
A First Course in Differential Equations for Scientists and Engineers - lainon
http://people.uncw.edu/hermanr/mat361/ODEBook/
======
gmiller123456
While the linked course seems a lot more thorough, I took the Udacity
"Differential Equations in Action" [1] course, which I found very well done.
For the homework you write Python programs to compute things like
gravitational slingshots, modeling epidemics, wildfires, and the n-body
problem.

[1] [https://www.udacity.com/course/differential-equations-in-
act...](https://www.udacity.com/course/differential-equations-in-action--
cs222)

~~~
nraynaud
Can we get to the text and videos without all the school-ish crud? (starting a
course, timelines etc.)

~~~
gmiller123456
Yes [1]. I haven't taken a Udacity course in quite a while, but at the time
all of their videos were hosted on Youtube, so you should be able to find a
lot of their courses just on Youtube. For the homework, I remember there was
an include file that they didn't provide the source code for, but a Google
search turned up a version someone wrote for using it locally. Usually it's
pretty obvious when you've solved the problem and have the correct code, but
to make absolutely sure, you have to upload your code to their server for
verification. But you can take the whole class without ever visiting Udacity.

[1]
[https://www.youtube.com/watch?v=8cLXVG2Q6D4&list=PLAwxTw4SYa...](https://www.youtube.com/watch?v=8cLXVG2Q6D4&list=PLAwxTw4SYaPlT4WYwf_SzNA9FV0qpGE5A)

~~~
nraynaud
thanks!

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tzs
Speaking of differential equations, an oldie (1997) but goodie, "Ten Lessons I
Wish I Had Learned Before I Started Teaching Differential Equations" by Gian-
Carlo Rota:
[https://web.williams.edu/Mathematics/lg5/Rota.pdf](https://web.williams.edu/Mathematics/lg5/Rota.pdf)

~~~
gp7
> 4\. Teach Changes of Variables

As someone who has basically no formal training in mathematics outside what's
required for undergraduate computer science this is a big one. The first time
I saw it I was blown away. Everyone who knows of it seems to treat it as
natural as breathing, and not worth the exposition

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sizzzzlerz
I took DiffEq as an EE undergrad and, to my surprise, aced the course. For
some reason, the concepts just resonated with me unlike other math courses
where I had to work to gain an understanding of the material. A few years
later, after graduating, I was taking courses leading to an MSEE and Partial
DiffEq was offered as an option that I took. Thinking it was going to be
similar to regular DE, I was soon in way over my head. Totally different
material and concepts. I did end up passing the course but I can honestly
state that I don't think I deserved it.

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spapas82
We used the Boyce and DiPrima book back when I was an electrical engineering
student (Elementary Differential Equations and Boundary Value Problems
[https://www.amazon.com/Elementary-Differential-Equations-
Bou...](https://www.amazon.com/Elementary-Differential-Equations-Boundary-
Problems/dp/0471089559)).

I remember it was an excellent book with many great examples and correlation
with physics topics like mechanics, waves etc. Too bad our other mathematics
books weren't at this high standard :/

Also, I really don't think that such topics can be self-studied. It seems
really difficult to me to understand such topics without a teacher!

~~~
jamescostian
> I really don't think that such topics can be self-studied

Can you explain this? What makes something extremely difficult to be studied
without a teacher? (I took calc in high school and never took diff eq, so my
knowledge in this specific domain is basically zero)

~~~
sampo
If you have some mathematical maturity (you can read notation, work to
understand each equation, have the patience to pretty much understand each
equation and each page, because later ideas are built on understanding the
previous ideas first), you can self-study a lot of mathematics. But almost
everyone (mathematicians, physicists, engineers) who has that maturity, has
probably taken a first course in differential equations during their undergrad
studies.

So the number of people who have developed some mathematical maturity without
ever taking a diff.eq. course is probably small. So we don't know much about
these people and how the topic of differential equations appears to them.

But yes, it would be interesting to hear about experiences from someone with
e.g. a strong background in theoretical computer science, probably including
calculus but not including diff.eqs., who has self-studied a book on
differential equations.

~~~
kenjackson
I had self-studied this and then later studied under a teacher as well.

I think the thing that I found hardest in my self-study was (and unfortunately
this is about 25 years ago so my recollection might be a bit off) that it
seemed like there was a lot written on just two equations (the heat equation
and the wave equation). I didn't get why is 50 pages dedicated to one
equation. Up until that point it felt like Calculus was about techniques to
solve equations, and then it suddenly became mostly about how to solve these
two equations (there was a third, but I can't recall what it was now), which
never really resonated with me.

~~~
sampo
Heat equation / diffusion equation (same thing): parabolic.

Wave equation: hyperbolic.

Laplace's equation: elliptic. Laplace's equation is the steady state
(equilibrium) solution of heat equation when the boundary conditions (or
anything) don't change in time.

~~~
kenjackson
Thanks. And yes, Laplace was the third one. I think even your simple
categorization would have made things much simpler for me. Or maybe I was just
an idiot as an undergrad. :-)

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alexibm
Look at Arnold's book on Diff, it is harder then others, but has absolutely
different outlook.

