Math 234A, Fall 2018

Mathematics 234A, Fall 2018

Graduate Complex Analysis

Lectures:

Section 1:
Tuesdays, Room 133, Yosemite Hall, and
Thursdays, Room 109, Brighton Hall

Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall

Tentative Office Hours:
Mondays 11-12, Tuesdays 12-1, Wednesdays 2-3, and Thursdays 2-3

A description of the course: Math 234A, Fall 2018 (pdf)

Drop Policy

Announcements:

We will be using the following textbook:
Complex Analysis, by Theodore W. Gamelin.
I also recommend the classic book by Lars V. Ahlfors.

Final Exam:
Thursday, December 13, 3-5pm

Homework:

Instructions for Formatting Homework

Homework 1, Due Tuesday, September 4:
Section I.1 (1ei, 8, 9ab)
Section I.2 (1bdh, 5, 8)
Section I.3 (4)
Section I.4 (1abc, 2abc, 3)
Section I.5 (1abcd, 2cf)

Homework 2, Due Tuesday, September 11:
Section I.6 (1ac, 2bc)
Section I.7 (1ab, 2, 7)
Section I.8 (1a, 4, 7)
Section II.1 (8, 11, 15)
Section II.2 (1bdg, 3)

"Homework 3" (don't turn it in), review for Exam 1 on Tuesday, September 18:
See Canvas.

Homework 4, Due Thursday, September 27:
Section III.1 (1, 2, 3, 4)
Section III.2 (1, 2)

Homework 5, Due Thursday, October 11: (changed by popular demand)
Section III.3 (5)
Section III.4 (1, 4)
Section III.5 (3)
Section IV.1 (1abc, 3abc, 4, 5)
Section IV.2 (5)
Section IV.4 (1)
Section IV.5 (2, 3)

Homework 6, Due Tuesday, October 30:
Section V.1 (1, 2, 3)
Section V.2 (1, 2, 7, 10)
Section V.3 (1ab, 2cd, 5ab, 6)
Section V.4 (1ade, 3, 7)

Homework 7, Due Friday, November 9:
Section V.5 (1ab)
Section V.7 (1efg,3,5)
Section VI.1 (1,2)
Section VI.2 (1bdfi)
and study for the exam on Tuesday, November 13.

Homework 8, Due ????:
Section VII.1 (1cdh, 3bce)
Section VII.2 (2, 4, 7)
Section VII.3 (2, 3)
Section VII.4 (1, 3)

Exams:

Exams and Solutions are posted on Sac CT.

Lecture Schedule

	Date	Topics	Book
Week 1	1. T 8/28	Different Representations of Complex Numbers.	Chapter I, § 1,2
	2. R 8/30	Elementary Complex Functions, I.	Chapter I, § 3,4,5
Week 2	3. T 9/4	Elementary Complex Functions, II.	Chapter I, § 6,7,8
	4. R 9/6	Analytic Functions, I.	Chapter II, § 1,2,3
Week 3	5. T 9/11	Analytic Functions, II.	Chapter II, § 4,5
	6. R 9/13	Analytic Functions, III: Conformal mappings.	Chapter II, § 6
Week 4	T 9/18	EXAM 1
	7. R 9/20	Line Integrals.	Chapter III, § 1,2
Week 5	8. T 9/25	Harmonic Functions.	Chapter III, § 3,4,5
	9. R 9/27	Complex Line Integrals, I.	Chapter IV, § 1,2
Week 6	10. T 10/2	Complex Line Integrals, II.	Chapter IV, § 3,4
	11. R 10/4	Complex Line Integrals, III.	Chapter IV, § 5
Week 7	12. T 10/9	Review and Morera's Theorem.	Chapter IV, § 6
	13. R 10/11	Review and Goursat's Theorem.	Chapter IV, § 7
Week 8	T 10/16	EXAM 2
	14. R 10/18	Power Series, I.	Chapter V, § 1,2
Week 9	15. T 10/23	Power Series, II.	Chapter V, § 3,4
	16. R 10/25	Power Series, III.	Chapter V, § 5,6,7
Week 10	17. T 10/30	Laurent Series, I.	Chapter VI, § 1,2
	18. R 11/1	Laurent Series, II.	Chapter VI, § 3,4
Week 11	19. T 11/6	Residue Calculus, I.	Chapter VII, § 1,2
	20. R 11/8	Review and extra topics.
Week 12	21. T 11/13	Cancelled due to Unhealthy Air.
	22. R 11/15	Cancelled due to Unhealthy Air.
Week 13	23. T 11/20	Cancelled due to Unhealthy Air.
	R-F 11/22-23	NO CLASS (Thanksgiving)
Week 14	T 11/27	EXAM 3
	24. R 11/29	Residue Calculus, II.	Chapter VII, § 3,4
Week 15	25. T 12/4	The Logarithmic Integral.	Chapter VIII, § 1,2
	26. R 12/6	Review.


		FINAL EXAM: Thursday, December 13, 3-5pm