Introduction to Complex Analysis Fall 2018

Math 185 (Lectures 003 and 004) at UC Berkeley

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

Spring 2018 Lecture 003: MWF 10-11am in 247 Cory Hall Lecture 004: MWF 11-noon in?289 Cory Hall (Room changed!) Prerequisites: Math 104 (or equivalent) Material: A description of the covered topics, homework assignments and all announcements will be posted weekly on the?course webpage. Office Hours: MF 9-10, W 5-6

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 003: MWF 10-11am in 247 Cory Hall
LEC 004: MWF 11-noon in 289 Cory Hall

Office Hours

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

Mo 9-10am, We 5-6pm, Fr 9-10am

GSI Office Hours

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 and other details differ, but all references will be posted for?both?versions on bCourses.

Grading

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 time of class (i.e. Berkeley Time). Please be on time for the exams to not interrupt your fellow students.

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, February 1.

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, February 1.