MAT 421 Complex Analysis, #
20108, Spring 2006
Class
meets MWF
Instructor:
e-mail address: sraianu@csudh.edu,
, URL: http://www.csudh.edu/math/sraianu;
office hours: Monday, Wednesday
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 should
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 three times, on the days of the three exams, 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 Friday, 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.
Makeup’s: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with your instructor, who may then substitute the relevant score from your final examination for the missing grade.
Students with Disabilities: Students who need special consideration because of any sort of disability are urged to see their instructor as soon as possible.
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 1/23: 1.1 Complex numbers. Introduction
W 1/25: 1.2 Geometry
F 1/27: 1.3 Polar coordinates
M 1/30: 2.1 Functions of a real varaiable
W 2/1: 2.2 Functions of a complex variable
F 2/3: 2.3 Derivatives
M 2/6: 3.1 Elementary
functions. Introduction
W 2/8: 3.2 The exponential function
F 2/10: 3.3 Trigonometric functions
M 2/13: 3.4 Logarithms and complex exponents
W 2/15: Review
F 2/17: Exam I
M 2/20: Presidents’ Day
W 2/22: 4.1 Integration. Introduction
F 2/24: 4.2 Evaluating
integrals
M 2/27: 4.3 Antiderivatives
W 3/1: 5.1 Homotopy
F 3/3: 5.2 Cauchy’s Theorem
M 3/6: 6.1 Cauchy’s Integral Formula
W 3/8: 6.2 Functions defined by integrals
F 3/10: 6.3 Liouville’s Theorem
M 3/13: 6.4 Maximum moduli
W 3/15: 7.1 The Laplace equation
F 3/17: 7.2 Harmonic functions
M 3/20: 7.3 Poisson’s integral
formula
W 3/22: Review
F 3/24: Exam II
M 3/27: Spring Recess
W 3/29: Spring Recess
F 3/31: Spring Recess
M 4/3: 8.1 Sequences
W 4/5: 8.1 Sequences
F 4/7: 8.2 Series
M 4/10: 8.3 Power series
W 4/12: 8.3 Power series
F 4/14: 8.4 Integration of power series
M 4/17: 8.5 Differentiation of power series
W 4/19: 9.1
F 4/21: 9.2 Laurent series
M 4/24: 9.2 Laurent series
W 4/26: Review
F 4/28: Exam III
M 5/1: 10.1 Residues
W 5/3: 10.2 Poles and other singularities
F 5/5: 10.2 Poles and other singularities
M 5/8: 11.2 Argument principle
W 5/10: 11.2 Rouché’s Theorem
F 5/12: Review
Final exam: Monday, May 15,