Symmetry Analysis of Differential Equations with Mathematica(r)

ISBN-13: 9781461274186 / Angielski / Miękka / 2014 / 521 str.

Gerd Baumann

Opis

The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

Recenzje

"The book is essentially an extensive user manual for the Mathematica program ... . The book concentrates very much on computational aspects and should be useful for engineers and scientists who want to learn fast the basic computational recipes for a symmetry analysis. ... The strength of the book are the close integration of computer algebra and the large number of examples often stemming from real applications." (Werner M.Seiler, zbMATH 0946.35002, 2021)

Spis treści

Introduction.- Elements of Symmetry Analysis.- Derivatives.- Symmetries of Ordinary Differential Equations.- Point Symmetries of Partial Differential Equations.- Non-Classical Symmetries of Partial Differential Equations.- Potential Symmetries of Partial Differential Equations.- Approximate Symmetries of Partial Differential Equations.- Generalized Symmetries of Partial Differential Equations.- Solution of Coupled Linear Partial Differential Equations.- Appendix.- Index.

O autorze

The first publication to offer speedy, computer-algebra based calulations and solutions using Lie's methods and techniques. An invaluable tool for scientists, mathematicians and engeineers, dealing with symmetry analysis of differential equations.