MAT 421 Complex Analysis, # 21174, Spring 2016


Class meets MW 11:30 AM - 12:45 PM in SCC 1300.


Instructor: Serban Raianu

Office: NSM E-108, office phone number: (310) 243-3139,

e-mail address:, , URL:;

Office hours: Monday: 12:55 PM – 2:15 PM, Wednesday: 4:00 PM - 5:20 PM, Friday: 11:40 AM – 1:00 PM, or by appointment.


Course Description: This course covers the algebra and geometry of the complex numbers; point sets, sequences and mappings; analytic functions; elementary functions; differentiation; integration; power series; the calculus of residues; and applications.


Text: Complex Analysis, by George Cain, available online at


Objectives: After completing MAT 421 the student will


Prerequisites: MAT 211 and MAT 271  or equivalent with a grade of "C" or better.


Grades: Grades will be based on three in‑class full‑period examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, and other assignments (15%) for the remainder. The exact grading system for your section is the following: each of the three full-period exams will be graded  on a 100 scale, then the sum of the scores is divided by 5 and denoted by E. Homework will be collected every Monday, and each homework is worth 5 points. No late homework will be accepted. The average of all homework scores is denoted by H.

5 to 10 minutes quizzes will be given in principle every Monday, with the exception of the review and exam days, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q. There are also 5 points awarded for attendance and class participation, this portion of the grade is denoted by A. The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F. 

To determine your final grade  compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

        A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

        C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D: 60‑69;   F: Less than 60.


Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, let me know in advance, and I may then substitute the relevant score from your final examination for the missing grade.


Accomodations for Students with Disabilities: Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH D180. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.


Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)



Tentative schedule:

M 1/25: 1.1 Complex numbers. Introduction; 1.2 Geometry  

W 1/27: 1.3 Polar coordinates; 2.1 Functions of a real variable

M 2/1: 2.2 Functions of a complex variable; 2.3 Derivatives

W 2/3: 3.1 Elementary functions. Introduction; 3.2 The exponential function

M 2/8: 3.2 The exponential function; 3.3 Trigonometric functions

W/2/10: 3.4 Logarithms and complex exponents  

M 2/15: Presidents’ Day Holiday  

W 2/17: Review  

M 2/22: Exam I   

W 2/24: 4.1 Integration. Introduction; 4.2 Evaluating integrals

M 2/29: 4.2 Evaluating integrals; 4.3 Antiderivatives

W 3/2: 5.1 Homotopy; 5.2 Cauchy’s Theorem

M 3/7: 5.2 Cauchy’s Theorem; 6.1 Cauchy’s Integral Formula

W 3/9: 6.2 Functions defined by integrals; 6.3 Liouville’s Theorem

M 3/14: 6.3 Liouville’s Theorem; 6.4  Maximum moduli

W 3/16: 7.1 The Laplace equation; 7.2 Harmonic functions

M 3/21: 7.2 Harmonic functions; 7.3 Poisson’s integral formula

W 3/23: Review

M 3/28: Spring Recess

W 3/30: Spring Recess

M 4/4: Exam II

W 4/6: 8.1 Sequences

M 4/11: 8.2 Series

W 4/13: 8.3 Power series

M 4/18: 8.4 Integration of power series; 8.5 Differentiation of power series

W 4/20: 8.5 Differentiation of power series; 9.1 Taylor series

M 4/25: 9.2 Laurent series

W 4/27: 10.1 Residues; 10.2 Poles and other singularities

M 5/2: 11.2 Argument principle; 11.2 Rouché’s Theorem

W 5/4: Review

M 5/9: Exam III

W 5/11: Review

Final exam: Wednesday, May 18, 11:30 AM – 1:30 PM



Important dates


January 23-February 11


Late Registration Add/Drop  (fees due 48 hours after registration)

February 1


Summer 2016 Graduation Application Deadline

February 5


Instructor Drop Deadline

February 11


Credit/No Credit and Audit Grading Deadline

February 11


Last Day to Drop from FT to PT Status with Refund

February 15


President’s Day Holiday- Campus Open, No Classes

February 19


Drop without Record of Enrollment Deadline

February 19


Student Census

February 20-April 21

Saturday- Thursday

Serious and Compelling Reason Required to Drop/Withdraw

March 14-May 22


Spring 2016 Intersession Registration

March 28-April 3

Monday- Sunday

Spring Recess (includes Cesar Chavez Holiday)

March 30


Last Day for Pro-rata Refund of Non-Resident Tuition and Tuition Fees

March 31


Cesar Chavez Holiday-Campus Closed, No Classes

April 15


Summer 2016 Graduation Application-Late Deadline (with late fee)

April 22-May 12


Serious Accident/Illness Required to Drop/Withdraw

April 25-August 19


Fall 2016 Registration

May 13


Last Day of Scheduled Classes

May 14


Study Day

May 14-May 20


Final Examinations

May 17


Grade  Submission Begins

May 20


Evaluation Day

May 20



May 21



May 25 3 pm


Final Grades Due-  *Extended Education grades always due 72 hours after course end date

May 25


Semester/Academic Year Ends