Differential Equations With Mathematica
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Introduction To Ordinary Differential Equations With Mathematica
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Author : Alfred Gray
language : en
Publisher: Springer
Release Date : 1997-06-20
Introduction To Ordinary Differential Equations With Mathematica written by Alfred Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-20 with Computers categories.
These materials - developed and thoroughly class tested over many years by the authors -are for use in courses at the sophomore/junior level. A prerequisite is the calculus of one variable, although calculus of several variables, and linear algebra are recommended. The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems. Liberal use is made of programs in Mathematica, both for symbolic computations and graphical displays. The programs are described in separate sections, as well as in the accompanying Mathematica notebooks. However, the book has been designed so that it can be read with or without Mathematica and no previous knowledge of Mathematica is required. The CD-ROM contains the Mathematica solution of worked examples, a selection of various Mathematica notebooks, Mathematica movies and sample labs for students. Mathematica programs and additional problem/example files will be available online through the TELOS Web site and the authors dedicated web site.
Differential Equations
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Author : Marian Mureşan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-06-17
Differential Equations written by Marian Mureşan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-17 with Mathematics categories.
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
Differential Equations With Mathematica
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Author : Martha L. Abell
language : en
Publisher: Academic Press
Release Date : 2016-09-19
Differential Equations With Mathematica written by Martha L. Abell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-19 with Computers categories.
Differential Equations with Mathematica, Fourth Edition is a supplementing reference which uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica's diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica's built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica's outstanding graphics capabilities. - Demonstrates how to take advantage of the advanced features of Mathematica 10 - Introduces the fundamental theory of ordinary and partial differential equations using Mathematica to solve typical problems of interest to students, instructors, scientists, and practitioners in many fields - Showcases practical applications and case studies drawn from biology, physics, and engineering
Symmetry Analysis Of Differential Equations With Mathematica
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Author : Gerd Baumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Symmetry Analysis Of Differential Equations With Mathematica written by Gerd Baumann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.
The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie-in honor of Sophus Lie---carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and en gineering is demonstrated by many examples. The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improve ments and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica.
Introduction To Ordinary Differential Equations With Mathematica
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Author : Alfred Gray
language : en
Publisher: Springer
Release Date : 1998-06-01
Introduction To Ordinary Differential Equations With Mathematica written by Alfred Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-01 with Mathematics categories.
The purpose of this companion volume to our text is to provide instructors (and eventu ally students) with some additional information to ease the learning process while further documenting the implementations of Mathematica and ODE. In an ideal world this volume would not be necessary, since we have systematically worked to make the text unambiguous and directly useful, by providing in the text worked examples of every technique which is discussed at the theoretical level. However, in our teaching we have found that it is helpful to have further documentation of the various solution techniques introduced in the text. The subject of differential equations is particularly well-suited to self-study, since one can always verify by hand calculation whether or not a given proposed solution is a bona fide solution of the differential equation and initial conditions. Accordingly, we have not reproduced the steps of the verification process in every case, rather content with the illustration of some basic cases of verification in the text. As we state there, students are strongly encouraged to verify that the proposed solution indeed satisfies the requisite equation and supplementary conditions.
Partial Differential Equations And Mathematica
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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Partial Differential Equations And Mathematica written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
Early training in the elementary techniques of partial differential equations is invaluable to students in engineering and the sciences as well as mathematics. However, to be effective, an undergraduate introduction must be carefully designed to be challenging, yet still reasonable in its demands. Judging from the first edition's popularity, instructors and students agree that despite the subject's complexity, it can be made fairly easy to understand. Revised and updated to reflect the latest version of Mathematica, Partial Differential Equations and Boundary Value Problems with Mathematica, Second Edition meets the needs of mathematics, science, and engineering students even better. While retaining systematic coverage of theory and applications, the authors have made extensive changes that improve the text's accessibility, thoroughness, and practicality. New in this edition: Upgraded and expanded Mathematica sections that include more exercises An entire chapter on boundary value problems More on inverse operators, Legendre functions, and Bessel functions Simplified treatment of Green's functions that make it more accessible to undergraduates A section on the numerical computation of Green's functions Mathemcatica codes for solving most of the problems discussed Boundary value problems from continuum mechanics, particularly on boundary layers and fluctuating flows Wave propagation and dispersion With its emphasis firmly on solution methods, this book is ideal for any mathematics curricula. It succeeds not only in preparing readers to meet the challenge of PDEs, but also in imparting the inherent beauty and applicability of the subject.
Introduction To Ordinary Differential Equations With Mathematica
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Author : Alfred Gray
language : en
Publisher: Springer
Release Date : 1998-10-02
Introduction To Ordinary Differential Equations With Mathematica written by Alfred Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-02 with Mathematics categories.
The purpose of this companion volume to our text is to provide instructors (and eventu ally students) with some additional information to ease the learning process while further documenting the implementations of Mathematica and ODE. In an ideal world this volume would not be necessary, since we have systematically worked to make the text unambiguous and directly useful, by providing in the text worked examples of every technique which is discussed at the theoretical level. However, in our teaching we have found that it is helpful to have further documentation of the various solution techniques introduced in the text. The subject of differential equations is particularly well-suited to self-study, since one can always verify by hand calculation whether or not a given proposed solution is a bona fide solution of the differential equation and initial conditions. Accordingly, we have not reproduced the steps of the verification process in every case, rather content with the illustration of some basic cases of verification in the text. As we state there, students are strongly encouraged to verify that the proposed solution indeed satisfies the requisite equation and supplementary conditions.
Scientific Computing With Mathematica
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Author : Addolorata Marasco
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-09
Scientific Computing With Mathematica written by Addolorata Marasco and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-09 with Computers categories.
CD-ROM includes: Mathematica files (ODE.m and 11 notebooks: Chapter1.nb - Chapter10.nb and Package.nb).
Differential Equations With Mathematica
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Author : Kevin Robert Coombes
language : en
Publisher: John Wiley & Sons
Release Date : 1995
Differential Equations With Mathematica written by Kevin Robert Coombes and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.
Partial Differential Equations
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Author : Ioannis P. Stavroulakis
language : en
Publisher: World Scientific
Release Date : 2004
Partial Differential Equations written by Ioannis P. Stavroulakis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This textbook is a self-contained introduction to partial differential equations.It has been designed for undergraduates and first year graduate students majoring in mathematics, physics, engineering, or science.The text provides an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations. Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered.