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Partial Differential Equations and Boundary Value Problems with Maple

Partial Differential Equations and Boundary Value Problems with Maple
A Book

by George A. Articolo

  • Publisher : Academic Press
  • Release : 2009-03-23
  • Pages : 744
  • ISBN : 0080885063
  • Language : En, Es, Fr & De
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Partial Differential Equations and Boundary Value Problems with Maple, Second Edition, presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours - an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. This updated edition provides a quick overview of the software w/simple commands needed to get started. It includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations. It also incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions. Numerous example problems and end of each chapter exercises are provided. Provides a quick overview of the software w/simple commands needed to get started Includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations Incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions Numerous example problems and end of each chapter exercises

Partial Differential Equations & Boundary Value Problems with Maple V

Partial Differential Equations & Boundary Value Problems with Maple V
A Book

by George A. Articolo

  • Publisher : Academic Press
  • Release : 1998-05-08
  • Pages : 628
  • ISBN : 9780120644759
  • Language : En, Es, Fr & De
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Integrating Maple V animation software and traditional topics of partial differential equations, this text discusses first and second-order differential equations, Sturm-Liouville eigenvalue problems, generalized Fourier series, the diffusion or heat equation and the wave equation in one and two spatial dimensions, the Laplace equation in two spatial dimensions, nonhomogenous versions of the diffusion and wave equations, and Laplace transform methods of solution. Annotation copyrighted by Book News, Inc., Portland, OR.

Elementary Partial Differential Equations with Boundary Value Problems

Elementary Partial Differential Equations with Boundary Value Problems
A Book

by Larry C. Andrews

  • Publisher : Harcourt College Pub
  • Release : 1986-01-01
  • Pages : 488
  • ISBN : 9780155210875
  • Language : En, Es, Fr & De
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Introductory Differential Equations

Introductory Differential Equations
with Boundary Value Problems, Student Solutions Manual (e-only)

by Martha L. Abell,James P. Braselton

  • Publisher : Academic Press
  • Release : 2010-04-20
  • Pages : 212
  • ISBN : 9780123846655
  • Language : En, Es, Fr & De
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This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging. Many different majors will require differential equations and applied mathematics, so there should be a lot of interest in an intro-level text like this. The accessible writing style will be good for non-math students, as well as for undergrad classes.

Differential Equations with Maple V

Differential Equations with Maple V
A Book

by Martha L. Abell,James P. Braselton

  • Publisher : Academic Press
  • Release : 2000
  • Pages : 719
  • ISBN : 9780120415601
  • Language : En, Es, Fr & De
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Through the use of numerous examples that illustrate how to solve important applications using Maple V, Release 2, this book provides readers with a solid, hands-on introduction to ordinary and partial differental equations. Includes complete coverage of constructing and numerically computing and approximating solutions to ordinary and partial equations.

Partial Differential Equations of Applied Mathematics

Partial Differential Equations of Applied Mathematics
A Book

by Erich Zauderer

  • Publisher : John Wiley & Sons
  • Release : 2011-10-24
  • Pages : 968
  • ISBN : 1118031407
  • Language : En, Es, Fr & De
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This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.

Partial Differential Equations for Computational Science

Partial Differential Equations for Computational Science
With Maple and Vector Analysis

by David Betounes

  • Publisher : Springer Science & Business Media
  • Release : 1998-05-15
  • Pages : 517
  • ISBN : 9780387983004
  • Language : En, Es, Fr & De
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This book will have strong appeal to interdisciplinary audiences, particularly in regard to its treatments of fluid mechanics, heat equations, and continuum mechanics. There is also a heavy focus on vector analysis. Maple examples, exercises, and an appendix is also included.

Beginning Partial Differential Equations

Beginning Partial Differential Equations
A Book

by Peter V. O'Neil

  • Publisher : John Wiley & Sons
  • Release : 2014-04-07
  • Pages : 438
  • ISBN : 1118629949
  • Language : En, Es, Fr & De
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"Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy"--

Computational Methods in Chemical Engineering with Maple

Computational Methods in Chemical Engineering with Maple
A Book

by Ralph E. White,Venkat R. Subramanian

  • Publisher : Springer Science & Business Media
  • Release : 2010-02-06
  • Pages : 860
  • ISBN : 9783642043116
  • Language : En, Es, Fr & De
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This book presents Maple solutions to a wide range of problems relevant to chemical engineers and others. Many of these solutions use Maple’s symbolic capability to help bridge the gap between analytical and numerical solutions. The readers are strongly encouraged to refer to the references included in the book for a better understanding of the physics involved, and for the mathematical analysis. This book was written for a senior undergraduate or a first year graduate student course in chemical engineering. Most of the examples in this book were done in Maple 10. However, the codes should run in the most recent version of Maple. We strongly encourage the readers to use the classic worksheet (*. mws) option in Maple as we believe it is more user-friendly and robust. In chapter one you will find an introduction to Maple which includes simple basics as a convenience for the reader such as plotting, solving linear and nonlinear equations, Laplace transformations, matrix operations, ‘do loop,’ and ‘while loop. ’ Chapter two presents linear ordinary differential equations in section 1 to include homogeneous and nonhomogeneous ODEs, solving systems of ODEs using the matrix exponential and Laplace transform method. In section two of chapter two, nonlinear ordinary differential equations are presented and include simultaneous series reactions, solving nonlinear ODEs with Maple’s ‘dsolve’ command, stop conditions, differential algebraic equations, and steady state solutions. Chapter three addresses boundary value problems.

