I am very excited to incorporate sound in animations. This blog post has five examples with links to videos enclosed in '+ + + +'.... 続きを読む >>

The Swinging Sticks is a kinetic sculpture that exhibits chaotic motion. The device became very popular after it upstaged Tony Stark in Iron Man 2. My daughter Carolyn gave me a desktop version of Swinging Sticks for Christmas. I immediately set out to simulate it.... 続きを読む >>

This is post number 300 of Cleve's Corner blog. The first post was on June 6, 2012, which is 600 weeks ago. So, I have averaged one post every two weeks for over a decade. The posts were more frequent in the early days and are less frequent today.... 続きを読む >>

Recently, I had email from a student in Italy.... 続きを読む >>

I am working with Indika Rajapakse and Steve Smale to investigate the stability of the dynamic system describing Kuramoto oscillators. Indika and Steve are interested in Kuramoto oscillators for two reasons; the self synchronization provides a model of the cells in a beating heart and the dynamic system is an example for Morse-Smale theory. I am personally interested in the Kuramoto model as it relates to deep brain stimulation (DBS) for open-loop control of human movement disorders. My kuramoto program demonstrates both stable and unstable critical points. Roundoff error may destabilize an unstable critical point.... 続きを読む >>

The ACM Special Interest Group on Programming Languages, SIGPLAN, expects to hold the fourth in a series of conferences on the History of Programming Languages in 2020, see HOPL-IV. The first drafts of papers are to be submitted by August 2018. That long lead time gives me the opportunity to write a detailed history of MATLAB. I plan to write the paper in sections, which I'll post in this blog as they are available.... 続きを読む >>

Three-term recurrence relations are the basis for computing Bessel functions. Contents A Familiar Three-Term Recurrence Friedrich Bessel Bessel Functions Miller's Algorithm ... 続きを読む >>

My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides a nice illustration of the underlying existence theory and error analysis.... 続きを読む >>

Gil Strang has produced a MOOC-style video course on Differential Equations and Linear Algebra. I have added some videos about the MATLAB ODE suite. The series is available from the MathWorks Web site, MIT OpenCourseWare and several other popular sources.... 続きを読む >>

A rectangular box, such as a book or a cell phone, thrown in the air can tumble stably about its longest axis, or about its shortest axis, but not about its middle axis.... 続きを読む >>