Methods of Applied Mathematics II Topics
Applied and Computational Mathematics at Florida State University
Reference:
- Complex Variables: Introduction and Applications, M.J. Ablowitz and A.S. Fokas, Cambridge University Press, 2003, Second Ediion
Topics:
- Complex Variables
- Analytic and multi-valued functions
- Complex integration
- Series, sequences and singularities of complex functions
- Differential equation in the complex plane and analytic continuation
- Residue calculus and applications
- Asymptotic evaluation of integrals
- Integration by parts
- Laplace method
- Method of stationary phase
- Method of steepest descent
- The Stokes phenomenon
- WKB method
- Integral transforms and applications
- Fourier-Laplace transforms
- Green's function in two and three dimensions
- Dispersive waves
- Radiation problems
- Instability waves, amplifying and evanescent waves
- Hankel transform
