##### Personal tools
You are here: Home Undergraduate Mathematics Seminar

— filed under:

Everywhere Continuous, Nowhere Differentiable Functions, by Michael McLaughlin (Ohio University, Mathematics)

What Seminar Mar 13, 2013 from 04:10 PM to 04:55 PM 226 Morton Hall Martin Mohlenkamp vCal iCal

Abstract: In a standard calculus course, one learns that the properties of continuity and differentiability are inherently related, i.e. a differentiable real-valued function is continuous. It is also understood that the converse is not necessarily true. This property begs the question, “Can a function be continuous everywhere, but differentiable nowhere?” In fact, the answer to this question is positive, which can be surprising. Nevertheless, Karl Weierstrass constructed his now-famous “Weierstrass function” which exhibits this property. In this seminar, I will discuss the properties of everywhere continuous, nowhere differentiable functions and I will prove the nowhere differentiability of the Weierstrass function. If time remains, continuity will also be discussed.

« October 2014 »
October
MoTuWeThFrSaSu
12345
6789101112
13141516171819
20212223242526
2728293031