Differential Equations: An Introduction for Engineers

This is the free, open-source, open-access textbook that I have created for Math 244 at Rutgers University - New Brunswick. It is based on Notes on Diffy Qs, a text by Jiří Lebl, but with adjustments made to better fit the version of a differential equations course that is run at Rutgers. The main adjustments and improvements to the text are:

• Addition of an appendix on MATLAB, providing an introduction to the basic syntax of coding and the code provided with the course,
• Addition of a section on Mathematical Modeling, including information on parameter estimation and bifurcations for autonomous equations,
• Rearrangement of topics in certain sections, including adding a section on Eigenvalues to the Linear Algebra chapter,
• Snippets of MATLAB code illustrating several concepts,
• Inclusion of a pre-requisite material appendix, containing information about polynomials, complex numbers, and differentiation/integration techniques, and
• Addition of many more exercises throughout the text, all of which have answers included.

The topics in the textbook are:

• First Order Equations
• Second Order Equations
• Linear Algebra
• Linear Systems of Differential Equations
• Non-Linear Systems of Differential Equations

The additional topics from Notes on Diffy Qs are generally covered in our Math 421 class, and so are excluded here.

Versions

The book is currently on version 1.0, released on August 1, 2026. It is available as a

• PDF (532 pages, 12 MB)
• Web version (HTML, created with PreTeXt)

An errata for this version of the book is also available. I’m hopeful that the book is mostly correct, but if you spot any errors, please let me know.