Math 01.430 - Introduction to Complex Analysis

Syllabus

Dr. Abdul Hassen

Office:  Robinson Hall, Mathematics Department 229E

Phone  (856) 256-4500 ext 3888. e-mail:  hassen@rowan.edu

Office Hours:   W 10:50 to 12:00pm and 5:30 to 6:30 and by appointment.

Prerequisite:  Math 01.330 Introduction to Real Analysis I

Text: Churchill, and Brown, COMPLEX VARIABLES AND APPLICATIONS, 10th ed., MacGraw-Hill Book Company, New York, 1990

Course Description:  This course includes properties of complex numbers and their conjugates, functions of a complex variable, limits, continuity and derivatives for complex functions.  Also included are: Integration and the Cauchy integral theorems, uniform convergence, Taylor's and Laurent's series, and conformal mapping.

OBJECTIVES:  This course is intended to provide an introduction to the techniques of complex analysis for majors in mathematics, physics and engineering.  This is an important course for serious students of both pure and applied mathematics who are considering graduate training.  While proofs of selected theorems are given, stress is on techniques and applications.

 

CONTENT:

1.                  Introduction: The complex numbers; Elementary algebraic and geometric properties; Complex sequences

2.                  Analytic Functions: Functions of Complex Variable; Limit and Continuity, Uniformly Continuous Functions; Derivatives and elementary properties; Cauchy-Riemann Equations; Further Properties of Analytical Functions

3.                  Elementary Functions: The Logarithmic Function; The Power Functions; Exponential and Trigonometric Functions; Hyperbolic Functions

4.                  Integrals: Curves and parameterization of curves; Contour Integrals; Cauchy-Goursat Theorem and Morera's Theorem; The Cauchy Integral Formula; Liouville Theorem and Fundamental Theorem of Algebra; Maximum Modulus Theorem

5.                  Series: Convergent Series; Taylor Series; Laurent Series

6.                  Residues and Poles:  Isolated Singularities;  Cauchy Residue Theorem; Evaluation of Improper Integrals; Zeros and Poles

Grading Policy: Your final grades will be determined by your results on three tests and homework assignments, and class participation. Thus attendance will be very important. The dates for each test will be announced in class two weeks before the test date. The materials covered in the four tests will be as follows:

Test 1            (25% of the total grade) covers all sections of Chapters 1 and 2

Test 2           (30% of the total grade) covers   Chapter 3 and 4

Test 3          (25% of the total grade) covers Chapters 5 and 6 

20% of your grade will be from homework assignments. A letter grade assignment will be as follows:

A(A-) = 90 to 100      B(-,+) = 80 to 89      C(-,+) =  70 to 79    D(-,+) = 55 to 69    F = 0 to 54

Homework:    Click here for homework problems

Attendance Policy: Attendance is mandatory. An attendance sheet will be passed around at the beginning of each class period. Please write your signature next to your printed name on the list. If you are absent/tardy from a class, you must submit a note requesting that the absence/tardiness be excused by the next class meeting. Each student is allowed a total of three unexcused absences/tardies (combined). If you miss a class, it is your responsibility to study the section(s) covered and do the homework.

If you are absent the day of a regularly scheduled test, a grade of zero is automatically recorded as your test score. You will be permitted to make up this zero only when you can confirm that you were absent for reasons beyond your control.  In such cases, you must telephone 256-4500 extension 3888 (or send me an e-mail) and leave a message including your name and telephone number, the reason for your absence and the date you anticipate returning. Students who fail to leave the above information will be assigned the grade of zero for that test.

Academic Honesty: Cheating on a test or assignment seriously undermines the integrity of the academic system and will not be tolerated.  If I determine that a student has cheated, I will assign the grade of F for this course and send a letter to this effect to his advisor.  Although a student is not cheating, he or she is expected to refrain from actions that could be suspicious.  Using common sense on your part should avoid unnecessary embarrassment.

You may visit the website http://www.rowan.edu/provost/policies/AcademicIntegrity.htm for more information on Academic Integrity policy at Rowan University.

Classroom rules:

· Students will abide by Rowan's student code of conduct and policy on academic honesty (p. 19 and p. 28 of Rowan 1999-2000 undergraduate catalog, respectively).  Improper behavior will not be tolerated.
· Students are not permitted to leave the classroom during class period except for emergencies or unless prior arrangements have been made with the instructor. Please use the restrooms before class begins.

Students with Disabilities and Special Needs: Please speak with me as early in the semester as possible so that we can make appropriate accommodations for you. If necessary, you can also contact the Office of Special Services.

Questions in Class: The best time to ask questions is during class. Many times students fear that their questions will seem foolish, while in fact, many others also have the same question.  I urge you to ask your questions during class. If you have questions that were not answered in class, you may stop by my office during my office hours