Practical Numerical and Scientific Computing with MATLAB® and Python concentrates on the practical aspects of numerical analysis and linear and non-linear programming. It discusses the methods for solving different types of mathematical problems using MATLAB and Python. Although the book focuses on the approximation problem rather than on error analysis of mathematical problems, it provides practical ways to calculate errors.
The book is divided into three parts, covering topics in numerical linear algebra, methods of interpolation, numerical differentiation and integration, solutions of differential equations, linear and non-linear programming problems, and optimal control problems.
This book has the following advantages:
- It adopts the programming languages, MATLAB and Python, which are widely used among academics, scientists, and engineers, for ease of use and contain many libraries covering many scientific and engineering fields.
- It contains topics that are rarely found in other numerical analysis books, such as ill-conditioned linear systems and methods of regularization to stabilize their solutions, nonstandard finite differences methods for solutions of ordinary differential equations, and the computations of the optimal controls. It provides a practical explanation of how to apply these topics using MATLAB and Python.
- It discusses software libraries to solve mathematical problems, such as software Gekko, pulp, and pyomo. These libraries use Python for solutions to differential equations and static and dynamic optimization problems.
- Most programs in the book can be applied in versions prior to MATLAB 2017b and Python 3.7.4 without the need to modify these programs.
This book is aimed at newcomers and middle-level students, as well as members of the scientific community who are interested in solving math problems using MATLAB or Python.
Table of Contents
Solving Linear Systems. Ill-conditioning and Regularization Techniques in solutions of linear systems. Solving a system of nonlinear equations. Solving the Eigenvalue Problem. Data Interpolation. Numerical Differentiation and Integration. Solving Systems of Linear Ordinary Differential Equations. Solving Systems of Nonlinear Ordinary Differential Equations. Non-standard Finite Difference Methods for Solving ODEs. Solving Optimization Problems: Linear Programming. Solving Optimization Problems: Nonlinear Programming. Solving Dynamical Optimization Problems
Eihab B. M. Bashier obtained his PhD in 2009 from the University of the Western Cape in South Africa. He is an associate professor of applied mathematics at the faculty of mathematical sciences and information technology, University of Khartoum, since 2013. Currently, he is an associate professor of applied Mathematics at the College of Arts and Applied Sciences at Dhofar University, Oman.
The research interests of Dr. Bashier are mainly in numerical methods for differential equations with applications to biology and in information and computer security with focus in cryptography. In 2011, Dr. Bashier won the African Union and the Third World Academy of Science (AU-TWAS) young scientists national award in basic sciences, technology and Innovation. Dr. Bashier is a reviewer for some international journals and a member of the IEEE and the EMS.