The more I teach linear algebra, the more I think that perhaps it -- and not calculus -- ought to be the standard introductory math course for those majoring in “technical” fields (science ...

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.

Such functions are called linear, for reasons that I'll explain soon enough (well, we generally want another condition for linear functions involving scalar multiples of the variable, but I'll ...