A First Course in Differential Equations for Scientists and Engineers • Hacker News Board

Re: A First Course in Differential Equations for Scientists and Engineers

#11

Post by saagarjha » Wed, Sep 05, 2018, 8:01 PM UTC

spapas82 wrote: post #5

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... ). 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 real…

Ugh, I hated that book. It never went into any detail in its “solutions” and the whole thing seemed like a bag of tricks for solving whatever example they were currently showing. Plus I had to deal with the monstrosity that is WileyPLUS.

Re: A First Course in Differential Equations for Scientists and Engineers

#12

Post by sampo » Wed, Sep 05, 2018, 8:04 PM UTC

jamescostian wrote: post #9

spapas82 wrote: post #5

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... ). 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 real…

> 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)

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.

Re: A First Course in Differential Equations for Scientists and Engineers

#13

Post by bgorman » Wed, Sep 05, 2018, 8:07 PM UTC

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/

Re: A First Course in Differential Equations for Scientists and Engineers

#14

Post by sampo » Wed, Sep 05, 2018, 8:14 PM UTC

gmiller123456 wrote: post #6

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...

While the linked course notes (I looked at the pdf, definitely good textbook quality and not just course notes, really) are absolutely more thorough in the classical undergrad diff.eq. topics, the Udacity course touches some further topics (stiffness, implicit methods, control theory) that the course notes don't.

Re: A First Course in Differential Equations for Scientists and Engineers

#15

Post by Luc » Wed, Sep 05, 2018, 8:14 PM UTC

sampo wrote: post #8

Luc wrote: post #4

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?

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,…

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

Re: A First Course in Differential Equations for Scientists and Engineers

#16

Post by TomMckenny » Wed, Sep 05, 2018, 8:16 PM UTC

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?

Re: A First Course in Differential Equations for Scientists and Engineers

#17

Post by rhaps0dy » Wed, Sep 05, 2018, 8:19 PM UTC

TomMckenny wrote: post #16

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?

you can use LaTeX notation and then render it with something.

For example MathJax, or emacs's org-preview-latex-toggle to show the rendered equations in the same buffer you write in.

Re: A First Course in Differential Equations for Scientists and Engineers

#18

Post by schitzapplebits » Wed, Sep 05, 2018, 8:21 PM UTC

TomMckenny wrote: post #16

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?

Don’t. Pay attention, write down the things that aren’t in the text book. And then learn to read the text book. It’s a hugely valuable skill.

Re: A First Course in Differential Equations for Scientists and Engineers

#19

Post by tanderson92 » Wed, Sep 05, 2018, 8:23 PM UTC

saagarjha wrote: post #11

spapas82 wrote: post #5

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... ). 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 real…

Ugh, I hated that book. It never went into any detail in its “solutions” and the whole thing seemed like a bag of tricks for solving whatever example they were currently showing. Plus I had to deal with the monstrosity that is WileyPLUS.

ODEs as taught in a first-course undergraduate course is precisely a bag of tricks.

Re: A First Course in Differential Equations for Scientists and Engineers

#20

Post by takk309 » Wed, Sep 05, 2018, 8:25 PM UTC

TomMckenny wrote: post #16

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?

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.