References on continuum based mathematical modelling and computation.

1. Neil Gershenfeld.
The Nature of Mathematical Modeling
Publisher: Cambridge University Press (November 28, 1998)
ISBN: 0521570956
Nice condense book covering "everything" needed for a simulation of reality.
No depth of course, but good - although a bit old - "selected references".
Ch: 2-8
Mathematical models (ODEs, PDEs, variational methods and stochastic systems) 
Numerical models (FD in time and space, FE, (and CA and LG))
(Observational models (all kinds of nice tools to fit experimental and model
results))

Background reading:
-------------------
Eriksson, Estep, Johnson.
Applied Mathematics: Body and Soul
Vol.I-III
Basics of calculus and linear algebra, with applications.
Very elaborate, but easy to read. Wrt numerical methods biased to FE.
(see http://www.phi.chalmers.se/bodysoul/)

Dahlquist, Bjorck
Numerical Methods
Prentice Hall (1974)
Old but good; numerical analysis "in general"
Approximation, numerical algebra, nonlinear equations, FD, DE, Fourier

And then, of course ...
-----------------------
William H. Press, Saul A. Teulosky, William T. Vetterling, Brian P. Flannery
Numerical Recipes in C, Fortran, ...
Publisher: Cambridge University Press
Free available: C, Fortran 77 and Fortran 90
http://www.nr.com/
Well-known set of programs + some background material


-- 
Joke Blom, M263a / CWI / Kruislaan 413 / 1098 SJ Amsterdam / the Netherlands
email: gollum@cwi.nl         phone: +31 20 592 4263        fax: +31 20 592
4199
URL: http://www.cwi.nl/~gollum/