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Spectral Methods Using Multivariate Polynomials On The Unit Ball
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Kendall Atkinson is Professor Emeritus at University of Iowa as well as Fellow of the Society for Industrial & Applied Mathematics (SIAM). He received his PhD from University of Wisconsin - Madison and has had Faculty appointments at Indiana University, University of Iowa as well as Visiting appointments at Colorado State University, Australian National University, University of New South Wales, University of Queensland. His research interests include numerical analysis, integral equations, multivariate approximation, spectral methods David Chien, PHD, is Professor in the Department of Mathematics at California State University San Marcos. He has authored journal articles in his areas of research interest, which include the numerical solution of integral equations and boundary integral equation methods. Olaf Hansen is Professor of Mathematics, California State University San Marcos. He received his PhD from Johannes Gutenberg University, Mainz, Germany in 1994 and his research interests include Analysis and Numerical Approximation of Boundary and Initial Value Problems and Integral Equations.
Chapter 1: Introduction Chapter 2: Multivariate Polynomials Chapter 3: Creating Transformations of Regions Chapter 4: Galerkin's method for the Dirichlet and Neumann Problems Chapter 5: Eigenvalue Problems Chapter 6: Parabolic problems Chapter 7: Nonlinear Equations Chapter 8: Nonlinear Neumann Boundary Value Problem Chapter 9: The biharmonic equation Chapter 10: Integral Equations