The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem - for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk.
The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem - for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk.
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.
Inhaltsangabe
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
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
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