ADDITIONAL MATERIAL
Wikipedia and mathworld on Apéry's constant ζ(3).
More proofs of ζ(2)=∑ 1⁄n² = π²⁄6
can be found here.
Handout "Evaluating ζ(2)=∑ 1⁄n²"
Handout "Evaluating ∫dx⁄(1+x^{4})"
Handout "Singularities"
Here is a Java applet that let's you explore some
Laurent series (author is again Terence Tao).
An animation on what is happening in Question 3 on Exercise sheet 8.
Handout "Analytic Continuation & Riemann's Zeta Function"
Here is a Java applet that let's you explore some multifunctions. By the way, the author is Terence Tao.
Handout showing the
principal values of the logarithm and the square root
Here is a physics YouTube video demonstrating
what you can do with a laminar fluid
Handout "Physical Applications (Fluid dynamics)"
"Mathlets" that demonstrate that f(x)=x sin(1/x) is not differentiable at 0 while g(x)=x^{2} sin(1/x) is, can be found here.
Here is a link to an article that uses level curves to study
Riemann's zeta function (written for students)
Here is a Java Applet that lets you draw the
image of vertical/horizontal lines (and circles) under some
holomorphic functions
Handout "Examples of
holomorphic functions"
Handout "CauchyRiemann revisited"
Here is a really nice YouTube video explaining
Möbius transformations
Handout "Derivative of
f:ℝ^{2}→ℝ^{2}"
Handout "Stereographic Projection"
