12 problems.
- The Laplacian under a holomorphic change of variables — Problem 1
- Harmonicity of \(U(x^2-y^2,2xy)\) — Problem 2
- The ratio limit bounds the root limit
- A power series has an expansion about every point of its disc of convergence
- Convergence of \(\sum nz^n\), \(\sum z^n/n^2\), and \(\sum z^n/n\) on the unit circle — Problem 5
- Continuity of the Riemann zeta function on \(\operatorname{Re} z>1\) — Problem 6
- Radius and boundary convergence of \(\sum\frac{(-1)^n}{n}z^{n(n+1)}\) — Problem 7
- \(e^z=\lim_{n\to\infty}(1+z/n)^n\) — Problem 8
- Real and imaginary parts of \(\sin z\) and \(\cos z\) and their unboundedness — Problem 9
- Poles of \(\tan z\) at odd multiples of \(\pi/2\) and their residues — Problem 10
- \(\int_{|z|=r}\frac{dz}{(z-\alpha)(z-\beta)}\) for \(|\alpha|<r<|\beta|\) — Problem 11
- Limit of integrals over vertical segments when \(f(x+iy)\to A\) uniformly — Problem 12