This is an Annotated Bibliography for my Math 259 Linear Algebra and Differential Equations course at the Bilgi University in Fall 2011.
- Jiri Lebl, Notes on Diffy Qs, http://www.jirka.org/diffyqs/diffyqs.pdf
These notes by Jiri Lebl will be our main reference for the course. These are a very readable set of notes, much lighter to carry than all of the standard texts on differential equations also they are free.
This is Jiri Lebl’s web site dedicated to the Notes on Diffy Qs. You can also find the related software here.
- Bob Terrell, Notes on Differential Equations, http://www.math.cornell.edu/~bterrell/dn.pdf
This is a wonderful set of notes by Bob Terrell. He explains how to read differential equations, perhaps the most important skill you will need about differential equations. This is a fun text to read, it is as interactive a text on paper can get. If you follow his advice and do the exercises as asked, you will have a good understanding of a differential equation.
This set of notes are perhaps the easiest to read by yourself.
Here you can find Bob Terrell’s web page, which contains software on differential equations. One of the nice sides of differential equations is that they can be visualized, and many tools are available.
- Mike Brown, Ge 108: Applications of Physics to the Earth Sciences, http://www.gps.caltech.edu/~mbrown/classes/ge108
If you read only few pages from Mike Brown’s notes, read the first lecture how an equation about population decay is formed. Same equation appears under the name Banker’s Equation in Bob Terrell’s notes. The two equations essentially differ only by a sign.
- F. Patrone, Introduction to modeling via differential equations, http://www.diptem.unige.it/patrone/differential_equations_intro.htm
Title explains is all. This is a short write-up which describes how one forms a differential equation to model a certain process. In the meantime, Patrone describes the crucial attributes in the theory of differential equations, existence, uniqueness, continuous dependence on the initial data etc.
In this issue, it collects all articles that are published in Plus on Mathematical Modeling.
- A. C. Fowler, Techniques of Applied Mathematics, http://people.maths.ox.ac.uk/fowler/courses/tech/technotes.pdf
This is the most advanced text of all. Still a pleasure to read. Would be educative to read the first chapter, Introduction, if nothing else.