Numerical Methods In Scientific Computing
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Numerical Methods in Scientific Computing:
This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.
Introduction to Numerical Analysis and Scientific Computing
Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple and double-precision standards as used in scientific computer environments such as MATLAB® version 7. Drawing on their years of teaching students in mathematics, engineering, and the sciences, the authors discuss computer arithmetic as a source for generating round-off errors and how to avoid the use of algebraic expression that may lead to loss of significant figures. They cover nonlinear equations, linear algebra concepts, the Lagrange interpolation theorem, numerical differentiation and integration, and ODEs. They also focus on the implementation of the algorithms using MATLAB®. Each chapter ends with a large number of exercises, with answers to odd-numbered exercises provided at the end of the book. Throughout the seven chapters, several computer projects are proposed. These test the students' understanding of both the mathematics of numerical methods and the art of computer programming.
An Introduction to Scientific Computing
Author: Ionut Danaila
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-03
This book demonstrates scientific computing by presenting twelve computational projects in several disciplines including Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to numerical formulation and programming and critical discussion of results. The text teaches practical methods not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.