Reference no: EM13910228
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
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