Introduction To Ordinary 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.
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.
Differential Equations
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Author : Clay C. Ross
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Differential Equations written by Clay C. Ross 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 2013-03-09 with Mathematics categories.
Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. There is no attempt here to use computing to avoid doing differential equations and linear algebra. The goal is to make some first ex plorations in the subject accessible to students who have had one year of calculus. Some of the sciences are now using the symbol-manipulative power of Mathemat ica to make more of their subject accessible. This book is one way of doing so for differential equations and linear algebra. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject. The theory of differential equations and of linear algebra permeates the discussion. Every topic is supported by a statement of the theory. But the primary thrust here is obtaining solutions and information about solutions, rather than proving theorems. There are other courses where proving theorems is central. The goals of this text are to establish a solid understanding of the notion of solution, and an appreciation for the confidence that the theory gives during a search for solutions. Later the student can have the same confidence while personally developing the theory.
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.
Ordinary Differential Equations
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Author : Morris Tenenbaum
language : en
Publisher: Courier Corporation
Release Date : 1985-10-01
Ordinary Differential Equations written by Morris Tenenbaum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-10-01 with Mathematics categories.
Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.
Differential Equations Theory And Applications
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Author : David Betounes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Differential Equations Theory And Applications written by David Betounes 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 2013-06-29 with Mathematics categories.
This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. His torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mathe matics, the material is organized so that the book can also be used in a wider setting within today's modern university and society (see "Ways to Use the Book" below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the in structor's or reader's preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend to gether the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab.
Ordinary Differential Equations And Dynamical Systems
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Author : Gerald Teschl
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-12
Ordinary Differential Equations And Dynamical Systems written by Gerald Teschl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-12 with Mathematics categories.
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Introduction To Ordinary Differential Equations With Mathematica
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Author : Alfred Gray
language : en
Publisher: Springer
Release Date : 2014-11-28
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 2014-11-28 with Mathematics 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.
Introduction To Ordinary Differential Equations
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Author : Shepley L. Ross
language : en
Publisher:
Release Date : 1966
Introduction To Ordinary Differential Equations written by Shepley L. Ross and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Differential equations categories.
An Introduction To Ordinary Differential Equations
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Author : Earl A. Coddington
language : en
Publisher:
Release Date : 1961
An Introduction To Ordinary Differential Equations written by Earl A. Coddington and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Differential equations categories.
This book is meant to be a text which can be used for a first course in ordinary differential equations. The student is assumed to have a knowledge of calculus but not what is usually called advanced calculus. The aim is to give an elementary, thorough systematic introduction to the subject. All significant results are stated as theorems, and careful proofs are given. The exercises in the book serve two purposes: to develop the student's technique in solving equations, or to help sharpen the student's understanding of the mathematical structure of the subject. The exercises also introduce the student to a variety of topics not treated in the text: stability, equations with periodic coefficients, and boundary value problems.