MAT 436/536 Theory of Functions of a Complex Variable
Textbook
No textbook is required for this course but the following book may be helpful for studying functions of a complex variable more in depth.
Topics
Class Meeting Times and Class Room
Office Hours
Grading
Math Forum
If you have a question on your homework or a general math question, you may post it on my Math Forum site. This forum site is equipped with MathJax which supports LaTex, a wonderful type setting system that is really good at formatting mathematical formulas and equations. MathJax allows us to write mathematical formulas and equations in popular web platforms using LaTex code.To include LaTex code in your posts and comments, use:
Weekly Schedule
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.
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.$your-LaTex-code-here$
You can find a list of Latex codes for math symbols here. You may practice your Latexing here.If you want to try Latex in your Windows computer, you may download it for free from MikTex Project Page. If you are using a Linux distribution, usually Latex is a part of the standard packages repository. (The package is called texlive.) To use Latex, you need an editor. Texmaker is a nice interface for using Latex. You can edit/compile/view all together in Texmaker. If you don't want to deal with commands, there is a WYSWYG (What You See is What You Get) interface for Latex called Lyx.
Click on linked topics to view/download scanned lecture notes.
Complex Algebra | Homework 1 | Homework 1 Solutions | Our class begins on Wednesday 1/14. Homework 1 is due on Wednesday 1/19. |
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Complex Algebra (continued): Complex Numbers in Exponential Form |
Homework 2 | Homework 2 Solutions | 1/19: Martin Luther King holiday 1/20: Last day to drop full semester classes and receive 100% financial credit 1/20: Last day to add/drop full-term classes without instructor permission |
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Complex Algebra (continued): Roots of Complex Numbers, Cauchy-Riemann Conditions: Differentiability of \(f(z)\) and Cauchy-Riemann Conditions |
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Cauchy-Riemann Conditions (continued): Analyticity of \(f(z)\), Differentiation Formulas, Cauchy-Riemann Conditions in Polar Coordinates |
Homework 2 is due on Monday 2/2. | ||||
Cauchy-Riemann Conditions (continued): Harmonic Functions, The Line Integral and Cauchy's Integral Theorem |
Homework 3 | Homework 3 Solutions | |||
The Line Integral and Cauchy's Integral Theorem (continued) | 2/16-2/17: Mardi Gras holiday | ||||
Cauchy Integral Formula | Homework 3 is due on Monday 2/23. | ||||
Morera's Theorem Cauchy's Inequality and Liouville's Theorem |
Homework 4 | Homework 4 Solutions | |||
Taylor Series Laurent series |
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Residues Cauchy's Residue Theorem |
Homework 5 | Homework 5 Solutions | Homework 4 is due on Monday 3/23. | ||
More on Residues The Three Types of Isolated Singularities |
4/3: Good Friday holiday | ||||
Residues at Poles Zeros and Poles |
Homework 6 | Homework 6 Solutions | Homework 5 is due on Wednesday 4/8. | ||
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) |
Homework 6 is due on Wednesday 4/15. | ||||
Jordan's Lemma Fresnel Integrals 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 | Homework 7 is due on Monday 5/4. |