A very basic book on mathematical modeling My question is relatively simple: what introductory textbooks on mathematical modeling exist out there that require only a background in calculus and linear algebra (but do not require that the reader has attended a course in differential equations per se)?
The only two such textbooks that I know of are Kai Velten's "Mathematical Modeling and Simulation" and Giordano et al's "A First Course in Mathematical Modeling". Giordano is great at building intuition but is outrageously expensive, and Velten - though being a wonderful book - sometimes approaches topics too abstractly given his intended audience or, rather, fails to appropriately expound on certain abstract definitions.
As such, I'm looking for additional sources that meet these criteria.
 A: There is the fantastic book 'Mathematical Modeling' by Ecke, Garcke and Knabner. It just came out two weeks ago in English (before it was published in German). We used it in a course on mathematical modeling in university and there was no prerequisite on ODEs (but of course it helps and I'd recommend that you have an ODE book as a reference). The table of content is as follows:


*

*Introduction/Motivation

*Systems of Linear Equations

*Basic Principles of Thermodynamics

*ODEs

*Continuum Mechanics

*PDEs

*Free Boundary Problems

A: I believe this is a good choice.
Elizabeth S. Allman and John A. Rhodes (2006) Mathematical Models in Biology: An Introduction, Cambridge University Press.
This book is used as the text for a freshman level applied mathematics course at my university. It is very readable and requires no background in calculus or linear algebra. It starts with difference equation, which I believe is probably the best place to start for modeling in general. The aim is toward biological processes, but the technique provided is applicable to other areas. In fact, it builds up to some major tools like Markov model and has additional computation component to it. The explanation is intuitive. You will find it to be a great place to start.
