A headline in the New York Times at the end of 2016 said "Growth of U.S. Population Is at Slowest Pace Since 1937". This prompted me to revisit an old chestnut about fitting and extrapolating census data. In the process I have added a couple of nonlinear fits, namely the logistic curve and the double exponential Gompertz model.... 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 >>

The MATLAB functions for the numerical evaluation of integrals has evolved from quad, through quadl and quadgk, to today's integral. ... 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 >>

An interactive graphical experiment lets you discover the value of one of the most important numerical quantities in mathematics. ... 続きを読む >>

Changing the value of a parameter in the equations that produce the famous Lorenz chaotic attractor yields nonlinear ordinary differential equations that have periodic solutions. ... 続きを読む >>

Complex step differentiation is a technique that employs complex arithmetic to obtain the numerical value of the first derivative of a real valued analytic function of a real variable, avoiding the loss of precision inherent in traditional finite differences.... 続きを読む >>

I first investigated the tower of powers... 続きを読む >>

Find the supremum of this function.... 続きを読む >>