This course is an introduction to complex analysis, which is the study of complex-valued functions of a complex variable. We will start by studying the structure of complex differentiation, and we will find it is far richer than its real counterpart. This additional structure leads to many surprising and counter-intuitive results. For example, we will find that we can compute complex integrals simply by studying complex functions at specific points. We will study topics including Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, and the residue theorem. Time-permitting we will studying conformal mappings, and some applications.

The image on the right is a plot of a complex-valued function. The hue represents the argument of the function, while the brightness represents the magnitude.

Course Information

Instructor Jeff Calder (Office: 1053 Evans, Email: jcalder at berkeley dot edu)
Lectures Mon, Wed, Fri, 11am–12pm in 160 Dwinelle Hall
Office Hours Mon, Wed, Fri 12pm-1pm in 1053 Evans
GSI Edward Scerbo (Office: 853 Evans)
GSI Office Hours Mon--Fri: 4pm-6pm in 853 Evans
Final Exam Tuesday, May 12, 2015: 7-10pm
Piazza This term we will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently from classmates and the instructor. Rather than emailing questions directly to the instructor, students are encouraged to post questions on Piazza. Our Piazza website can be found here. To sign up for Piazza and join our class, click here .
Textbook Brown and Churchill. Complex variables and Applications, 9th Edition, 2013.
Readings The instructor will assign readings for each lecture on a weekly basis. They will be posted on the schedule page on this website and announced during class. It is very important to do the readings before attending the associated lecture.
Additional Resources Theodore W. Gamelin, Complex Analysis, Springer, 2001.
Tristan Needham, Visual Complex Analysis, Oxford University Press, 1999.
Homework There will generally be weekly homework assignments posted on this website that will be due each Friday. Collaboration on homework is encouraged, but you must write up the solutions in your own words and cite any class members that you worked with. Homework will be graded on a scale from 0 to 10, and solutions to selected problems will be posted on this website. Homework will not be accepted via email and must be handed in during class. Late homework will not be accepted for any reason. The two lowest homework grades will be dropped in the computation of your final grade.
Midterms There will be two 50-minute in-class midterms scheduled for February 13 and March 20. There will be no homework due on the weeks of the midterms.
Grade Corrections Exam grades will be changed only if there is an obvious error on the part of the grader. Any problems with exam grades must be brought to the attention of the lecturer immediately after exams are returned.
Grades The final grade will be based on homework assignments (20%), midterm I (20%), midterm II (20%), and the final exam (40%). A higher score on the final exam will erase any lower midterm score, hence your final grade will be calculated as follows:

Grade = (H + max{M_1,F} + max(M_2,F) + 2F)/5
where H is the homework grade, M1 and M2 are the first and second midterm grades, respectively, and F is the final exam grade. All exams grades will be given in terms of a letter grade, which will be used in the weighted average above.
Incomplete Grades Incomplete “I” grades are rarely given. The only justification is a documented serious medical problem or genuine personal/family emergency. Students requesting incomplete grades must currently have a passing grade in the course. For more information, please see George Bergman's notes on incomplete grades.
Special Arrangements If you are a student with a disability registered by the Disabled Student Services (DSS) on UCB campus, and if you require special arrangements for exams, please see the instructor as soon as possible. You will need to provide the DSS document detailing the special arrangements at least 10 days before any exam.
Academic Honesty The mathematics department expects that students in mathematics courses will not engage in cheating or plagiarism. Cheating, plagiarism, or other forms of academic dishonesty will result in a grade of zero on the homework assignment or exam in question, and, in severe cases, a failing grade in the course and a referral to the Center for Student Conduct. Please see Michael Hutchings' description of academic honesty in mathematics courses for more information.