Applications of Complex Analysis (AMATH 567)#
This course focuses on practical applications of complex analysis. In particular we focus on the use of contour integration to solve otherwise troublesome real integrals and partial differential equations. Important topics covered in this course are:
- Analyticity of complex functions
- Introduction of branch cuts to define single-valued functions from multi-valued functions
- Cauchy’s theorem
- Taylor and Laurent series and their region of applicability
- Calculation of contour integrals by computing residues of singularities
- Principal value integrals
- Fourier and Laplace transforms and their application to partial differential equations
- Conformal mappings with applications to inviscid irrotational fluid flow
Integration is fun!