This course explored topics such as complex algebra and functions, analyticity, contour integration, Cauchy’s theorem, singularities, Taylor and Laurent series, residues, evaluation of integrals, multivalued functions, potential theory in two dimensions, Fourier analysis and Laplace transforms.
I. Complex Algebra and Functions
Simple Mappings: az+b, z2, √z Idea of Conformality
Complex Trigonometric and Hyperbolic Functions
II. Complex Integration
Bounds, Liouville’s Theorem, Maximum Modulus Principle
Toomre, Alar. 18.04 Complex Variables with Applications, Fall 2003. (Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed 31 Jul, 2012). License: Creative Commons BY-NC-SA