Mathematics 455: Basic Complex Analysis

 

Prerequisites: Math 350

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Textbook: "Basic Complex Analysis," By J.~E.~Marsden and M.~J.~Hoffman, 3rd Edition, Publisher: Freeman

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Syllabus: Chapters 1 – 5, and time permitting topics from chapters 7 and 8.

 

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Course Coverage:

 

·       Complex numbers

·       Analytic Functions

·       Complex Integration

·       Cauchy’s Theorem

·       Series Representation of Analytic Functions

·       Calculus of Residues

·       Conformal Mappings

·       Asymptotic Methods

·       Laplace Transform and Application

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Grading:

 

·       Quizzes: Weekly or bi-weekly     (50%)

·       Homework:  assigned and collected daily/weekly   (30%)

·       Final Exam:  comprehensive and common exam (no makeup finals)   (20%)

 

+/- grading system will be used.

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References:

 

·       Ahlfors: Complex Variable

·       Saff and Snider: Fundamentals of Complex Analysis with Applications to Engineering and Science

·       Rudin: Real and Complex Analysis

·       Hille: Analytic Function Theory

·       Whittaker and Watson: A Course of Modern Analysis

·       Nehari: Conformal Mapping

·       Conway: Functions of One Complex Variable

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Remarks:

 

·       To pass this class (letter grade D) your total course score (computed according to the above percentages) must be at least 50.

 

·       There are absolutely no makeup final exam, quizzes, or homework.

 

·       If you miss a test, quiz, or a due homework because you had an emergency, after providing the appropriate documentation you can makeup the missed assignment.

 

·       All exams and quizzes including the final exam will be closed books and closed notes.  You may only use a 3 x 5 index card for each quiz or test. Tests and quizzes are based on the lecture notes, homework problems, and the suggested exercises.

 

·       The final exam is a comprehensive common final.

 

·       There will be absolutely no makeup final exams. Make sure that you don't have any conflicts with the time and day of the final exam for this class.

 

·       Students are required to strictly comply with the University Code of Conduct. Any disturbance during lectures or cheating during exams will have severe consequences.

 

·       During each test, quiz, and the final exam students will be randomly asked to show their picture ID.

 

·       For the duration of each test, quiz, and the final exam you are required to turn your phone off and leave it directly below your seat where your proctor can see it. In case you need to use the restroom, you can ask your proctor to keep your phone until you are back in the classroom. You are not allowed to leave the room with your phone.

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University Policy for Adds and Drops:

 

Please read the university policy for adds and drops. It is your responsibility to drop a class.