Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Math Club


Thursday, February 6th, 2020

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 110

Speaker: Francesco Cellarosi (Queen's University)

Title: Breaking the Fundamental Theorem of Calculus?

Abstract: In this talk we will ‘challenge’ the statement of the Fundamental Theorem of Calculus for the Riemann integral by constructing:

  • a function $g$ such that $G(x)=\int_0^x g(t)dt$ exists for all $x\in\mathbb R$ but $G$ is not differentiable at many points.
  • a differentiable function $F$ such that $\int_0^x F’(t)dt\neq F(x)-F(0)$.

To do so, we will use some ill-behaved functions constructed by B. Riemann and V. Volterra.