Summer 2018 MATH 185 002 LEC

Introduction to Complex Analysis
002 LECMoTuWeTh 02:00PM - 03:59PMCory 289Francisco A Grunbaum13714
UnitsEnrollment Status
Additional Information: 

Prerequisites: 104

Description: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.

Office: 903 Evans Hall

Office Hours: MTWTh 1pm-2pm

Required Text: 

Recommended Reading: Complex analysis, 4th edition Springer, Serge Lang.

Comments: The material in this class is both deep and very useful. We will study functions defined on the complex plane and taking values in the complex plane. This innocent looking replacement of $\mathbb R$ by $\mathbb C$ brings in many consequences. We will be learning about tools that are crucial both in mathematics itself as well as in many applications, like mechanics, hydrodynamics, the design of airfoils, etc.

Since all these ideas have to be mastered in eight weeks students should be ready to work hard from the very beginning. There is no chance to catch up with the material later on. The class is structured in such a way that everything that we do will play a role later on ( for us this may mean in the same or following weeks after new concepts are introduced).

A list of topics includes:

  • Complex numbers
  • Differentiability
  • Power series
  • Cauchy's theorem
  • Winding numbers
  • Laurent series
  • Residues
  • Evaluation of definite integrals
  • Conformal mappings
  • Harmonic functions

In the first hour or each 2 hours day we will do some theory, and in the second hour we will discuss problems that have been assigned previously. Class participation in this second hour will be an important part of the grade. Details about the grading policy follow:

Grading: Homework will be assigned in class and collected every Monday in class. Students will get credit for attempting complete solutions. This work will count for 30% of the class grade.

In class discussion of the homework will count for an extra 20% of the grade. Students should be prepared to discuss on the blackboard what they have done as homework the previous week.

We will have a midterm on the Thursday of the fourth week. It will take one hour and will count for 20% of the grade.

We will have a final exam on the last day of classes, it will take two hours and will count for 30% of the grade.

No one should be surprised if the problems in the midterm and/or final are very similar to problems that have been discussed (maybe assigned as homework) during the course of the eight weeks. A good way to prepare for these tests is to take the homework very seriously.

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