Lesson I-Complex Variables with Applications

Course Description

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.

Lecture Notes

I. Complex Algebra and Functions

Simple Mappings: az+b, z², √z Idea of Conformality

Complex Exponential

Complex Trigonometric and Hyperbolic Functions

II. Complex Integration

Contour Integrals

Bounds, Liouville’s Theorem, Maximum Modulus Principle

Source

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