Theory of Functions of a Complex Variable 1, Summer 2018

IMPORTANT announcment from Prof. Shalom regarding the Moed B results - PLEASE READ!

Announcements

• The final exercise, exerecise 7, is to be submitted directly to box #76, until 30.08 at 17:00. Note that it will NOT be possible to submit this exercise by email.
• All marked and returned exercises will be available in box #149 (Dan's). All exercises up to and including exercise 6 have been returned.
• The required number of submitted exercises is 5 out of 7. If you wish to verify that all your submitted exercises have been marked and counted, contact Dan by email.

Exam Solutions

Exercises

• Exercise 1, due date: 19.7.2018
• Exercise 2, due date: 26.7.2018
• Exercise 3, due date: 2.8.2018
• Exercise 4, due date: 9.8.2018
• Exercise 5, due date: 16.8.2018
• Exercise 6, due date: 23.8.2018
• Exercise 7, due date: 30.8.2018

Solutions

• Solution 1
• Solution 2
• Solution 3
• Solution 4
• Solution 5
• Solution 6
• Solution 7

Extras

• Proof of claim from the end of Tirgul 3
• Jordan's Curve Theorem - Statement and full proof, from Tirgul 4 (and a bit further)
• Hyperbolic Metric - Enrichment exercise on the hyperbolic metric in the open unit disk, and its relation to Schwarz's Lemma
• Marty's Theorem - Proof of Marty's theorem (slightly different than the one shown in Tirgul 6)
• Zoo of Conformal Equivalences - Constructions of explicit conformal maps between certain domains and the unit disc / half plane (updated!)
• Background image by Robert Bosch, and more images by Craig S. Kaplan.