Find 4 applications of complex analysis to applied math

Question

Find 4 applications of Complex Analysis to Applied Math. This includes Differential Equations, Engineering Math, but not limited to these areas.

Requirements: An essay of 4-5 pages with details on the applications, slides and presentations.

List of Applications for Complex Analysis in Applied Mathematics and Sciences

•Utilization of Euler's Identity in Laplace Transforms

• Potential Flow Problems
o All Potentials still function as Potentials under Conformal Mappings
• Electro and Magnetostatics
o Dirichlet boundary conditions are invariant under Conformal Mappings

• Gravity Fields
o Gravitational Potential Fields and Green's Functions

• Heat Conduction and Convection

• Aerodynamics

• Electrical Circuits
o Utilization of Impedance in AC Circuits

• Waves

• Optics
o Kramers-Koenig Analysis on the real and imaginary parts of energy dependence on optical permittivity
o Integral Dispersion Relations in regard to Hadronic scattering

• Quantum Mechanics
o Utilizing Propagators as Green's Functions for the Schrodinger Equation

• Fluid Dynamics
o Joukowsky transform

• Computer Science
o Barinvok's Algorithm for Polynomial Time Algorithms
o Fast Fourier Transforms

Answer 1

Please provide a 4 to 5 pages typed word document, having 1.5 inch margin from all the sides, single-spaced, in Arial Black font and citations & references must follow APA guidelines. The task is basically to write an essay all along with the details on applications, slides and presentations for Complex Analysis in the Applied Mathematics and Sciences. By including the following, complete the task: 1) Use of Euler's Identity in the Laplace Transforms 2) Potential Flow Problems 3) Electro and Magnetostatics 4) Heat Conduction and Convection