Numerical Methods Using Mathcad

This book presents the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences in a way that is both interesting and understandable. Using a wide range of examples and problems, this book focuses on the use of MathCAD functions and worksheets to illustrate the methods used when discussing the following concepts: solving linear and nonlinear equations, numerical linear algebra, numerical methods for data interpolation and approximation, numerical differentiation and integration, and numerical techniques for solving differential equations. For professionals in the fields of engineering, mathematics, computer science, and physical or life sciences who want to learn MathCAD functions for all major numerical methods.

An Introduction to Numerical Methods using Mathcad is designed to be used in any introductory level numerical methods course. It provides excellent coverage of numerical methods while simultaneously demonstrating the general applicability of Mathcad to problem solving. This textbook also provides a reliable source of reference material to practicing engineers and scientists and in other junior and senior-level courses where Mathcad can be effectively utilized as a software tool in problem solving. A principal goal of this book is to furnish the background needed to create Mathcad documents for the generation of solutions to a variety of problems. Specific applications involving root-finding, interpolation, curve-fitting, matrices, derivatives, integrals and differential equations are discussed and the broad applicability of Mathcad demonstrated. Wherever appropriate, the use of Mathcad functions offering shortcuts and alternatives to otherwise long and tedious numerical solutions is also demonstrated.

This comprehensive book illustrates how MathCAD can be used to solve many mathematical tasks, and provides the mathematical background to the MathCAD package. Based on the latest Version 8 Professional for Windows, this book Market: contains many solutions to basic mathematical tasks and is designed to be used as both a reference and tutorial for lecturers and students, as well as a practical manual for engineers, mathematicians and computer scientists.

An Introduction to Numerical Methods using MATLAB is designed to be used in any introductory level numerical methods course. It provides excellent coverage of numerical methods while simultaneously demonstrating the general applicability of MATLAB to problem solving. This textbook also provides a reliable source of reference material to practicing engineers, scientists, and students in other junior and senior-level courses where MATLAB can be effectively utilized as a software tool in problem solving. The principal goal of this book is to furnish the background needed to generate numerical solutions to a variety of problems. Specific applications involving root-finding, interpolation, curve-fitting, matrices, derivatives, integrals and differential equations are discussed and the broad applicability of MATLAB demonstrated. This book employs MATLAB as the software and programming environment and provides the user with powerful tools in the solution of numerical problems. Although this book is not meant to be an exhaustive treatise on MATLAB, MATLAB solutions to problems are systematically developed and included throughout the book. MATLAB files and scripts are generated, and examples showing the applicability and use of MATLAB are presented throughout the book. Wherever appropriate, the use of MATLAB functions offering shortcuts and alternatives to otherwise long and tedious numerical solutions is also demonstrated. At the end of every chapter a set of problems is included covering the material presented. A solutions manual to these exercises is available to instructors.

Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model iscrucial anddifficult in engineering. As a hands-on approach to learn how to pose a differential mathematical modelthe authors have selected 9 examples with important practical application and treat them as following:- Problem-setting and physical model formulation- Designing the differential mathematical model- Integration of the differential equations- Visualization of results Each step of the development ofa differential model isenriched by respective Mathcad 11commands, todays necessary linkage of engineering significance and high computing complexity. TOC:Differential Mathematical Models.- Integrable Differential Equations.- Dynamic Model of the System with Heat Engineering.- Stiff Differential Equations.- Heat Transfer near the Critical Point.- The Faulkner- Skan Equation of Boundary Layer.- The Rayleigh Equation: Hydronamic Instability.- Kinematic Waves of Concentration in Ion- Exchange Filters.- Kinematic Shock Waves.- Numerical Modelling of the CPU-board Temperature Field.- Temperature Waves.

This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.