But I argued that it would be more helpful to students’ understanding of the derivative to start with a simpler case first, namely to use only piecewise-linear functions at the beginning.

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

When I first taught high school precalculus, my students couldn’t make heads or tails of piecewise-defined functions. Then I lost a whole lesson to a ramble about federal income taxes — and saw their ...

Stochastic calculus for these processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper. The relevance of the extended ...

We consider piecewise H¹ functions and vector fields associated with a class of meshes generated by independent refinements and show that they can be effectively analyzed in terms of the number of ...