MAT 436/536 Theory of Functions of a Complex Variable
Textbook
Topics
Class Meeting Times and Class Room
Office Hours
Grading
Weekly Schedule
Mathematical Methods for Physicists, A Comprehensive Guide, 7th Edition, George B. Arfken, Hans J. Weber, Frank E. Harris, Acedemic Press, 2012. I will roughly follow Chapters Functions of a Complex Variable I and II of this book. In addition, the following book may be helpful for studying functions of a complex variable more in depth.
Complex Variables and Applications, James Brown and Ruel Churchill, 8th Edition, McGraw-Hill, 2008
Complex Algebra, Cauchy-Riemann Conditions, Cauchy's Integral Theorem, Cauchy's Integral Formula, Taylor Expansion, Laurent Expansion, Singularities, Calculus of Residues, Applications of Residues, Analytic Continuation
Monday/Wednesday 3:30-4:45pm in SH 303
Monday/Wednesday 2:00-3:30pm and by appointment.
For students on the Gulf Coast campus, office hours may be arranged through skype by appointment. My skype id is sunglee7.
No tests. The final grade for the course is based on cummutative grades from homework assignments.
You can view your grade here. You can identify yours by the last four digits of your student id.Click on linked topics to view/download scanned lecture notes.
| Complex Algebra | Homework 1 | Homework 1 Solutions | |||
| Complex Algebra (continued) | 1/20: Martin Luther King holiday | ||||
| Complex Algebra (continued) | 1/28: Last day to drop full semester classes and receive 100% financial credit | ||||
| Cauchy-Riemann Conditions | |||||
| Cauchy-Riemann Conditions (continued) | Homework 2 | Homework 2 Solutions | |||
| The Line Integral and Cauchy's Integral Theorem | |||||
| Cauchy Integral Formula | Homework 3 | Homework 3 Solutions | 2/24: Last day to drop full-semester classes without academic penalty | ||
| Morera's Theorem Cauchy's Inequality and Liouville's Theorem |
3/4: Mardi Gras holiday | ||||
| Taylor Series Laurent series |
Homework 4 Homework 5 |
Homework 4 Solutions Homework 5 Solutions |
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| Residues Cauchy's Residue Theorem |
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| More on Residues The Three Types of Isolated Singularities Residues at Poles |
Homework 6 | Homework 6 Solutions | |||
| Zeros and Poles Applications of Residues: Evaluation of Improper Integrals Applications of Residues: Evaluation of Improper Integrals 2 (Improper Integrals of the Form \(\int_{-\infty}^\infty f(x)\sin axdx\) or\(\int_{-\infty}^\infty f(x)\cos axdx\) where \(a\) is a positive constant) |
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| Fresnel Integrals Jordan's Lemma Applications of Residues: Evaluation of Improper Integrals 3 (Indented Paths) |
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| Application of Residues: Definite Integrals Involving Sines and Cosines Analytic Continuation |
Homework 7 | Homework 7 Solutions | |||
| Special Topics: Riemann-Zeta Functions |