Numerical Mathematics

Jeffrey S. Ovall (Autor)

Buch | Softcover

604 Seiten

2024
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-1-61197-806-3 (ISBN)

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Numerical methods for calculus, differential equations, and linear algebra are explored through rigorous error analysis and theoretical foundations. Detailed computational examples—including Fourier analysis of the trapezoid rule, finite volume methods, and strategies for eigenvalue clusters—illustrate convergence behavior.

This textbook introduces key numerical algorithms used for problems arising in three core areas of scientific computing: calculus, differential equations, and linear algebra. Theoretical results supporting the derivation and error analysis of algorithms are given rigorous justification in the text and exercises, and a wide variety of detailed computational examples further enhance the understanding of key concepts.

Numerical Mathematics includes topics not typically discussed in similar texts at this level, such as a Fourier-based analysis of the trapezoid rule, finite volume methods for the 2D Poisson problem, the Nyström method for approximating the solution of integral equations, and the relatively new FEAST method for targeting clusters of eigenvalues and their eigenvectors. An early emphasis is given to recognizing or deducing orders of convergence in practice, which is essential for assessing algorithm performance and debugging computational software. Numerical experiments complement many of the theorems concerning convergence, illustrating typical behavior of the associated algorithms when the assumptions of the theorems are satisfied and when they are not.

Jeffrey S. Ovall is a Maseeh Professor of Mathematics at Portland State University. He has held postdoctoral positions at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, and at the California Institute of Technology. His research primarily concerns numerical methods for partial differential equations and integral equations, with particular interest in eigenvalue problems, nonstandard discretization techniques, and effective treatment of singular solutions.

Erscheinungsdatum	03.09.2024
Verlagsort	New York
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-61197-806-8 / 1611978068
ISBN-13	978-1-61197-806-3 / 9781611978063
Zustand	Neuware