# Download Differential Equations with Mathematica Ebook PDF

**Introduction to Ordinary Differential Equations with Mathematica**

An Integrated Multimedia Approach

#### by **Alfred Gray,Michael Mezzino,Mark A. Pinsky**

- Publisher : Springer
- Release : 2013-09-01
- Pages : 890
- ISBN : 9781461274698
- Language : En, Es, Fr & De

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.

**Partial Differential Equations and Mathematica**

A Book

#### by **Prem K. Kythe,Michael R. Schäferkotter,Pratap Puri**

- Publisher : CRC Press
- Release : 2002-11-12
- Pages : 440
- ISBN : 9781584883142
- Language : En, Es, Fr & De

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®**

A Book

#### by **Gerd Baumann**

- Publisher : Springer
- Release : 2014-01-20
- Pages : 521
- ISBN : 9781461274186
- Language : En, Es, Fr & De

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.

**Introduction to Ordinary Differential Equations with Mathematica**

An Integrated Multimedia Approach

#### by **Alfred Gray,Michael Mezzino,Mark A. Pinsky**

- Publisher : Springer
- Release : 1997-06-20
- Pages : 890
- ISBN : 9876543210XXX
- Language : En, Es, Fr & De

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 with Mathematica**

A Book

#### by **Martha L. Abell,James P. Braselton**

- Publisher : AP Professional
- Release : 1997
- Pages : 807
- ISBN : 9876543210XXX
- Language : En, Es, Fr & De

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.

**Differential Equations with Mathematica**

A Book

#### by **Martha L. L. Abell,James P. Braselton**

- Publisher : Academic Press
- Release : 2016-09-19
- Pages : 880
- ISBN : 0128047771
- Language : En, Es, Fr & De

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

**Calculus and Differential Equations with Mathematica**

A Book

#### by **Pramote Dechaumphai**

- Publisher : Unknown Publisher
- Release : 2016
- Pages : 428
- ISBN : 9789740335436
- Language : En, Es, Fr & De

**Integral Calculus and Differential Equations Using Mathematica**

A Book

#### by **Cesar Perez Lopez**

- Publisher : Createspace Independent Publishing Platform
- Release : 2016-01-16
- Pages : 166
- ISBN : 9781523434176
- Language : En, Es, Fr & De

This book provides all the material needed to work on Integral Calculus and Differential Equations using Mathematica. It includes techniques for solving all kinds of integral and its applications for calculating lengths of curves, areas, volumes, surfaces of revolution... With Mathematica is possible solve ordinary and partial differential equations of various kinds, and systems of such equations, either symbolically or using numerical methods (Euler's method,, the Runge-Kutta method,...). It also describes how to implement mathematical tools such as the Laplace transform, orthogonal polynomials, and special functions (Airy and Bessel functions), and find solutions of differential equations in partial derivatives.The main content of the book is as follows:PRACTICAL INTRODUCTION TO MATHEMATICA 1.1 CALCULATION NUMERIC WITH MATHEMATICA 1.2 SYMBOLIC CALCULATION WITH MATHEMATICA 1.3 GRAPHICS WITH MATHEMATICA 1.4 MATHEMATICA AND THE PROGRAMMING INTEGRATION AND APPLICATIONS 2.1 INDEFINITE INTEGRALS 2.1.1 Inmediate integrals 2.2 INTEGRATION BY SUBSTITUTION (OR CHANGE OF VARIABLES) 2.2.1 Exponential, logarithmic, hyperbolic and inverse circular functions 2.2.2 Irrational functions, binomial integrals 2.3 INTEGRATION BY PARTS 2.4 INTEGRATION BY REDUCTION AND CYCLIC INTEGRATION DEFINITE INTEGRALS. CURVE ARC LENGTH, AREAS, VOLUMES AND SURFACES OF REVOLUTION. IMPROPER INTEGRALS 3.1 DEFINITE INTEGRALS 3.2 CURVE ARC LENGTH 3.3 THE AREA ENCLOSED BETWEEN CURVES 3.4 SURFACES OF REVOLUTION 3.5 VOLUMES OF REVOLUTION 3.6 CURVILINEAR INTEGRALS 3.7 IMPROPER INTEGRALS 3.8 PARAMETER DEPENDENT INTEGRALS 3.9 THE RIEMANN INTEGRAL INTEGRATION IN SEVERAL VARIABLES AND APPLICATIONS. AREAS AND VOLUMES. DIVERGENCE, STOKES AND GREEN'S THEOREMS 4.1 AREAS AND DOUBLE INTEGRALS 4.2 SURFACE AREA BY DOUBLE INTEGRATION 4.3 VOLUME CALCULATION BY DOUBLE INTEGRALS 4.4 VOLUME CALCULATION AND TRIPLE INTEGRALS 4.5 GREEN'S THEOREM 4.6 THE DIVERGENCE THEOREM 4.7 STOKES' THEOREM FIRST ORDER DIFFERENTIAL EQUATIONS. SEPARATES VARIABLES, EXACT EQUATIONS, LINEAR AND HOMOGENEOUS EQUATIONS. NUMERIACAL METHODS 5.1 SEPARATION OF VARIABLES 5.2 HOMOGENEOUS DIFFERENTIAL EQUATIONS 5.3 EXACT DIFFERENTIAL EQUATIONS 5.4 LINEAR DIFFERENTIAL EQUATIONS 5.5 NUMERICAL SOLUTIONS TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER HIGH-ORDER DIFFERENTIAL EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS 6.1 ORDINARY HIGH-ORDER EQUATIONS 6.2 HIGHER-ORDER LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.3 NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS. VARIATION OF PARAMETERS 6.4 NON-HOMOGENEOUS LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. CAUCHY-EULER EQUATIONS 66.5 THE LAPLACE TRANSFORM 6.6 SYSTEMS OF LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.7 SYSTEMS OF LINEAR NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS HIGHER ORDEN DIFFERENTIAL EQUATIONS AND SYSTEMS USING APPROXIMATION METHODS. DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 7.1 HIGHER ORDER EQUATIONS AND APPROXIMATION METHODS 7.2 THE EULER METHOD 7.3 THE RUNGE-KUTTA METHOD 7.4 DIFFERENTIAL EQUATIONS SYSTEMS BY APPROXIMATE METHODS 7.5 DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 7.6 ORTHOGONAL POLYNOMIALS 7.7 AIRY AND BESSEL FUNCTIONS

