By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month. Last month I tried to convey why complex numbers should be of interest to someone teaching regular real-valued calculus. This month I want to tackle an even more basic question: How did anybody even think to include the...

By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month./ And now something else remarkable happens. If our function is differentiable at every point inside an open disc that contains x, no matter how small that disc might be, then the second derivative must exist everywhere inside that...