A First Course in Differential Equations for Scientists and Engineers
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Re: A First Course in Differential Equations for Scientists and Engineers
#2Collection of PDFs, more/less like a textbook. Looks worthwhile.
Re: A First Course in Differential Equations for Scientists and Engineers
#3On 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.
Re: A First Course in Differential Equations for Scientists and Engineers
#4Lately 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?
Re: A First Course in Differential Equations for Scientists and Engineers
#5We 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 really don't think that such topics can be self-studied. It seems really difficult to me to understand such topics without a teacher!
Re: A First Course in Differential Equations for Scientists and Engineers
#6While 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...
Re: A First Course in Differential Equations for Scientists and Engineers
#7Look at Arnold's book on Diff, it is harder then others, but has absolutely different outlook.
Re: A First Course in Differential Equations for Scientists and Engineers
#8Lately 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, diseases and epidemiology, and sometimes also a chapter on chemical kinetics (these are all modelled with differential equations).
Re: A First Course in Differential Equations for Scientists and Engineers
#9We 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)
Re: A First Course in Differential Equations for Scientists and Engineers
#10IMO, Paul's notes http://tutorial.math.lamar.edu/Classes/DE/DE.aspx are a lot easier to use.