Instructor: | Dmytro Savchuk | |

Office: |
LN 2212 | |

Phone: | (607) 777-4221 | |

Fax: | (607) 777-2450 | |

e-mail: | dsavchuk at math dot binghamton dot edu | |

Office Hours: | MW 10:50am - 12:20pm or by appontment |

Class Location: | SL 306 MWF 9:40am-10:40am |

SW 331 R 10:05am-11:30am |

**Class web-page:** http://savchuk.myweb.usf.edu/teaching/2012A_math375_complex/

**Text:** A First Course in Complex Analysis, by Beck, Marchesi, Pixton, and Sabalka.

**Course Content:** We will cover most of the material in the notes up to at least Chapter 9.

Complex Analysis is a fundamental field of mathematics that, in a quite literal sense, `completes' what we can do with real numbers. Roughly, the complex numbers are formed from the real numbers by adding an extra number "the square root of -1" to be able to state answers for some previously unanswerable problems. Many of the tools from calculus on real numbers can be generalized to apply to the complex numbers, but there are also many differences between the reals and the complexes. This is especially apparent in many amazingly powerful tools for complex numbers which have no real analogue.

The goal of this course is to explore the complex numbers and many results which work with them. We will generalize calculus to deal with differentiating and integrating functions defined over the complex numbers. We will then concentrate on a few big hammers in complex analysis: Cauchy's Theorem, harmonic functions, Taylor series, and the Residue Theorem.

**Prerequisites:** Math 330 (Number Systems) or instructor approval .

**Grading:** There will be one midterm exam and a final, also you will
have a grade for homeworks and quizzes. Your final grade will be calculated according to the following table.

Midterm | = | 30% |

Final Exam | = | 40% |

Daily Grade Scores (homeworks, quizzes, etc.) | = | 30% |

I will consider any grade appeals only within one week after the assignemnt was returned. It is your responsibility to check your grades in the Blackboard.

**Attendance:** Attendance is required at all classes. This
includes the Thursday meeting, which is a regular class, *not* a
discussion session.

**Homework:** I will assign the homework regularly and you will be required to submit it. The assignments will
be available at

http://savchuk.myweb.usf.edu/teaching/2012A_math375_complex/homeworks.html

Solving homework problems is a crucial part in learning process. No matter how hard you study you will not learn the material
unless you solve the problems on your own. Besides, this is the best way to prepare yourself for the exams.
You can discuss homework problems with other students in the class, but you are required to write the solutions on your own.
Homework is due at the beginning of each class. If you are unable to come to class due to illness, you may turn in your
homework to me either via email or by putting the assignment under my office door. In either case, however, the assignment
must be turned in before the class period when it is due. You must then come to my office hours or make an appointment to
meet with me within the next seven days, to explain to me your situation. If your explanation is satisfactory, then I
will grade and give you credit for the homework assignment.
**Not all homework will be graded.** The problems will be graded on the scale similar to the one below

2 pts = | well written correct solution |

1 pt = | mostly correct solution, or correct but sloppily written solution |

0 pts = | everything else (including correct solutions without justification) |

**Quizzes:** Sometimes quizzes will be given in class. They may or may not be announced. There will be NO
make-up quizzes, but at least two quizzes with the lowest grade will be dropped. I will post the solutions to the quizzes at
http://savchuk.myweb.usf.edu/teaching/2011C_math461_topology/quizzes.html

**Getting Help:** If you are having problems, please stop by my office
LN 2212 during office hours or by appointment. Again, do not hesitate to ask questions - by far this is the most effective way of learning. To make our joint work more efficient, please,
come to office hours prepared. Please have particular questions that cause you difficulties ready.

**Copyright Policy:** All printed materials distributed in class or on the web are
protected by Copyright laws. One xerox copy (or download from the web) is allowed
for personal use only. Multiple copies or sale of any of the materials is strictly
prohibited.