEs (in addition to CS 476 mind you...), ODEs 2, and PDEs? I know Black-Scholes is a PDE; and I really should have taken AMATH 350 instead of 250 -- ... but too late now. …”
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