Differential Equations With Maple V

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.

Accompanying CD-ROM includes all Maple V input that appears in the book.

This comprehensive book helps students tap into the power of Maple®, thereby simplifying the computations and graphics that are often required in the practical use of mathematics. Numerous examples and exercises provide a thorough introduction to the basic Maple® commands that are needed to solve differential equations. Topics include: numerical algorithms, first order linear systems, homogeneous and nonhomogeneous equations, beats and resonance, Laplace Transforms, qualitative theory, nonlinear systems, and much more.

The Maple ODE Lab Book is intended to provide a thorough introduc tion to using symbolic computation software to model, solve, explore, and visualize ordinary differential equations. It is best used as a supplement to existing texts (see the bibliography for some of our recommended texts). Maple was chosen as our software package because of its ease-of-use, affordability, and popularity at many universities and colleges around the world. The version being used is Maple V Release 4. If you have a previous release of Maple, some of the commands shown in this lab book will work differently (or not at all), but the basic groundwork for solving ODEs hasn't changed. Speak to your system administrator about upgrading to Release 4, or contact: Waterloo Maple Inc. 450 Phillip Street Waterloo, Ontario CANADA N2L 5J2 Phone: (519) 747-2373 FAX: (519) 747-5284 E-mail: [email protected] WWW: http://www.maplesoft.com 1 2 • Chapter 1. Introduction How This Lab Book Is Organized Each subsequent chapter of this lab book contains information and ex amples of how to apply Maple to various elements of ordinary differential equations. It is suggested that you read the chapters with your computer on and Maple V Release 4 running. You can then execute many of the com mands yourself and experiment by changing various parameters and/or initial conditions, observing the corresponding changes in the results.

Partial Differential Equations and Boundary Value Problems with Maple 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. Maple files can be found on the books website. 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.

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.

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.

This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. The accompanying CD contains Maple worksheets for the exercises, and special Maple code for performing various tasks. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.