CourseKU2017.pdf - Advanced Applied Mathematics: Complex...

Advanced Applied Mathematics: Complex Analysis with Applications to
Hydro- and Aerodynamics, Heat and Mass Transfer, Electricity, Control
Theory and the Theory of Elasticity
Topics to be covered (tentative):
1. Complex numbers and plane
2. Functions of complex variables
3. The Cauchy-Riemann conditions. Complex potential
4. Simple complex potentials
5. Coordinate transformation
6. Conformal mapping
7. Some applications of conformal mapping in fluid mechanics and heat and mass transfer:
(a) Potential flows about an ellipse and a plate; (b) Coffee stain effect; (c) Airfoils and
rudders; (d) Flows with separation; (e) Mapping to the hodograph plane
8. Impact hydrodynamics: Impact of a plate
onto a half-plane filled with liquid
9.
The Wagner problem: Entry of a very wide wedge into a half-plane filled with liquid
10. Contour integration
11. Cauchy’s integral theorem
12. Morera’s theorem
13. The Cauchy formula
14. Poisson’s integral formula for the upper half-plane. Steady-state temperature field
15. Drop impact onto a pore
16. Solutions of the Dirichlet and Neumann problems
17.