The basic object of study is a class of functions defined on a region in the plane, taking values in the plane. Consequently the major prerequisite for the course is multi-variable calculus. However, unlike that subject which in its generality has little coherence, complex analysis limits its view to the class of holomorphic or analytic functions. Each of these functions individually has important and properties that give it substance, and the class of all such functions has attributes that provide a certain rigidity that is very useful.
Complex analysis is one of the most beautiful parts of mathematics. It is filled with surprises in itself, and its applications to other parts of mathematics and to other areas of science and engineering are many and exciting.
In order to use holo you will need to download the filec holo.m.
All homework is due in class on the date announced. This will typically be about a week after the assignment is posted. Each student will be allowed to have at most one late homework assignment during the semester. The one late homework will be accepted up to seven days after the due date, with or without excuse, and without penalty. No other late homeworks will be accepted even with an excuse. There will be absolutely no exceptions to these rules.
Many of the Exercises in the book extend the material in the text. Therefore they are as important as the text itself. Many homework assignments will contain more problems to be done than are to be turned in. It should be emphasized that a person learns mathematics by doing problems. You are encouraged to at least look at all of the exercises in the book.
A homework assignment is meant to convince the grader that you understand the material. The best way to do that is to use complete sentences and to organize your work in paragraphs. In your writing, attempt to achieve the same clarity you find in textbooks. The grader has instructions that if he cannot understand your writing, he is not to grade your paper.
The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However each student is responsible for the final preparation of his or her own homework papers.