MA 367 Functions of a Complex Variable
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From the catalog
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Prerequisites: MA 113 |
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Course Description: Elementary properties of analytic functions including Cauchy's theorem and
its consequences, Laurent series, the Residue Theorem, and mapping properties of analytic
functions. | |
This is a course on the calculus of functions of a complex variable and how it differs from functions
of real variables. The course will emphasize a geometrical approach and an applications based approach, with some
of the theoretical and analytical background for those who have had more advanced courses, than MA 113.
Functions of complex variables have a variety of applications and have been studied for centuries from
their use in providing the correct framework for solving ordinary differential equations and partial
differential equations. They are also used for generating dynamics and fractals, and the geometric structure
of Riemann surfaces. The figure depicts the Riemann surface generated by the square root of z
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Text Book:
Visual Complex Analysis by Tristan Needham
Click on Picture to GoTo Oxford University Press
to find out more about
the text.
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Topics:
- Geometry and Complex Arithmetic
- Complex Functions as Transformations
- Mobius Transformations and Inversions
- Differentiation
- Geometry of Differentiation
- Non-Euclidean Geometry
- Winding Numbers and Topology
- Complex Integration
- Cauchy's Theorem and Formula
- Applications
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| Evaluation will be by
homework(50%), quizzes (25%),
final exam (25%) and class participation
(+/- 5%). |
