Complex Variables

MATH 4283


Time and Place: MWF 11:30-12:20 in MSCS 514
Professor: Igor E. Pritsker
Office: MSCS 519C
Office Hours: MW 10:45 - 11:30 a.m. F 10:30-11:30 a.m.
Office Phone: 744-8220
E-mail: igor@math.okstate.edu
Web: http://www.math.okstate.edu/~igor/math4283/math4283_fall2017.html
Textbook: Fundamentals of Complex Analysis with Applications to Engineering and Science, by E. B. Saff and A. D. Snider, 3rd ed.


Complex analysis is a classical and beautiful part of mathematics with numerous applications in mechanics, thermodynamics, electrostatics, fluid mechanics and many other sciences. The course and our textbook are tailored for mathematics, science and engineering students who completed the calculus sequence.


Grading: There will be three semester tests and the Final Exam. The break up of your course grade is as follows:
Tests 1-3 60% (20% each)
Homework 10%
Final Exam 30%
Your grade will be determined according to the scale
A 90-100
B 80-89
C 70-79
D 60-69
F 59 and lower
Note that the above numbers are percentages of the highest possible score in the course.

Attendance is mandatory in this class.

Homework will be assigned daily (see the detailed schedule below), and will be collected periodically. It is required that you complete all homework.

Extra Credit: I plan to give a number of extra credit problems. They will be optional, of course.

Make-up Exams are given only in cases of serious illness or extreme emergency that prevents you from taking a test at the specified time. You have to contact me before the test and communicate all circumstances.

University Syllabus Attachment: Contains drop deadlines and procedures, as well as many other important dates and university policies.

Brief Schedule
Chapter 1 Chapter 2 Test 1 Chapter 3 Chapter 4 Test 2 Chapter 5 Chapter 6 Test 3 Chapter 7 Final Exam

Dictionary of Conformal Maps

Schwarz-Christoffel toolbox for MATLAB


Note: The homework problems below are assumed to be odd numbered, unless it is indicated otherwise.

Detailed Schedule
Week Date Sec Page Topic Homework
1 M, Aug 21 1.1-2 1, 7 Algebra and Representation of Complex Numbers 3-15, 19-23 (p. 5); 1-13 (p. 12)
W, Aug 23 1.3 14 Vectors and Polar Forms 3-11, 17
F, Aug 25 1.4 26 The Complex Exponential 1-13
2 M, Aug 28 1.5 33 Powers and Roots 1-13
W, Aug 30 1.6 39 Planar Sets 1-15
F, Sep 1 2.1-2 53, 58 Functions of a Complex Variable, Limits and Continuity 1-7 (p. 56); 1-5, 9-11 (p. 63)
3 M, Sep 4 Labor Day
W, Sep 6 2.3 65 Analyticity 3-11
F, Sep 8 2.4 73 The Cauchy-Riemann Equations 1-11
4 M, Sep 11 2.5 79 Harmonic Functions 1-11
W, Sep 13 2.6 87 Steady State Temperature as a Harmonic Function 1, 3
F, Sep 15 Test 1 (1.1-1.6, 2.1-2.5)
5 M, Sep 18 3.1 99 Polynomials and Rational Functions 1-7, 11, 13
W, Sep 20 3.2 110 The Exponential, Trigonometric, and Hyperbolic Functions 1-9, 15, 17
F, Sep 22 3.3 118 The Logarithmic Function 1-5, 9-15
6 M, Sep 25 3.4 125 Washers, Wedges, and Walls 1, 2, 3, 4, 5
W, Sep 27 3.5 131 Complex Powers and Inverse Trigonometric Functions 1-11
F, Sep 29 4.1 149 Contours 1-11
7 M, Oct 2 4.2 161 Contour Integrals 1-11
W, Oct 4 4.3 173 Independence of Path 1-7
F, Oct 6 4.4 180 Cauchy's Integral Theorem 1-5, 9-13
8 M, Oct 9 4.4-5 180, 204 Cauchy's Integral Theorem and Formula 15-17 (p. 202), 1-5 (p. 212)
W, Oct 11 4.5 204 Cauchy's Integral Formula 7-13
F, Oct 13 4.6 214 Bounds for Analytic Functions 1-7, 11
9 M, Oct 16 4.7 221 Applications to Harmonic Functions 1-5, 11
W, Oct 18 Test 2 (3.1-3.5, 4.1-4.7)
F, Oct 20 Fall Break
10 M, Oct 23 5.1 235 Sequences and Series 1-11
W, Oct 25 5.2 242 Taylor Series 1-7, 13
F, Oct 27 5.3 252 Power Series 1-7, 11
11 M, Oct 30 5.5 269 Laurent Series 1-9
W, Nov 1 5.6 277 Zeros and Singularities 1-5
F, Nov 3 5.6 277 Zeros and Singularities 7-11
12 M, Nov 6 6.1 307 The Residue Theorem 1-7
W, Nov 8 6.2 314 Trigonometric Integrals 1-9
F, Nov 10 6.3 318 Improper Integrals 1-7
13 M, Nov 13 6.7 355 The Argument Principle and Rouche's Theorem 1-5
W, Nov 15 6.7 355 The Argument Principle and Rouche's Theorem 7, 9, 13
F, Nov 17 Test 3 (5.1-5.3, 5.5, 5.6, 6.1-6.3, 6.7)
14 M, Nov 20 7.1 369 Invariance of Laplace's Equation 1, 3, 7
W, Nov 22 Thanksgiving Holidays
F, Nov 24 Thanksgiving Holidays
15 M, Nov 27 7.2 377 Geometric Considerations 1-7, 11
W, Nov 29 7.3 383 Moebius Transformations 1-7, 11
F, Dec 1 7.4 395 Moebius Transformations, Continued 1-9, 15, 17
16 M, Dec 4 7.5 407 The Schwarz-Christoffel Transformation 1-5
W, Dec 6 7.6 419 Applications to Electrostatics, Heat Flow, and Fluid Mechanics 1-5
F, Dec 8 7.7 432 Further Applications of Conformal Mapping ???
17 F, Dec 15 Final Exam (MSCS 514, 10-11:50 a.m.)