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

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
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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).

A Course in Differential Equations with Boundary Value Problems, Second Edition

A Course in Differential Equations with Boundary Value Problems, Second Edition
A Book

by Stephen A. Wirkus,Randall J. Swift,Ryan Szypowski

  • Publisher : CRC Press
  • Release : 2016-11-26
  • Pages : 848
  • ISBN : 9781498736053
  • Language : En, Es, Fr & De
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Previous title: A course in ordinary differential equations / Stephen A. Wirkus, Randall J. Swift (Boca Raton: CRC Press, 2015).

Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems
A Book

by C. Henry Edwards,David E. Penney

  • Publisher : Pearson Prentice Hall
  • Release : 2007-09-01
  • Pages : 760
  • ISBN : 9780132358811
  • Language : En, Es, Fr & De
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For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus. The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.

Numerical Integration of Space Fractional Partial Differential Equations

Numerical Integration of Space Fractional Partial Differential Equations
Vol 1 - Introduction to Algorithms and Computer Coding in R

by Younes Salehi,William E. Schiesser

  • Publisher : Morgan & Claypool Publishers
  • Release : 2017-11-27
  • Pages : 201
  • ISBN : 1681732084
  • Language : En, Es, Fr & De
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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. 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. The Caputo derivative is defined as a convolution integral. Thus, rather than being local (with a value at a particular point in space), the Caputo derivative is non-local (it is based on an integration in space), which is one of the reasons that it has properties not shared by integer derivatives. A principal objective of the two volumes is to provide the reader with a set of documented R routines that are discussed in detail, and can be downloaded and executed without having to first study the details of the relevant numerical analysis and then code a set of routines. In the first volume, the emphasis is on basic concepts of SFPDEs and the associated numerical algorithms. The presentation is not as formal mathematics, e.g., theorems and proofs. Rather, the presentation is by examples of SFPDEs, including a detailed discussion of the algorithms for computing numerical solutions to SFPDEs and a detailed explanation of the associated source code.

Partial Differential Equations

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
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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.

The Cumulative Book Index

The Cumulative Book Index
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1999
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Fourier Series and Numerical Methods for Partial Differential Equations

Fourier Series and Numerical Methods for Partial Differential Equations
A Book

by Richard Bernatz

  • Publisher : John Wiley & Sons
  • Release : 2010-07-30
  • Pages : 332
  • ISBN : 9780470651377
  • Language : En, Es, Fr & De
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The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.

Partial Differential Equations

Partial Differential Equations
Analytical and Numerical Methods, Second Edition

by Mark S. Gockenbach

  • Publisher : SIAM
  • Release : 2010-12-02
  • Pages : 654
  • ISBN : 0898719356
  • Language : En, Es, Fr & De
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A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.

Engineering Mathematics with Maple

Engineering Mathematics with Maple
A Book

by John S. Robertson

  • Publisher : McGraw-Hill Science, Engineering & Mathematics
  • Release : 1996
  • Pages : 278
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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This book is intended for use as a supplemental tool for courses in engineering mathematics, applied ordinary and partial differential equations, vector analysis, applied complex analysis, and other advanced courses in which MAPLE is used. Each chapter has been written so that the material it contains may be covered in a typical laboratory session of about 1-1/2 to 2 hours. The goals for every laboratory are stated at the beginning of the chapter. Mathematical concepts are then discussed within a framework of abundant engineering applications and problem-solving techniques using MAPLE. Each chapter is also followed by a set of exploratory exercises that are intended to serve as a starting point for a student's mathematical experimentation. Since most of the exercises can be solved in more than one way, there is no answer key for either students or professors.

Boundary Value Problems

Boundary Value Problems
A Book

by David L. Powers

  • Publisher : Unknown Publisher
  • Release : 1972
  • Pages : 238
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Fundamentals of Differential Equations and Boundary Value Problems

Fundamentals of Differential Equations and Boundary Value Problems
A Book

by R. Kent Nagle,E. B. Saff,Arthur David Snider

  • Publisher : Addison Wesley
  • Release : 2000
  • Pages : 859
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The third edition of this student-oriented text features new sections on qualitative features and vibrations. There group projects at the end of each chapter, technical writing exercises, as well as a new dedicated website.