Help me teach myself partial differential equations

August 9, 2018 11:35 AM

After a long slog, I'm finally one credit short of graduating! I have a math elective left, and the most efficient/affordable way to do this is by earning credit for Calculus IV (a.k.a. PDEs) through a placement exam in about three weeks. But it's been a few years since I've done any math in earnest, and working through the textbook is proving to be a nightmare. Please recommend some resources for self-teaching!

I'm a quick study, I used to be pretty sharp at math, and this is the only thing I have to do over the next few weeks. Since I only need to do well enough to pass, I'm not overly concerned about the time frame, provided I can find a good resource to learn from.

The syllabus for the exam is based on Haberman's Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition, but it's kind of a nightmare to work through. To make things worse, the only solutions I can find for the textbook are behind a paywall.

Khan Academy is sorely lacking on this subject, sadly, so I'm reaching out to the AskMeFi hive mind for any solid, well-made, and (ideally) free resources on the subject. I'm not picky about the medium – interactive, video, or text are all great, as long as they're well-made and understandable.

posted by amohield to Education (15 answers total)

Where are you located? In the US, PDE's are not the same as Calculus IV at any school that I know of. This might explain Khan Academy's lack of helpful content.
Have you tried Mathworld?
posted by MillyMath at 11:48 AM on August 9, 2018

Response by poster: MillyMath, I'm at the University of Pennsylvania. Peep the syllabus if you want more detail, but apparently Calculus IV = PDEs here.

I took a glance at Mathworld, but I couldn't find anything about PDEs beyond this page?
posted by amohield at 11:53 AM on August 9, 2018

MIT OpenCourseWare: Introduction to Partial Differential Equations
Saylor.org MA222: Introduction to Partial Differential Equations
posted by the man of twists and turns at 11:58 AM on August 9, 2018 [2 favorites]

Best answer: Unfortunately, as opposed to a lot of other areas of math, PDEs are very non-general, in that every class of PDE turns out to be wildly different in the techniques you use to solve it (although there are a few standard tricks that come up frequently). Even researchers in the field tend to specialize in a particular type of PDE rather than PDEs in general. So my main advice (which you are probably already taking) is to learn exactly the subjects that will be on the exam, because if you just start learning some PDE material from somewhere else, you may find that you "wasted" a lot of time on very specific techniques that have no chance of appearing on the test.

That said, I like Farlow's Partial Differential Equations for Scientists and Engineers, and it's cheap for a textbook. Again, I would use it primarily to supplement the official material.

(I assume that you are already quite familiar with ordinary differential equations or this is going to be tough.)
posted by dfan at 12:24 PM on August 9, 2018

You have not told us what we need, or what you are doing in enough detail.

Are you trying to gain entry to this calc iv class, or are you looking for resources to learn that syllabus without talking to your instructor?

This syllabus is basically PDE lite; much like pre-calc is often advanced algebra, trig, and analytic geometry.

But since I can not determine if you need resources to cover this class or to prepare for an entrance exam, I cannot help further.
posted by SaltySalticid at 2:36 PM on August 9, 2018 [1 favorite]

It reads to me like you need to pass this exam to get credit for PDE so you can get admission to another course. Is that right? If so, I would caution you to make sure that prepping to pass the exam will also mean you have prepped enough to actually use the PDE stuff in your next/final course. I once slogged through some math classes that hinged on bits of calculus I didn’t remember all the way (or had never learned, in the version of the prerequisite I’d taken) and god, it was so painful. I’d been okay at math years prior but it does fade. You don’t want to fail your last course in college, or come close, because of half forgotten calculus.
posted by eirias at 3:00 PM on August 9, 2018

Response by poster: Clarification: All that stands between me and graduation is a single math class. I'm taking this exam instead of taking the class.

In other words, if I pass this exam, I will be granted the credit for that class without having to take the class, and I can immediately graduate. Otherwise, I'd have to stay an extra semester, which is not ideal financially or personally.

I'm not planning on taking any more classes or entering a field that depends on this material, so I just need enough mastery to pass the exam.

I should have been more clear about this in the first post, so I'm sorry about that!
posted by amohield at 3:58 PM on August 9, 2018 [1 favorite]

Best answer: If it's not apparent to you, neither of the man of twists and turns's links are to PDE courses at the level you're looking for--they're aimed at math majors who've taken real analysis.

FWIW, there are old final exams available for that course which will hopefully give you some idea of what to expect. Unfortunately, I never attended a university that devoted a semester to PDEs at this level, so I don't really have anything for you.
posted by hoyland at 4:54 PM on August 9, 2018 [1 favorite]

Is it an option to find someone who has recently taken the class and has good notes?
posted by batter_my_heart at 6:16 PM on August 9, 2018 [2 favorites]

Best answer: Can you afford some tutoring? A grad student who’s taken this class or senior undergrad could probably help you with putting together a plan.
posted by Valancy Rachel at 8:07 PM on August 9, 2018

Engineering uses lots of PDEs, a very cursory google pulled up this university help sheet which may help steer you in the right direction, provided you've got differentiation down.
posted by london explorer girl at 8:56 AM on August 10, 2018

Rifting on tutoring, how about hiring a recent TA from this course as your tutor?
posted by bdc34 at 11:24 AM on August 10, 2018

Hacker News A First Course in Differential Equations for Scientists and Engineers (uncw.edu)
posted by the man of twists and turns at 1:29 PM on September 5, 2018

the man of twists and turns: the OP is taking an exam in the field of partial differential equations, which is more advanced and significantly more annoying than introductory single-variable differential equations.

(Also, the exam would have been around a week ago, if it took place three weeks from August 9. I hope that if they took it they did well!)
posted by dfan at 7:03 AM on September 8, 2018

Best answer: Hi folks,

Thanks so much for your answers! The tutors available to me ended up being way, way out of my price range.

So I spent a frenzied two weeks teaching myself from the course textbook and syllabus, as some of you pointed out that the field of PDEs is vast and I'd do well to stick to the material the syllabus outlined.

The resources you guys pointed me to, plus a healthy dollop of Paul's Online Math Notes, were a huge aid.

I learned a lot before the placement exam, but unfortunately I missed passing by just a few points. :(

I'm still very grateful, though! I've been taking the class this semester.

Thanks to how your suggestions influenced my studying, I've been doing pretty well in the class, including a 96% on the first midterm that I'm particularly proud of.

Thank y'all for all your help again! :)
posted by amohield at 1:48 PM on November 28, 2018