~~~
selimthegrim
That book is totally mindblowing, and obliterates artificial boundaries
between physics and mathematics. It also (in the older Dover editions) had a
cover where the phase portrait on the front looked like two angry eyes glaring
at you that you hadn't learned enough math yet.

~~~
Koshkin
Well, modern theoretical physics seems to be nothing but mathematics (mostly
advanced differential geometry and group theory). And this is a good thing, as
it is the sign of how far along the subject has gone in its evolution. The
theory of differential equations also reduces to differential geometry, which
is what Arnold’s book seems to be striving to show, as does his other
excellent text on mathematical principles of classical mechanics.

------
gattr
On a related note, I can recommend Stanley J. Farlow's "Partial Differential
Equations for Scientists and Engineers", which I bought around 2004 to better
understand a fluid simulation paper I was trying to implement. (My Maths
course ended with linear algebra and ODEs). Very good read with nice physics
examples.

------
qwerty_danny
IMO, Paul's notes
[http://tutorial.math.lamar.edu/Classes/DE/DE.aspx](http://tutorial.math.lamar.edu/Classes/DE/DE.aspx)
are a lot easier to use.

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fizixer
The usage of terms 'initial value' and 'boundary value' is a massive failure
of mathematics education.

'Initial' refers to time-like variables, and 'boundary' refers to space-like
variables.

There is no notion of time in mathematics. There is only a notion of space,
due to geometry. I had the longest time coming to grips with the question,
"mathematically what is the difference between initial value and boundary
value?" only to realize the distinction is meaningless in mathematics. It's a
relic of the past when differential equations were studied under physics,
where time and space are a huge part of the conceptual foundation.

Sometimes I wonder how much progress we would make in education if we didn't
confuse the heck of our students in the name of convention and historical
baggage.

~~~
ASipos
Since time is 1D while space may have more dimensions, initial values are
connected to ODEs while boundary ones with PDEs. Their behavior is quite
different.

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mindcrime
Huh... didn't expect to find a UNC-Wilmington link on HN today. I vaguely
remember Dr. Herman. I think we used one of his other books in a class, or
maybe he taught one of my classes. This brings back memories.

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miles_matthias
This was my favorite course in college. Super beneficial materials.

On a side note, one of the reasons I loved this course was because it was
online and only had 2 tests with no other assignments. The professor allowed
you to schedule office hours any time you needed, but the course setup was
sweet for self-studiers like me. Here's the book, Chapters 1-10 are on the
midterm, Chapters 10-20 are on the final. No homework busy work, no other
tests. Just 2 exams. Go.

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bgorman
When I was in college I supplemented my learning with Notes on Diffyqs, which
I thought explained things much clearer and concisely than my assigned
textbook. It is available for free and has tools for modeling systems in
Octave/Matlab.

[https://www.jirka.org/diffyqs/](https://www.jirka.org/diffyqs/)

------
TomMckenny
On a related note, how do you take notes for math subjects with their
multiline integrals and sumation and subscripts, division etc?

I'm very much attached to recording every thing in simple text editors. Is
there a "Notepad" or "TextEdit" for mathematical notation?

~~~
takk309
I could not imagine trying to take notes with a computer in a math heavy
subject. I had to use paper for everything during my undergrad in Civil
Engineering. However, if you already have a computer with you, record the
lecture and review it later.

~~~
mclehman
Just as a partial counterpoint to this and overall agreement with everyone
else who responded, I've had success taking realtime notes on my laptop in a
math class. It took a bit of practice and I'm sure I can't do it anymore, but
it's not insurmountable by any means.

I used latex and made liberal use of keyboard and software macros to do it,
and one of the tricks was to realize that if I needed a quick-to-type way to
typeset new thing X, I should just pretend I had such an implementation and
make up its command on the spot. At my leisure, I could write up a conforming
latex command that worked with all the notes I'd taken in realtime.

That said, I've since come to realize that math notes don't help me as much as
they seem to help others. I have greater success primarily listening during
class and leaning on the textbook as well as online resources outside of
class. I do second the use of emacs to handle the latex, but I don't think
that realtime rendering is particularly important in a notes setting.

~~~
takk309
Excellent counterpoint. Keep in mind that I was a Civil Engineering student,
not computer science. My abilities to use Latex were little-to-none at the
time. I didn't get any exposure to it until I was in grad school and we used
it to format journal article submissions.

------
Luc
Lately I have been looking for a practical (not too much theory) book on how
to model problems with differential equations, with lots of examples. I
imagine I'd plug them into Wolfram Alpha to get a solution.

Does anyone have recommendations?

~~~
sampo
Almost all textbooks named "Mathematical Modeling" should have chapters on
modelling continuous change with differential equations, hopefully also a
chapter on how to model systems of interacting variables with a system of
differential equations.

Then also textbooks with names like "Mathematical Models in Biology" or
"Mathematical Biology" should have chapters on population growth, a two-
species predator-prey model, diseases and epidemiology, and sometimes also a
chapter on chemical kinetics (these are all modelled with differential
equations).

~~~
Luc
Thank you. Knowing the right search terms will help a lot.

------
ericand
Collection of PDFs, more/less like a textbook. Looks worthwhile.

