# introduction to partial differential equations for scientists and engineers using mathematica

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## Introduction To Partial Differential Equations For Scientists And Engineers Using Mathematica

**Author :**Kuzman Adzievski

**ISBN :**9781466510579

**Genre :**Mathematics

**File Size :**76. 56 MB

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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 interpretation of concepts. They also present exercises in each chapter and solutions to selected examples. Topics discussed include Laplace and Fourier transforms as well as Sturm-Liouville boundary value problems.

## Linear Partial Differential Equations For Scientists And Engineers

**Author :**Tyn Myint-U

**ISBN :**0817645608

**Genre :**Mathematics

**File Size :**45. 36 MB

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This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.

## Solution Techniques For Elementary Partial Differential Equations

**Author :**Christian Constanda

**ISBN :**9781498704984

**Genre :**Mathematics

**File Size :**53. 56 MB

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Solution Techniques for Elementary Partial Differential Equations, Third Edition remains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). Making the text even more user-friendly, this third edition covers important and widely used methods for solving PDEs. New to the Third Edition New sections on the series expansion of more general functions, other problems of general second-order linear equations, vibrating string with other types of boundary conditions, and equilibrium temperature in an infinite strip Reorganized sections that make it easier for students and professors to navigate the contents Rearranged exercises that are now at the end of each section/subsection instead of at the end of the chapter New and improved exercises and worked examples A brief Mathematica® program for nearly all of the worked examples, showing students how to verify results by computer This bestselling, highly praised textbook uses a streamlined, direct approach to develop students’ competence in solving PDEs. It offers concise, easily understood explanations and worked examples that allow students to see the techniques in action.

## Solving Nonlinear Partial Differential Equations With Maple And Mathematica

**Author :**Inna Shingareva

**ISBN :**9783709105177

**Genre :**Mathematics

**File Size :**56. 80 MB

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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).

## Numerical Integration Of Space Fractional Partial Differential Equations

**Author :**Younes Salehi

**ISBN :**9781681732107

**Genre :**Mathematics

**File Size :**57. 40 MB

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Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: •Vol 1: Introduction to Algorithms and Computer Coding in R •Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: •Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions •Fisher-Kolmogorov SFPDE •Burgers SFPDE •Fokker-Planck SFPDE •Burgers-Huxley SFPDE •Fitzhugh-Nagumo SFPDE. These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order ?? with 1 ≤ ?? ≤ 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).

## Partial Differential Equations

**Author :**Ioannis P. Stavroulakis

**ISBN :**981238815X

**Genre :**Mathematics

**File Size :**79. 13 MB

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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 And Mathematica

**Author :**Prem K. Kythe

**ISBN :**1584883146

**Genre :**Mathematics

**File Size :**86. 31 MB

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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 Partial Differential Equations With Matlab

**Author :**Jeffery M. Cooper

**ISBN :**0817639675

**Genre :**Mathematics

**File Size :**55. 20 MB

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The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience. This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide an up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes. Topic and Features: • Nonlinear equations including nonlinear conservation laws; • Dispersive wave equations and the Schrodinger equation; • Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform; • Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this web site. This text/reference is an excellent resources designed to introduce advanced students in mathematics, engineering and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.

## An Introduction To Partial Differential Equations With Matlab Second Edition

**Author :**Matthew P. Coleman

**ISBN :**9781439898475

**Genre :**Mathematics

**File Size :**56. 23 MB

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An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website.

## Partial Differential Equations

**Author :**Bhamra

**ISBN :**9788120339170

**Genre :**Differential equations, Partial

**File Size :**66. 55 MB

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