11 problems.
- Complex differentiability via small circle integrals — Problem 1
- Cauchy’s integral formula for an exterior region
- Liouville’s theorem via \(\int_{|z|=R}\frac{f(z)}{(z-a)(z-b)}\,dz\) — Problem 3
- Entire functions with \(f(z)/z\to0\) are constant — Problem 4
- \(\int_\gamma\frac{f'(z)}{z-z_0}\,dz=\int_\gamma\frac{f(z)}{(z-z_0)^2}\,dz\) — Problem 5
- \(\int_0^{2\pi}\cos^{2n}\theta\,d\theta\) via a contour integral — Problem 6
- Fresnel integrals \(\int_0^\infty\sin(x^2)\,dx=\int_0^\infty\cos(x^2)\,dx=\frac{\sqrt{2\pi}}{4}\)
- \(\int_0^\infty\frac{\sin x}{x}\,dx=\frac\pi2\) — Problem 8
- Goursat’s theorem for \(C^1\) functions via Green’s theorem
- Goursat’s theorem with one exceptional point — Problem 10
- Cauchy estimates for derivatives of polynomially bounded functions on a strip — Problem 11