Explorations In Numerical Analysis: Python Edition

James V Lambers, Amber C Sumner, Vivian Ashley Montiforte (Autoren)

Buch | Hardcover

692 Seiten

2021
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-12-2793-6 (ISBN)

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This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

James V Lambers is a Professor in the School of Mathematics and Natural Sciences at The University of Southern Mississippi, and an ACUE Distinguished Teaching Scholar. His research interests span numerical methods for partial differential equations and numerical linear algebra. Amber C Sumner is an Assistant Professor of Mathematics at William Carey University. She was a PhD student of Lambers at USM. Her research interests include deep learning and numerical linear algebra. Vivian A Montiforte is a PhD student of Lambers at USM. Her research pertains to spectral methods and meshless methods for partial differential equations.

Preface; Preliminaries:What is Numerical Analysis?; Understanding Error; Numerical Linear Algebra:Direct Methods for Linear Systems; Least Squares Problems; Iterative Methods for Linear Systems; Eigenvalue Problems; Data Fitting and Function Approximation:Polynomial Interpolation; Approximation of Functions; Differentiation and Integration; Nonlinear Equations and Optimization:Zeros of Nonlinear Functions; Optimization; Differential Equations:Initial Value Problems; Two-Point Boundary Value Problems; Partial Differential Equations; Appendices:Review of Calculus; Review of Linear Algebra; Bibliography; Index;

Erscheinungsdatum	04.02.2021
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	981-12-2793-4 / 9811227934
ISBN-13	978-981-12-2793-6 / 9789811227936
Zustand	Neuware