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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 and Boundary Value Problems with Maple V

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

by George A. Articolo

  • Publisher : Unknown Publisher
  • Release : 1998
  • Pages : 628
  • ISBN : 9780120644766
  • Language : En, Es, Fr & De
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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.

Student Solutions Manual, Partial Differential Equations & Boundary Value Problems with Maple

Student Solutions Manual, Partial Differential Equations & Boundary Value Problems with Maple
A Book

by George A. Articolo

  • Publisher : Academic Press
  • Release : 2009-07-22
  • Pages : 744
  • ISBN : 012381412X
  • Language : En, Es, Fr & De
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Student Solutions Manual, Partial Differential Equations & Boundary Value Problems with Maple

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 : 2017-01-24
  • Pages : 788
  • ISBN : 1498736084
  • Language : En, Es, Fr & De
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A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®,?Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. ? Features MATLAB®,?Mathematica®, and MapleTM are incorporated at the end of each chapter. All three software packages have parallel code and exercises; There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages. Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book

A Course in Differential Equations with Boundary Value Problems

A Course in Differential Equations with Boundary Value Problems
A Book

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

  • Publisher : CRC Press
  • Release : 2017-01-24
  • Pages : 768
  • ISBN : 1498736068
  • Language : En, Es, Fr & De
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A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®, Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. Features MATLAB®, Mathematica®, and MapleTM are incorporated at the end of each chapter. All three software packages have parallel code and exercises; There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages. Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book

Introduction to Partial Differential Equations (with Maple), An: A Concise Course

Introduction to Partial Differential Equations (with Maple), An: A Concise Course
A Book

by Zhilin Li,Larry Norris

  • Publisher : World Scientific Publishing Company
  • Release : 2021-09-23
  • Pages : 220
  • ISBN : 9789811228629
  • Language : En, Es, Fr & De
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The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations. The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions. The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.

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).

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 in Mechanics 2

Partial Differential Equations in Mechanics 2
The Biharmonic Equation, Poisson’s Equation

by A.P.S. Selvadurai

  • Publisher : Springer Science & Business Media
  • Release : 2013-06-29
  • Pages : 698
  • ISBN : 3662092050
  • Language : En, Es, Fr & De
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This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Partial Differential Equations in Mechanics 1

Partial Differential Equations in Mechanics 1
Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation

by A.P.S. Selvadurai

  • Publisher : Springer Science & Business Media
  • Release : 2000-10-19
  • Pages : 596
  • ISBN : 9783540672838
  • Language : En, Es, Fr & De
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This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

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"--

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.

Introductory Differential Equations

Introductory Differential Equations
A Book

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

  • Publisher : Elsevier
  • Release : 2014-08-19
  • Pages : 530
  • ISBN : 0124172822
  • Language : En, Es, Fr & De
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Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. It follows a traditional approach and includes ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple. 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 array of exercises ranging from straightforward to challenging. There are also new applications and extended projects made relevant to everyday life through the use of examples in a broad range of contexts. This book will be of interest to undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering. Provides the foundations to assist students in learning how to read and understand the subject, but also helps students in learning how to read technical material in more advanced texts as they progress through their studies Exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging Includes new applications and extended projects made relevant to "everyday life" through the use of examples in a broad range of contexts Accessible approach with applied examples and will be good for non-math students, as well as for undergrad classes

Partial Differential Equations

Partial Differential Equations
An Introduction with Mathematica and Maple

by Ioannis P Stavroulakis,Stepan A Tersian

  • Publisher : World Scientific Publishing Company
  • Release : 1999-12-13
  • Pages : 308
  • ISBN : 9813105534
  • Language : En, Es, Fr & De
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This textbook is a self-contained introduction to partial differential equations. It is designed for undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give 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 material is illustrated with model examples. Mathematics software products such as Mathematica and Maple in ScientificWorkPlace are used in both graphical and computational aspects. Request Inspection Copy

Boundary Value Problems of Applied Mathematics

Boundary Value Problems of Applied Mathematics
Second Edition

by John L. Troutman,Maurino P. Bautista

  • Publisher : Courier Dover Publications
  • Release : 2017-06-21
  • Pages : 512
  • ISBN : 0486812227
  • Language : En, Es, Fr & De
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This text is geared toward advanced undergraduates and graduate students in mathematics who have some familiarity with multidimensional calculus and ordinary differential equations. Includes a substantial number of answers to selected problems. 1994 edition.

