The files below were on my teaching page when I was a college teacher. Since I retired, they disappeared. Samuel Lelièvre found an archived copy on the web, so I’m posting them here.
The files are licensed under the Attribution-ShareAlike Creative Commons license.
- Partial fractions handout, pdf
- Introduction to matrix determinants handout, pdf
- Impulse-response handout, pdf
- Introduction to ODEs, pdf
- Initial value problems, pdf
- Existence and uniqueness, pdf
- Euler’s method for numerically approximating solutions to DEs, pdf.
Includes both 1st order DE case (with Euler and improved Euler) and higher order DE and systems of DEs cases, without improved Euler.
- Direction fields and isoclines, pdf
- 1st order ODEs, separable and linear cases, pdf
- A falling body problem in Newtonian mechanics, pdf
- A mixing problem, pdf
- Linear ODEs, I, pdf
- Linear ODEs, II, pdf
- Undetermined coefficients for non-homogeneous 2nd order constant coefficient ODEs, pdf
- Variation of parameters for non-homogeneous 2nd order constant coefficient ODEs, pdf.
- Annihilator method for non-homogeneous 2nd order constant coefficient ODEs, pdf.
I found students preferred (the more-or-less equivalent) undetermined coefficient method, so didn’t put much effort into these notes.
- Springs, I, pdf
- Springs, II, pdf
- Springs, III, pdf
- LRC circuits, pdf
- Power series methods, I, pdf
- Power series methods, II, pdf
- Introduction to Laplace transform methods, I, pdf
- Introduction to Laplace transform methods, II, pdf
- Lanchester’s equations modeling the battle between two armies, pdf
- Row reduction/Gauss elimination method for systems of linear equations, pdf.
- Eigenvalue method for homogeneous constant coefficient 2×2 systems of 1st order ODEs, pdf.
- Variation of parameters for first order non-homogeneous linear constant coefficient systems of ODEs, pdf.
- Electrical networks using Laplace transforms, pdf
- Separation of variables and the Transport PDE, pdf
- Fourier series, pdf.
- one-dimensional heat equation using Fourier series, pdf.
- one-dimensional wave equation using Fourier series, pdf.
- one-dimensional Schroedinger’s wave equation for a “free particle in a box” using Fourier series, pdf.
- All these lectures collected as one pdf (216 pages).
While licensed Attribution-ShareAlike CC, in the US this book is in the public domain, as it was written while I was a US federal government employee as part of my official duties. A warning – it has lots of typos. The latest version, written with Marshall Hampton, is a JHUP book, much more polished, available on amazon and the JHUP website. Google “Introduction to Differential Equations Using Sage”.
Course review: pdf
Love, War, and Zombies, pdf
This set of slides is of a lecture I would give if there was enough time towards the end of the semester