Solving ODEs with MATLAB

This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems. Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples. This Book Is For People Who Need To Solve Ordinary Differential Equations (odes), Both Initial Value Problems (ivps) And Boundary Value Problems (bvps) As Well As Delay Differential Equations (ddes). These Topics Are Usually Taught In Separate Courses Of Length One Semester Each, But Solving Odes With Matlab Provides A Sound Treatment Of All Three In About 250 Pages. The Chapters On Each Of These Topics Begin With A Discussion Of The Facts Of Life For The Problem, Mainly By Means Of Examples. Numerical Methods For The Problem Are Then Developed - But Only The Methods Most Widely Used. Although The Treatment Of Each Method Is Brief And Technical Issues Are Minimized, The Issues Important In Practice And For Understanding The Codes Are Discussed. Often Solving A Real Problem Is Much More Than Just Learning How To Call A Code. The Last Part Of Each Chapter Is A Tutorial That Shows How To Solve Problems By Means Of Small But Realistic Examples.--jacket. Getting Started -- Initial Value Problems -- Boundary Value Problems -- Delay Differential Equations. L.f. Shampine, I. Gladwell, S. Thompson. Includes Bibliographical References (p. 251-256) And Index. This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples. Ordinary differential equations (ODEs) are used throughout engineering, mathematics, and science to describe how physical quantities change, so an introductory course on elementary ODEs and their solutions is a standard part of the curriculum in these fields.