**Differential Equations with Mathematica, Revised for Mathematica 3.0**

A Book

#### by **Kevin R. Coombes,Brian R. Hunt,Ronald L. Lipsman**

- Publisher : John Wiley & Sons Incorporated
- Release : 1998-01-05
- Pages : 240
- ISBN : 9876543210XXX
- Language : En, Es, Fr & De

This book changes the emphasis in the traditional ordinary differential equations (ODE) course by using a mathematical software system to introduce numerical methods, geometric interpretation, symbolic computation, and qualitative analysis into the course in a basic way. Includes concise instructions for using Mathematica on three popular computer platforms: Windows, Macintosh, and the X Window System. It focuses on the specific features of Mathematica that are useful for analyzing differential equations, and it also describes the features of the Mathematica "Notebook" interface that are necessary for creating a finished document.

**Partial Differential Equations and Mathematica**

A Book

#### by **Prem K. Kythe,Michael R. Schäferkotter,Pratap Puri**

- Publisher : CRC Press
- Release : 2018-10-03
- Pages : 440
- ISBN : 1482296322
- Language : En, Es, Fr & De

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.

**Differential Equations with Mathematica**

Revised for Mathematica 3.0

#### by **Anonim**

- Publisher : Unknown Publisher
- Release : 1998
- Pages : 240
- ISBN : 9876543210XXX
- Language : En, Es, Fr & De

**Introduction to Ordinary Differential Equations with Mathematica®**

Solutions Manual

#### by **Alfred Gray,Mike Mezzino,Mark Pinsky**

- Publisher : Springer
- Release : 1998-06-01
- Pages : 530
- ISBN : 9780387982328
- Language : En, Es, Fr & De

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.

**Symmetry Analysis of Differential Equations with Mathematica®**

A Book

#### by **Gerd Baumann**

- Publisher : Springer Science & Business Media
- Release : 2000-04-20
- Pages : 521
- ISBN : 9780387985527
- Language : En, Es, Fr & De

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 with Mathematica**

A Book

#### by **Martha L Abell,James P. Braselton**

- Publisher : Academic Press
- Release : 2014-05-09
- Pages : 640
- ISBN : 1483213919
- Language : En, Es, Fr & De

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.

**Partial Differential Equations**

An Introduction with Mathematica and MAPLE

#### by **Ioannis P. Stavroulakis,Stepan A. Tersian**

- Publisher : World Scientific
- Release : 2004
- Pages : 306
- ISBN : 9789812388155
- Language : En, Es, Fr & De

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.

**Partial Differential Equations: An Introduction With Mathematica And Maple (2nd Edition)**

An Introduction with Mathematica and Maple Second Edition

#### by **Stavroulakis Ioannis P,Tersian Stepan A**

- Publisher : World Scientific Publishing Company
- Release : 2004-04-27
- Pages : 320
- ISBN : 9813106301
- Language : En, Es, Fr & De

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.

**Differential Equations with Mathematica**

A Book

#### by **Coombes**

- Publisher : Unknown Publisher
- Release : 1994-11-01
- Pages : 85
- ISBN : 9780471118404
- Language : En, Es, Fr & De

**Scientific Computing with Mathematica®**

Mathematical Problems for Ordinary Differential Equations

#### by **Addolorata Marasco,Antonio Romano**

- Publisher : Springer Science & Business Media
- Release : 2012-12-06
- Pages : 270
- ISBN : 1461201519
- Language : En, Es, Fr & De

Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica for Ordinary Differential Equations provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use ODEs and Mathematica in the Dynamics of rigid bodies. Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ordinary differential equations such as, phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica. Topics and Features:*Explains how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving *End-of- chapter exercise sets incorporating the use of Mathematica programs *Detailed description and explanation of the mathematical procedures underlying the programs written in Mathematica *Appendix describing the use of ten notebooks to guide the reader through all the exercises. This book is an essential text/reference for students, graduates and practitioners in applied mathematics and engineering interested in ODE's problems in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-

**VisualDSolve**

Visualizing Differential Equations with Mathematica®

#### by **Dan Schwalbe,Stan Wagon**

- Publisher : Springer
- Release : 2011-09-17
- Pages : 271
- ISBN : 9781461274735
- Language : En, Es, Fr & De

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.

**Solving Nonlinear Partial Differential Equations with Maple and Mathematica**

A Book

#### by **Inna Shingareva,Carlos Lizárraga-Celaya**

- Publisher : Springer Science & Business Media
- Release : 2011-07-24
- Pages : 357
- ISBN : 370910517X
- Language : En, Es, Fr & De

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).