Numerical And Analytical Methods For Scientists And Engineers Using Mathematica

The electronic component of the book is based on the widely used and highly praised Mathematica software package. Each chapter of the bookis a Mathematica notebook with links to web-based material. The methods are applied to a range of problems taken from physics and engineering. The book covers elementary and advaned numerical methods used in modern scientific computing.

Written from the perspective of a physicist rather than a mathematician, the text focuses on modern practical applications in the physical engineering sciences, attacking these problems with a range of numerical and analytical methods, both elementary and advanced. Incorporating the widely used and highly praised Mathematica® software package, the author offers solution techniques for the partial differential equations of mathematical physics such as Poisson's equation, the wave equation, and Schrödinger's equation, including Fourier series and transforms, Green's functions, the method of characteristics, grids, Galerkin and simulation methods, elementary probability theory, and statistical methods.

Numerical Methods for Scientists and Engineers: With Pseudocodes is designed as a primary textbook for a one-semester course on Numerical Methods for sophomore or junior-level students. It covers the fundamental numerical methods required for scientists and engineers, as well as some advanced topics which are left to the discretion of instructors. The objective of the text is to provide readers with a strong theoretical background on numerical methods encountered in science and engineering, and to explain how to apply these methods to practical, real-world problems. Readers will also learn how to convert numerical algorithms into running computer codes. Features: Numerous pedagogic features including exercises, “pros and cons” boxes for each method discussed, and rigorous highlighting of key topics and ideas Suitable as a primary text for undergraduate courses in numerical methods, but also as a reference to working engineers A Pseudocode approach that makes the book accessible to those with different (or no) coding backgrounds, which does not tie instructors to one particular language over another A dedicated website featuring additional code examples, quizzes, exercises, discussions, and more: https://github.com/zaltac/NumMethodsWPseudoCodes A complete Solution Manual and PowerPoint Presentations are available (free of charge) to instructors at www.routledge.com/9781032754741

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

This practical guide to Mathematica focuses on the specific needs of scientists and engineers. Problems in these fields often are non-trivial, and can push Mathematica (and any computer system) to its limits. Here the author, providing carefully chosen examples, shows how these problems can be solved.

Here we present numerical analysis to advanced undergraduate and master degree level grad students. This is to be done in one semester. The programming language is Mathematica. The mathematical foundation and technique is included. The emphasis is geared toward the two major developing areas of applied mathematics, mathematical finance and mathematical biology.

The desire for numerical answers to applied problems has increased manifold with the advances made in various branches of science and engineering and rapid development of high-speed digital computers. Although numerical methods have always been useful, their role in the present day scientific computations and research is of fundamental importance. numerous distinguishing features. The contents of the book have been organized in a logical order and the topics are discussed in a systematic manner. concepts; algorithms and numerous exercises at the end of each chapter; helps students in problem solving both manually and through computer programming; an exhaustive bibliography; and an appendix containing some important and useful iterative methods for the solution of nonlinear complex equations.

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).