MAT 421 Complex Analysis, Section 01, 21826, Spring 2018
Class meets MW 1:00 PM  2:15 PM
in NSM D129.
Instructor: Serban Raianu
Office: NSM E108, office phone number: (310) 2433139,
email address: sraianu@csudh.edu, , URL: http://math.csudh.edu/~sraianu;
Office hours: Monday, Wednesday, Friday:
8:50 AM  9:50 AM, Friday: in the Toro Learning Center: 11:30 AM – 12:30 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 http://www.math.gatech.edu/~cain/winter99/complex.html
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
fullperiod 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.
Accommodations
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 Student disAbility Resource Center (SdRC)
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 SdRC in WH
D180. For information call (310) 2433660 or to use telecommunications Device
for the Deaf, call (310) 2432028.
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 1/22:
1.1 Complex numbers. Introduction; 1.2 Geometry
W 1/24: 1.3 Polar coordinates; 2.1 Functions
of a real variable
M 1/29: 2.2 Functions of a complex
variable; 2.3 Derivatives
W 1/31:
3.1 Elementary functions. Introduction; 3.2 The exponential function
M 2/5:
3.2 The exponential function; 3.3 Trigonometric functions
W/2/7:
3.4 Logarithms and complex exponents
W 2/12:
Review
M 2/14: Exam I
M 2/19:
Presidents’ Day Holiday
W 2/21: 4.1
Integration. Introduction; 4.2 Evaluating integrals
M 2/26:
4.2 Evaluating integrals; 4.3 Antiderivatives
W 2/28:
5.1 Homotopy; 5.2 Cauchy’s Theorem
M 3/5: 5.2 Cauchy’s Theorem; 6.1
Cauchy’s Integral Formula
W 3/7: 6.2 Functions defined by integrals;
6.3 Liouville’s Theorem
M 3/12:
6.3 Liouville’s Theorem; 6.4 Maximum moduli
W 3/14:
7.1 The Laplace equation; 7.2 Harmonic functions
M 3/19: 7.2
Harmonic functions; 7.3 Poisson’s integral formula
W 3/21: Review
M 3/26:
Spring Recess
W 3/28: Spring Recess
M 4/2: Exam II
W 4/4: 8.1
Sequences
M 4/9:
8.2 Series
W 4/11: 8.3
Power series
M 4/16: 8.4
Integration of power series; 8.5 Differentiation
of power series
W 4/18: 8.5 Differentiation of power series; 9.1 Taylor series
M 4/23: 9.2 Laurent series
W 4/25: 10.1 Residues; 10.2 Poles and
other singularities
M 4/30: 11.2 Argument principle; 11.2 Rouché’s Theorem
W 5/2: Review
M 5/7: Exam III
W 5/9: Review
Final exam: Monday,
May 14, 1:00 PM – 3:00 PM
Important dates:
January 20February 6 
Saturday Tuesday 
Late Registration Add/Drop
(fees due 48 hours after registration) 
February 78 
Wednesday Thursday 
Late Registration Add/Drop
(fees due at time of registration) 
February 1 
Thursday 
Summer 2018 Graduation
Application Deadline 
February 2 
Friday 
Instructor Drop Deadline 
February 8 
Thursday 
Credit/No Credit and Audit
Grading Deadline 
February 8 
Thursday 
Last Day to Drop from FT to
PT Status with Refund 
February 16 
Friday 
Drop without Record of
Enrollment Deadline 
February 16 
Friday 
Student Census 
February 17April 19 
SaturdayThursday 
Serious and Compelling Reason
Required to Drop/Withdraw 
February 19 
Monday 
Presidents’ Day Holiday
Campus Open, No Classes 
March 12May 20 
MondaySunday 
Spring 2018 Intersession
Registration 
March 19July 6 
MondayFriday 
Summer 2018 Registration 
March 26March 31 
MondaySaturday 
Spring Recess (includes Cesar
Chavez Holiday) 
March 27 
Tuesday 
Last Day for Prorata Refund
of NonResident Tuition and Tuition Fees 
March 30 
Friday 
Cesar Chavez Holiday (observed)Campus
Closed, No Classes 
April 16 
Monday 
Summer 2018 Graduation
ApplicationLate Deadline (with late fee) 
April 20May 10 
FridayThursday 
Serious Accident/Illness
Required to Drop/Withdraw 
April 23August 17 
SundayThursday 
Fall 2018 Registration 
May 11 
Friday 
Last Day of Scheduled Classes

May 11 
Friday 
Study Day 
May 12May 18 
SaturdayFriday 
Final Examination 
May 15 
Tuesday 
Grades Submission Begin 
May 18 
Friday 
Commencement 
May 21 
Monday 
Evaluation Day 
May 23, 3 pm 
Wednesday 
Final Grades Due *Extended
Education grades always due 72 hours after course end date 
May 23 
Wednesday 
Semester/Academic Year Ends 