13 problems.
- State the Casorati–Weierstrass theorem — Section 1.1, item 1
- State the Residue Theorem — Section 1.1, item 2
- State the most general version of Cauchy’s Theorem — Section 1.1, item 3
- State the Open Mapping Theorem — Section 1.1, item 4
- Examples of removable, pole, and essential singularities at the origin — Section 1.2, item 1
- Cauchy–Riemann equations everywhere do not imply analyticity — Section 1.2, item 2
- An entire function with real part bounded above is constant — Section 1.3, problem 1
- Unions and intersections of two simply connected planar domains — Section 1.3, problem 2
- Evaluate a contour integral around a spiral closed by a segment — Section 1.3, problem 3
- An analytic function satisfying \(v=u^2\) is constant — Section 1.3, problem 4
- Uniform convergence on the boundary controls a holomorphic sequence inside — Section 1.3, problem 5
- Entire functions with pointwise modulus bound are proportional — Section 1.3, problem 6; exact existing owner after swapping f and g
- Order of the singularity of a sum of two functions with poles — Section 1.3, problem 7