MATH 8051, Functions of a Complex Variable
3 credits.
In-person.
TR 11:00 AM - 12:20 PM
Wachman 617.
Wachman 1020.
(215) 204-6741.
On-campus or via Zoom:
- Tuesdays: 13:30 PM - 14:30 PM
- Wednesdays: 14:30 PM - 15:30 PM (virtual)
- Thursdays: 13:30 PM - 14:30 PM
- By appointment, send an email.
Textbook:
Introduction to Complex Analysis by Michael E. Taylor.
Additional References:
- Functions of One Complex Variable I by John Conway.
- Complex Analysis by Serge Lang.
- Complex Analysis by Joseph Bak and Donald J. Newman.
- Complex Made Simple by David C. Ullrich.
- Complex Analysis by Elias M. Stein and Rami Shakarchi.
- Homework work counts for 40%
- Mid Semester poster presentation counts for 20%
- End of Semester student oral presentation counts for 25%
- Professional Development Sessions contribution counts for 15%
- Extra credit can be obtained by making a presentation about a Complex Analysis topics in oneof the following venues: Math Club, EPaDel MAA Spring 2025 Meeting, PhiladelphiaUndergraduate Mathematics Conference.
The grading scale is A: 90-100; B: 80-89; C: 70-79; D 60-69; F: <60.
- An undergraduate course in complex analysis is helpful but not necessary.
- Level Registration Restrictions: Must be enrolled in one of the following Levels: Graduate.
- Repeatability: This course may not be repeated for additional credits.
The main goal of the course is for students to master fundamental concepts in ComplexAnalysis of a single variable. This is achieved through:
- knowing all relevant definitions and statements of major theorems, including hypotheses and limitations,
- being able to provide examples and counterexamples of the various fundamental concepts,and solving non-trivial problems based on the course material.
Other goals include:
- Develop and strengthen advanced critical thinking and problem-solving skills.
- Be informed of Complex Analysis applications to other scientific fields such as fluid dynamics,electrical engineering, signal processing, and potential theory.
- Learn some of the historical details behind the mathematical advances in Complex Analysis.
This course is an introduction to analytic functions of one complex variable. Topics include:
- Basic Calculus in the Complex Plane
- Holomorphic Functions, Derivatives and Path Integrals
- Power Series
- Exponential and Trigonometric Functions
- Square Roots, Logs
- The Cauchy Integral Theorem and Consequences (maximum principle, Liouville's Theorem,the Fundamental Theorem of Algebra, Morerra's Theorem, Schwarz' Reflection Principle, and Goursat's Theorem)
- Harmonic Functions in the Plane
- Residue Calculus
- Conformal Maps
- Poster Presentations are scheduled for Thursday, March 13th
- End of Semester Presentations are scheduled for Tuesday, May 6th, 10:30 am - 12:30 am
- The Professional Development Sessions (two) will be scheduled and announced, one in thefirst part of the semester, and the second in the second part.
- Homework will be assigned through the semester (5 assignments). Each student will be incharge of writing complete solutions for one of the assignments to be posted in Canvas.
Students are expected to attend class. If you have an excuse for missing a class, please let me know. If you have 3 or more unexcused absences, your grade will drop half a notch (e.g. B to B-) for each 3 classes you miss.
To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.
It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse.
Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.
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The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.
The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).
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