Most physical problems can be written and approximated in the form of mathematical equations (differential, integral, etc.). Mathematicians have always sought to find analytical solutions to the equations encountered in the different engineering sciences (mechanics, physics, biology, automation, etc.). These equations are sometimes so complicated that it takes a lot of effort to simplify them.
This book introduces and studies the basic and advanced numerical methods proposed to perform scientific computing. The latter refers to the implementation of approaches adapted to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or engineering (structural mechanics, fluid mechanics, signal processing, etc.). It deals with the approximation of functions and provides the different methods for solving linear systems: direct, iterative methods, calculation of eigenvalues and eigenvectors.
Each chapter of this book recalls the key points of various methods of resolution and presents several applications in the field of the engineer, as well as programs developed under the Matlab® software.
Part 1. Introduction
1. Review of Linear Algebra.
2. Numerical Precision.
Part 2. Approximating Functions
3. Polynomial Interpolation.
4. Numerical Differentiation.
5. Numerical Integration.
Part 3. Solving Linear Systems
6. Matrix Norm and Conditioning.
7. Direct Methods.
8. Iterative Methods.
9. Numerical Methods for Computing Eigenvalues and Eigenvectors.
10. Least-squares Approximation.
Part 4. Appendices
Appendix 1. Introduction to Matlab.
Appendix 2. Introduction to Optimization.
Bouchaib Radi is Professeur des universités at the Faculty of Science and Technology of the Hassan First University in Morocco and the author or co-author of 15 books. He is a specialist in digital methods and system reliability.
Abdelkhalak El Hami is Professeur des universités at the Institut National des Sciences Appliquées (INSA-Rouen) in France and the author or co-author of more than 25 books. He is director of the Department of Mechanics and is in charge of the Chair of Mechanics at the Normandy Conservatoire National des Arts et Metiers (CNAM) as well as several European educational and research projects. He is a specialist in the resolution and reliability of multiphysics systems.
Table of Contents
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