Which Books Focus on the Formulation of Differential Equations?

[avarmaavarma]

I have seen a few articles outlining the 'derivation' of certain differential equations - e.g. Heat flow equation, vibrating string wave equation etc.

Does this correctly fall under 'mathematical modeling of physical phenomenon?

Can anyone recommend a book that deals primarily with such derivations - I.e. The original formulation of the DE or the PDE - not so much the solutions of the equations.

Any mathematical publications ( magazines) that are relevant would also be appreciated.

Thanks

 

[SteamKing]

I have seen a few articles outlining the 'derivation' of certain differential equations - e.g. Heat flow equation, vibrating string wave equation etc.

Does this correctly fall under 'mathematical modeling of physical phenomenon?

Can anyone recommend a book that deals primarily with such derivations - I.e. The original formulation of the DE or the PDE - not so much the solutions of the equations.

Any mathematical publications ( magazines) that are relevant would also be appreciated.

Thanks

It depends on what you're looking for. Most texts discussing heat flow or vibration, for example, contain derivations of the basic equations governing such phenomena from first principles. If you are interested in a particular topic, you can usually find an article by doing a web search. If you are looking for a text which covers a variety of topics, most physics texts, at least the ones which are calculus-based, have the derivation of the basic equations.

You need to find an academic text, rather than one which is geared to a general reading audience and which contains minimal mathematics.

 

[avarmaavarma]

Thanks. I do have such academic texts - and am able to find bits and pieces here and there. However, the closest thing I got to what I was looking for was -'Mathematical modeling techniques' a dover text. Am still curious to see if other books deal with this topic singlepointedly...thanks

 

[bigfooted]

Partial differential equations by Walter Strauss treats the mathematics of PDE's and also derives the PDE's from basic principles (It takes him less then half a page each). The vibrating string, and heat conduction are derived in chapter 1. He then spends half of the book explaining how to solve these equations for different boundary conditions.
Most PDE's are derived in the introduction chapter of a book dealing only with that specific equation, e.g. the navier stokes equation in a book on fluid dynamics, or the Schrödinger equation in a quantum mechanics book. Like SteamKing said, it depends on what you're looking for.