Math 185 (Lecture 003) at UC Berkeley

This is not the official course website. Please visit bcourses.berkeley.edu for more detailed course information and updates.

About the Course

The course Introduction to Complex Analysis explores the additional structure provided by complex differentiation.

While real analysis conveys a rather pessimistic point of view, you will quickly realize that in complex analysis the world is beautiful: basically everything you could wish for is true. As a basic example: If a complex function is differentiable (in an open set!), it is twice differentiable, three times differentiable,..., and even analytic. We will see that Cauchy's Integral Theorem (or the Cauchy-Goursat Theorem) and Cauchy's Residue Theorem will allow us to compute integrals very easily. We will explore the rigidity coming from the complex structure, which manifests for example in the Maximum Modulus Principle, the Mean Value Property and Liouville's Theorem. The course will encompass Chapters 1-7 of the textbook.

Working knowledge in Math 104 is assumed. Some theorems will be reminiscent of those in real analysis so that these proofs will only be sketched. Furthermore, it will be assumed that you are able to write rigorous proofs.

Lectures

LEC 001: MWF 9-10am in 241 Cory Hall
LEC 003: MWF 10-11 in 3109 Etcheverry Hall

Office Hours

You can find me in 895 Evans Hall by appointment or during my regular office hours:

Mo 11-noon, We 1-2pm, Fr 11-noon

GSI Office Hours

August 22 - 31 (Nick Ryder) in Evans 961:
MWF noon-2pm
TuTh 3:30-5:30pm

September 1 - End of semester (Ben Filippenko) in Evans 961:
Weekdays 3-5pm

Textbook

Brown and Churchill: Complex variables and applications (9th Ed.), McGraw-Hill.

You may as well use the 8th edition of the book. Some section numbers are different, but all references will be posted for both versions on bCourses.

Additional recommended reading:
Lang: Complex Analysis (4th Ed.), Springer (free pdf with Berkeley IP address.)

Grading

Homework	20%
Midterm 1	20%
Midterm 2	20%
Final Exam	40%

When computing your final score, the lowest score of your homework assignments will be dropped. If your score in the final exam is better than any of your two midterm scores, the latter will be replaced by the former.

Homework

There will be weekly homework assignments posted on the course webpage at least one week prior to the due date. You can hand in your solutions at the beginning of class, or in my office by 9:30 am the same day, either in person or by sliding them under my door. Late homework will not be accepted; but the lowest score will be dropped when computing your final grade.

Group work is highly encouraged but each student has to write the final solution in there own words. Please acknowledge who you collaborated with by writing their names on the top of your homework. Copying homework from other students or from other sources will be considered cheating. A good rule of thumb for you is: Discussing the problem and explaining ideas is acceptable, but reading another student's solution (or having it read to you) is not.

Exams

The midterm exams take place in the classroom at the usual class time (i.e. Berkeley Time). Please be on time for the exams to not interrupt your fellow students.

Midterm 1: September 21
Midterm 2: October 31
Final Exam: According to the final exam schedule

There will be no make-up exams but the final exam can replace your score in one of the two midterms.

Special Accommodations

If you have a documented disability and require special accommodations of any kind, please e-mail me as soon as possible, and no later than Friday, September 7.

If you are officially representing the university and if there is a conflict with any of the midterms or the final exam, please e-mail me as soon as possible, and no later than Friday, September 7.