Teaching
CU-Boulder, APPM 2360: Introduction to Differential Equations with Linear Algebra (Fall 2026)
I am teaching CU-Boulder’s APPM 2360 course this semester. The course is taught out of “Differential Equations & Linear Algebra” by Farlow, Hall, McDill, and West. In Unit 1 of the course, we cover chapters 1-2: the basics of individual ordinary differential equations, mostly first-order linear ones. Unit 2 gives students a crash course on linear algebra (chapter 3 of the book) so that, in unit 3, we have the tools necessary to discuss systems of linear differential equations. I generally like this book quite a lot, but I do disagree with some of the choices made in chapter 3 (how to motivate some ideas, and which concepts to cut over others to condense the material)—Also, it subtly but importantly botches the definition of linear independence/dependence of functions and of the Wronskian. So, I created some notes for my students to have an alternative explanation of the material in case they prefer it over the book. I haven’t done this with every section of the book, just with sections where I especially disagree with the book’s discussion.
I provide these lecture notes here in case others find them helpful, and as something of a teaching demonstration for job applications.
I hand-wrote the originals of these notes. After lecture, I scanned and uploaded them to Claude to typeset a first draft of them. Then, I heavily edited the resulting .TeX source into what you see below.