Differential Equations Book

Differential Equations


  • Author : Robert P. Gilbert
  • Publisher : CRC Press
  • Release Date : 2021-06-28
  • Genre: Mathematics
  • Pages : 243
  • ISBN 10 : 9781000402520
  • Total Read : 80
  • File Size : 11,5 Mb

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Differential Equations Summary:

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. Gi

Introduction To Partial Differential Equations  With Maple   An  A Concise Course Book

Introduction To Partial Differential Equations With Maple An A Concise Course


  • Author : Zhilin Li
  • Publisher : World Scientific
  • Release Date : 2021-09-23
  • Genre: Mathematics
  • Pages : 220
  • ISBN 10 : 9789811228643
  • Total Read : 91
  • File Size : 16,6 Mb

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Introduction To Partial Differential Equations With Maple An A Concise Course Summary:

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.

A Course in Differential Equations with Boundary Value Problems Book

A Course in Differential Equations with Boundary Value Problems


  • Author : Stephen A. Wirkus
  • Publisher : CRC Press
  • Release Date : 2017-01-24
  • Genre: Mathematics
  • Pages : 768
  • ISBN 10 : 9781498736060
  • Total Read : 71
  • File Size : 10,5 Mb

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A Course in Differential Equations with Boundary Value Problems Summary:

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

Traveling Wave Analysis of Partial Differential Equations Book

Traveling Wave Analysis of Partial Differential Equations


  • Author : Graham Griffiths
  • Publisher : Academic Press
  • Release Date : 2010-12-09
  • Genre: Mathematics
  • Pages : 461
  • ISBN 10 : 0123846536
  • Total Read : 92
  • File Size : 18,9 Mb

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Traveling Wave Analysis of Partial Differential Equations Summary:

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net Includes a spectrum of applications in science, engineering, applied mathematics Presents a combination of numerical and analytical methods Provides transportable computer codes in Matlab and Maple

Solving Nonlinear Partial Differential Equations with Maple and Mathematica Book

Solving Nonlinear Partial Differential Equations with Maple and Mathematica


  • Author : Inna Shingareva
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-07-24
  • Genre: Mathematics
  • Pages : 357
  • ISBN 10 : 9783709105177
  • Total Read : 89
  • File Size : 18,5 Mb

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Solving Nonlinear Partial Differential Equations with Maple and Mathematica Summary:

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).

Handbook of Linear Partial Differential Equations for Engineers and Scientists Book

Handbook of Linear Partial Differential Equations for Engineers and Scientists


  • Author : Andrei D. Polyanin
  • Publisher : CRC Press
  • Release Date : 2001-11-28
  • Genre: Mathematics
  • Pages : 800
  • ISBN 10 : 9781420035322
  • Total Read : 82
  • File Size : 16,8 Mb

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Handbook of Linear Partial Differential Equations for Engineers and Scientists Summary:

Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with

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


  • Author : George A. Articolo
  • Publisher : Academic Press
  • Release Date : 1998-04-24
  • Genre: Business & Economics
  • Pages : 646
  • ISBN 10 : 0120644754
  • Total Read : 95
  • File Size : 7,6 Mb

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Partial Differential Equations Boundary Value Problems with Maple V Summary:

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.