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Differential Equations With Mathematica

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Differential Equations with Mathematica

Differential Equations with Mathematica Book
Author : Martha L. Abell,James P. Braselton
Publisher : AP Professional
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The second edition of this groundbreaking book integrates new applications from a variety of fields, especially biology, physics, and engineering. The new handbook is also completely compatible with Mathematica version 3.0 and is a perfect introduction for Mathematica beginners. The CD-ROM contains built-in commands that let the users solve problems directly using graphical solutions.

Partial Differential Equations and Mathematica

Partial Differential Equations and Mathematica Book
Author : Prem K. Kythe,Michael R. Schäferkotter,Pratap Puri
Publisher : CRC Press
Release : 2018-10-03
ISBN : 1482296322
Language : En, Es, Fr & De

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Book Description :

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.

Symmetry Analysis of Differential Equations with Mathematica

Symmetry Analysis of Differential Equations with Mathematica   Book
Author : Gerd Baumann
Publisher : Springer Science & Business Media
Release : 2013-11-21
ISBN : 1461221102
Language : En, Es, Fr & De

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Book Description :

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.

Differential Equations

Differential Equations Book
Author : Clay C. Ross
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475739494
Language : En, Es, Fr & De

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Book Description :

The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.

A Course in Ordinary Differential Equations

A Course in Ordinary Differential Equations Book
Author : Stephen A. Wirkus,Randall J. Swift
Publisher : CRC Press
Release : 2006-10-23
ISBN : 1420010417
Language : En, Es, Fr & De

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Book Description :

The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB, Mathematica, and Maple A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics student's field o

Differential Equations with Mathematica

Differential Equations with Mathematica Book
Author : Brian R. Hunt,Ronald L. Lipsman,John E. Osborn,Donald A. Outing,Jonathan Rosenberg
Publisher : Wiley
Release : 2009-01-09
ISBN : 9780471773160
Language : En, Es, Fr & De

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Book Description :

Differential Equations with Mathematica 3e is a supplemental text that can enrich and enhance any first course in ordinary differential equations. Designed to accompany Wiley’s ODE texts written by Brannan/Boyce, Boyce/DiPrima, Borrelli/Coleman and Lomen/Lovelock, this supplement helps instructors move towards an earlier use of numerical and geometric methods, place a greater emphasis on systems (including nonlinear ones), and increase discussions of both the benefits and possible pitfalls in numerical solution of ODEs. By providing an introduction to the software that is integrated with the relevant mathematics, Differential Equations with Mathematica can bring students to a level of expertise in the mathematical software system that will allow them to use it in other mathematics, engineering, or science courses.

Partial Differential Equations with Mathematica

Partial Differential Equations with Mathematica Book
Author : Dimitri Dimitrievich Vvedensky
Publisher : Addison Wesley Publishing Company
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

An introduction to linear and nonlinear partial differential equations with extensive use of the popular computational mathematics computer program, Mathematica, to illustrate techniques and solutions and to provide examples that in many cases would not be practical otherwise. No prior knowledge of

Numerical Solutions for Partial Differential Equations

Numerical Solutions for Partial Differential Equations Book
Author : Victor Grigor'e Ganzha,Evgenii Vasilev Vorozhtsov
Publisher : CRC Press
Release : 2017-11-22
ISBN : 1351427520
Language : En, Es, Fr & De

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Book Description :

Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra Mathematica® can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion.

Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica

Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica Book
Author : Kuzman Adzievski,Abul Hasan Siddiqi
Publisher : CRC Press
Release : 2016-04-19
ISBN : 1466510579
Language : En, Es, Fr & De

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Book Description :

With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use Mathematica along with graphics to improve understanding and int

Calculus and Differential Equations with Mathematica

Calculus and Differential Equations with Mathematica Book
Author : Pramote Dechaumphai
Publisher : Alpha Science International, Limited
Release : 2016-05-04
ISBN : 9781783322640
Language : En, Es, Fr & De

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Book Description :

Symbolic mathematics software have played an important role in learning calculus and differential equations. MATHEMATICA is one of the most powerful software being used to solve various types of problems in mathematics. This book presents a clear and easy-to-understand on how to use MATHEMATICA to solve calculus and differential equation problems. The book contains essential topics that are taught in calculus and differential equation courses. These topics are the limits, differentiation, integration, series, ordinary differential equations, Laplace and Fourier transforms, as well as special functions normally encountered in solving science and engineering problems. Numerical methods, in addition, are employed when the exact solutions are not available. The finite element method developed in the latest MATHEMATICA version is used to analyse partial differential equations for problems with complex geometry. The partial differential equations could be in elliptic, parabolic and hyperbolic forms. A large number of examples are presented with detailed derivation for their solutions before using MATHEMATICA to confirm the same results. With the clear explanation of all topics in this book and with the help of MATHEMATICA software, students will enjoy learning calculus and differential equations as compared to the traditional way in the past.

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

Solving Nonlinear Partial Differential Equations with Maple and Mathematica Book
Author : Inna Shingareva,Carlos Lizárraga-Celaya
Publisher : Springer Science & Business Media
Release : 2011-07-24
ISBN : 370910517X
Language : En, Es, Fr & De

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Book Description :

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).