Differential Equations with Maple V®

Differential Equations with Maple V®
A Book

by Martha L Abell,James P. Braselton

  • Publisher : Academic Press
  • Release : 2014-05-09
  • Pages : 698
  • ISBN : 1483266575
  • Language : En, Es, Fr & De
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Differential Equations with Maple V provides 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 Maple V 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 Maple V 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 also provided. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.

Differential Equations

Differential Equations
A MapleTM Supplement

by Robert P. Gilbert,George C. Hsiao,Robert J. Ronkese

  • Publisher : CRC Press
  • Release : 2021-06-28
  • Pages : 243
  • ISBN : 1000402525
  • Language : En, Es, Fr & De
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This book illustrates how MAPLE can be used to supplement a standard, elementary text in ordinary and partial differential equation. MAPLE is used with several purposes in mind. The authors are firm believers in the teaching of mathematics as an experimental science where the student does numerous calculations and then synthesizes these experiments into a general theory. Projects based on the concept of writing generic programs test a student's understanding of the theoretical material of the course. A student who can solve a general problem certainly can solve a specialized problem. The authors show MAPLE has a built-in program for doing these problems. While it is important for the student to learn MAPLEŚ in built programs, using these alone removes the student from the conceptual nature of differential equations. The goal of the book is to teach the students enough about the computer algebra system MAPLE so that it can be used in an investigative way. The investigative materials which are present in the book are done in desk calculator mode DCM, that is the calculations are in the order command line followed by output line. Frequently, this approach eventually leads to a program or procedure in MAPLE designated by proc and completed by end proc. This book was developed through ten years of instruction in the differential equations course. Table of Contents 1. Introduction to the Maple DEtools 2. First-order Differential Equations 3. Numerical Methods for First Order Equations 4. The Theory of Second Order Differential Equations with Con- 5. Applications of Second Order Linear Equations 6. Two-Point Boundary Value Problems, Catalytic Reactors and 7. Eigenvalue Problems 8. Power Series Methods for Solving Differential Equations 9. Nonlinear Autonomous Systems 10. Integral Transforms Biographies Robert P. Gilbert holds a Ph.D. in mathematics from Carnegie Mellon University. He and Jerry Hile originated the method of generalized hyperanalytic function theory. Dr. Gilbert was professor at Indiana University, Bloomington and later became the Unidel Foundation Chair of Mathematics at the University of Delaware. He has published over 300 articles in professional journals and conference proceedings. He is the Founding Editor of two mathematics journals Complex Variables and Applicable Analysis. He is a three-time Awardee of the Humboldt-Preis, and. received a British Research Council award to do research at Oxford University. He is also the recipient of a Doctor Honoris Causa from the I. Vekua Institute of Applied Mathematics at Tbilisi State University. George C. Hsiao holds a doctorate degree in Mathematics from Carnegie Mellon University. Dr. Hsiao is the Carl J. Rees Professor of Mathematics Emeritus at the University of Delaware from which he retired after 43 years on the faculty of the Department of Mathematical Sciences. Dr. Hsiao was also the recipient of the Francis Alison Faculty Award, the University of Delaware’s most prestigious faculty honor, which was bestowed on him in recognition of his scholarship, professional achievement and dedication. His primary research interests are integral equations and partial differential equations with their applications in mathematical physics and continuum mechanics. He is the author or co-author of more than 200 publications in books and journals. Dr. Hsiao is world-renowned for his expertise in Boundary Element Method and has given invited lectures all over the world. Robert J. Ronkese holds a PhD in applied mathematics from the University of Delaware. He is a professor of mathematics at the US Merchant Marine Academy on Long Island. As an undergraduate, he was an exchange student at the Swiss Federal Institute of Technology (ETH) in Zurich. He has held visiting positions at the US Military Academy at West Point and at the University of Central Florida in Orlando.

Applied Partial Differential Equations

Applied Partial Differential Equations
A Book

by J. David Logan

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 181
  • ISBN : 1468405330
  • Language : En, Es, Fr & De
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This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard equations of mathemati cal physics (including the heat equation, the· wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. Prerequisites include calculus and a post-calculus differential equations course. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. These books gen erally have enough material for two, three, or even four semesters. Yet, many undergraduate courses are one-semester courses. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. This text was written to proVide a brief, one-semester introduction to partial differential equations.