13 problems.
- Define analyticity on an open set — Section I, item 1; exact repeated analyticity-definition prompt
- Define a branch of an inverse function — Section I, item 2
- State the local Cauchy Theorem — Section I, item 3
- Define uniform continuity on an open set — Section I, item 4; exact repeated uniform-continuity prompt
- Bound a contour integral along \(\gamma(t)=te^{it}\) — Section I, item 5
- Winding number of a circle about a distant point — Section I, item 6; exact repeated winding-number computation
- State the Maximum Principle — Section I, item 7; exact repeated Maximum Principle prompt
- Define the arc length of a path — Section I, item 8
- An entire map with unit Jacobian is affine with unit-modulus slope — Section II, problem 1
- Evaluate a twice-wound contour integral — Section II, problem 2
- A disk automorphism maps the disk onto itself — Section III, problem 1
- A quadratic Schwarz-type estimate from a derivative bound — Section III, problem 2
- Does \(v=u^2\) force an analytic function to be constant? — Section III, problem 3