Part 1: Theory and Conformal Maps
1 Introduction
2 Conformal Mapping
3 Linear and Bilinear Transformations
4 Algebraic Functions
5 Exponential Family of Functions
6 Joukowski Airfoils
7 Schwarz-Christoffel Transformation
Part 2: Numerical Methods
8 Schwarz-Christoffel Integrals
9 Nearly Circular Regions
10 Integral Equation Methods
11 Theodorsen’s Integral Equation
12 Symm’s Integral Equation
13 Airfoils and Singularities
14 Doubly Connected Regions
15 Multiply Connected Regions
Part 3: Applications
16 Grid Generation
17 Field Theories
18 Fluid Flows
19 Heat Transfer
20 Vibrations and Acoustics
21 Electromagnetic Field
22 Transmission Lines and Waveguides
23 Elastic Medium
24 Finite Element Method
25 Computer Programs and Resources
Biography
Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/co-author of 12 books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Green’s functions, and coding theory.
