Posts

I’ve spent the last two spring semesters teaching ODEs (ordinary differential equations) to a total of about 170 biomedical and chemical engineering majors. The content is dictated by a number of constraints: the perceived desires of the client departments, multiple instructors, all of whom have more experience with the course than I do, and traditional expectations.

I’ve used MATLAB for over 25 years. (And before that, I even used MATRIXx, a late, unlamented attempt at a spinoff, or maybe a ripoff.) It’s not the first language I learned to program in, but it’s the one that I came of age with mathematically.

At long last, I’ve refreshed the look for this site. Previously it was based on a “Metro UI” style for HTML, which looked nice to me at the time. Actually it still looks pretty nice, but it was named for the Metro design introduced with Windows 8, which tells you that it wasn’t exactly a modern look.

For a few years, I’ve been a fan of clickers (aka personal response systems) for large lecture sections. Clickers are a simple–and scalable–way to incorporate a little widespread active learning in the classroom.

I’m going to wrap up the long-paused MATLAB versus Julia comparison on Trefethen & Bau by chugging through all the lectures on iterative methods in one post. I’m back to using gists–not thrilled with any of the mechanisms for sharing this stuff.

I’ve just finished one of the most remarkable fiction reading experiences I’ve had in quite some time: It Can’t Happen Here, by Sinclair Lewis. ICHH is a satirical novel written and set in 1935 America.

Part V of T&B is on dense methods for eigenvalue and singular value problems. For my course, this is the part of the text that I condense most severely. In part that’s due to the need to cover unconstrained nonlinear solving and optimization stuff later on.

Three in one this time: Lecture 20, which is on Gaussian elimination / LU factorization, Lecture 21, on row pivoting, and Lecture 23, on Cholesky factorization. I mainly skipped over Lecture 22, about the curious case of the stability of pivoted LU, but the main example is dropped into the end of my coverage of pivoting.

Here are the notebooks in MATLAB and Julia. The new wrinkle in these codes is extended precision. In MATLAB you need to have the Symbolic Math toolbox to do this in the form of vpa.

I’ve run into trouble managing gists with lots of files in them, so I’m back to doing one per lecture. Here are Lecture 12 and Lecture 13. We’ve entered Part 3 of the book, which is on conditioning and stability matters.