Discrete Dynamical Systems and Difference Equations with Mathematica

Discrete Dynamical Systems and Difference Equations with Mathematica Book
Author : Mustafa R.S. Kulenovic,Orlando Merino
Publisher : CRC Press
Release : 2002-02-27
ISBN : 1420035355
Language : En, Es, Fr & De

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Book Description :

Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and find basins of attraction. Modern computer algebra systems have opened the door to the use of symbolic calculation for studying difference equations. This book offers an introduction to discrete dynamical systems and difference equations and presents the Dynamica software. Developed by the authors and based on Mathematica, Dynamica provides an easy-to-use collection of algebraic, numerical, and graphical tools and techniques that allow users to quickly gain the ability to: Find and classify the stability character of equilibrium and periodic points Perform semicycle analysis of solutions Calculate and visualize invariants Calculate and visualize Lyapunov functions and numbers Plot bifurcation diagrams Visualize stable and unstable manifolds Calculate Box Dimension While it presents the essential theoretical concepts and results, the book's emphasis is on using the software. The authors present two sets of Dynamica sessions: one that serves as a tutorial of the different techniques, the other features case studies of well-known difference equations. Dynamica and notebooks corresponding to particular chapters are available for download from the Internet.

Advanced Engineering Mathematics with Mathematica

Advanced Engineering Mathematics with Mathematica Book
Author : Edward B. Magrab
Publisher : CRC Press
Release : 2020-02-26
ISBN : 100003450X
Language : En, Es, Fr & De

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Book Description :

Advanced Engineering Mathematics with Mathematica® presents advanced analytical solution methods that are used to solve boundary-value problems in engineering and integrates these methods with Mathematica® procedures. It emphasizes the Sturm–Liouville system and the generation and application of orthogonal functions, which are used by the separation of variables method to solve partial differential equations. It introduces the relevant aspects of complex variables, matrices and determinants, Fourier series and transforms, solution techniques for ordinary differential equations, the Laplace transform, and procedures to make ordinary and partial differential equations used in engineering non-dimensional. To show the diverse applications of the material, numerous and widely varied solved boundary value problems are presented.

Introduction to Ordinary Differential Equations with Mathematica

Introduction to Ordinary Differential Equations with Mathematica   Book
Author : Alfred Gray,Mike Mezzino,Mark Pinsky
Publisher : Springer
Release : 1998-06-01
ISBN : 9780387982328
Language : En, Es, Fr & De

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Book Description :

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.

VisualDSolve

VisualDSolve Book
Author : Dan Schwalbe,Stan Wagon
Publisher : Springer
Release : 2011-09-17
ISBN : 9781461274735
Language : En, Es, Fr & De

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Book Description :

This title presents new ideas on the visualization of differential equations with user-configurable tools. The authors use the widely-used computer algebra system, Mathematica, to provide an integrated environment for programming, visualizing graphics, and running commentary for learning and working with differential equations.

Mathematica by Example

Mathematica by Example Book
Author : Martha L Abell,James P. Braselton
Publisher : Academic Press
Release : 2014-05-09
ISBN : 1483259285
Language : En, Es, Fr & De

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Book Description :

Mathematica by Example presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 10 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapters 7, 8, and 9 introduce Mathematica Packages that are not found in most Mathematica reference book. The final chapter covers the Mathematica Help feature. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Differential Equations with Mathematica

Differential Equations with Mathematica Book
Author : Martha L Abell,James P. Braselton
Publisher : Academic Press
Release : 2014-05-09
ISBN : 1483213919
Language : En, Es, Fr & De

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Book Description :

Differential Equations with Mathematica presents an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Mathematica is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Mathematica can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are provided as well. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Mathematica

Mathematica Book
Author : Stephen Wolfram
Publisher : Unknown
Release : 1991
ISBN : 9780201515022
Language : En, Es, Fr & De

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Book Description :

Download Mathematica book written by Stephen Wolfram, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introduction to Mathematica with Applications

Introduction to Mathematica   with Applications Book
Author : Marian Mureşan
Publisher : Springer
Release : 2017-02-21
ISBN : 3319520032
Language : En, Es, Fr & De

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Book Description :

Starting with an introduction to the numerous features of Mathematica®, this book continues with more complex material. It provides the reader with lots of examples and illustrations of how the benefits of Mathematica® can be used. Composed of eleven chapters, it includes the following: A chapter on several sorting algorithms Functions (planar and solid) with many interesting examples Ordinary differential equations Advantages of Mathematica® dealing with the Pi number The power of Mathematica® working with optimal control problems Introduction to Mathematica® with Applications will appeal to researchers, professors and students requiring a computational tool.

The Mathematica GuideBook for Programming

The Mathematica GuideBook for Programming Book
Author : Michael Trott
Publisher : Springer
Release : 2013-12-21
ISBN : 1441985034
Language : En, Es, Fr & De

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Book Description :

This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes -- Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises. This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists. An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering.