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.

The book introduces numerical analysis, with a focus on the implementation of methods and algorithms to solve a variety of mathematical problems in use within a variety of applications. It applies programming in MATLAB and Python to a variety of numerical analysis tasks.

This textbook is written for the first introductory course on scientific computing. It covers elementary numerical methods for linear systems, root finding, interpolation, numerical integration, numerical differentiation, least squares problems, initial value problems and boundary value problems. It includes short Matlab and Python tutorials to quickly get students started on programming. It makes the connection between elementary numerical methods with advanced topics such as machine learning and parallel computing. This textbook gives a comprehensive and in-depth treatment of elementary numerical methods. It balances the development, implementation, analysis and application of a fundamental numerical method by addressing the following questions. •Where is the method applied? •How is the method developed? •How is the method implemented? •How well does the method work? The material in the textbook is made as self-contained and easy-to-follow as possible with reviews and remarks. The writing is kept concise and precise. Examples, figures, paper-and-pen exercises and programming problems are deigned to reinforce understanding of numerical methods and problem-solving skills.

This easy-to-understand textbook presents a modern approach to learning numerical methods (or scientific computing), with a unique focus on the modeling and applications of the mathematical content. Emphasis is placed on the need for, and methods of, scientific computing for a range of different types of problems, supplying the evidence and justification to motivate the reader. Practical guidance on coding the methods is also provided, through simple-to-follow examples using Python. Topics and features: provides an accessible and applications-oriented approach, supported by working Python code for many of the methods; encourages both problem- and project-based learning through extensive examples, exercises, and projects drawn from practical applications; introduces the main concepts in modeling, python programming, number representation, and errors; explains the essential details of numerical calculus, linear, and nonlinear equations, including the multivariable Newton method; discusses interpolation and the numerical solution of differential equations, covering polynomial interpolation, splines, and the Euler, Runge–Kutta, and shooting methods; presents largely self-contained chapters, arranged in a logical order suitable for an introductory course on scientific computing. Undergraduate students embarking on a first course on numerical methods or scientific computing will find this textbook to be an invaluable guide to the field, and to the application of these methods across such varied disciplines as computer science, engineering, mathematics, economics, the physical sciences, and social science.

This textbook is written for the first introductory course on scientific computing. It covers elementary numerical methods for linear systems, root finding, interpolation, numerical integration, numerical differentiation, least squares problems, initial value problems and boundary value problems. It includes short Matlab and Python tutorials to quickly get students started on programming. It makes the connection between elementary numerical methods with advanced topics such as machine learning and parallel computing. This textbook gives a comprehensive and in-depth treatment of elementary numerical methods. It balances the development, implementation, analysis and application of a fundamental numerical method by addressing the following questions. *Where is the method applied? *How is the method developed? *How is the method implemented? *How well does the method work? The material in the textbook is made as self-contained and easy-to-follow as possible with reviews and remarks. The writing is kept concise and precise. Examples, figures, paper-and-pen exercises and programming problems are deigned to reinforce understanding of numerical methods and problem-solving skills.

This book targets programmers and scientists who have basic Python knowledge and who are keen to perform scientific and numerical computations with SciPy.

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.