Elegant Memo

Office Hours for TA: M-F, 10:00 AM - 12:00 PM; T, Th, F: 2:00 - 5:00 PM (Ball 308)

The course covers the main topics in complex variables and applications including: Complex numbers, Argand plane, derivatives of complex numbers, limits and continuity, derivative and Cauchy Riemann conditions, analytic functions, integration in the complex plane, Cauchy’s integral formula, infinite series for complex variables, Taylor series, Laurent series, residue theory, evaluation of integrals around indented contours. Additionally, the following topics in linear algebra will be covered: Linear vector spaces, matrices and determinants, eigenvalues and eigenvectors. Prerequisites: 16.201 and 92.236.

1. Cheating will not be tolerated! If you are caught cheating, proper actions will be taken according to the University policies. This will include a letter describing the cheating incident that will be put in the student's file. Further actions, such as "0" on the HW or exam the students are caught cheating on could also be administered.

2. You may not leave the room for any reason during any of the exams, including the final exam.

3. You must attend all exams. Failure to attend will result in a grade of “F”. If you have a “valid” reason for not coming to an exam, you must let the instructor know in advance!

4. Solutions to exams will NOT be provided. It is up to the students to ask for help on the questions they got wrong or do not understand!

6. Homework must be turned in on time in the beginning of class. Late HW is not accepted!

7. The homework is graded by the TA and it is the student’s responsibility to check the homework solutions posted on the class web site and understand the homework. If there is a concern about the grade on the homework, please consult the TA first and if the problem is still unresolved, please speak to the Professor.

1. The student will be able to perform arithmetic of complex numbers and represent complex numbers in polar form.

2. The student will be able to show the existence of a derivative and investigate the analyticity of a function.

3. The student will be able to integrate complex functions through various methods.

4. The student will be able to represent analytic complex functions in terms of power series, Taylor series, and Laurent series.

5. The student will be able to find the residue of a function and be able to integrate using residue calculus.

6. The student will be able to identify and classify singularities of complex functions.

7. The student will be able perform basic matrix manipulations, understand Gauss elimination, and sole eigenvalue problems.

Course Topics

· Intro to Complex Analysis; Polar Form of Complex Numbers

· Complex functions, derivatives, and analyticity

· Cauchy-Riemann Equations & Laplace’s Equation

· Exponential, Trig, Hyperbolic Functions and Logarithms

· Complex Integration including Cauchy’s Integral Theorem and Formula

· Sequences, series, convergence

· Taylor and Laurent Series

· Residue Theorem

· Evaluation of real integrals

· Eigenvalue problems

Homework & Pop Quizzes	20%
Exams (3)	40%
Final Exam	40%