Ordinary Differential Equations: Applications, Models, and Computing / Edition 1

Ordinary Differential Equations: Applications, Models, and Computing / Edition 1

by Charles Roberts
     
 

ISBN-10: 1439819084

ISBN-13: 9781439819081

Pub. Date: 04/05/2010

Publisher: Taylor & Francis

In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing

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Overview

In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations.

Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems. The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions.

Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software. A solutions manual is available for qualifying instructors.

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Product Details

ISBN-13:
9781439819081
Publisher:
Taylor & Francis
Publication date:
04/05/2010
Series:
Textbooks in Mathematics Series, #10
Edition description:
New Edition
Pages:
600
Product dimensions:
6.30(w) x 9.30(h) x 1.30(d)

Table of Contents

1 Introduction 1

2 The Initial Value Problem y' = f(x,y); y(c) = d 33

3 Applications of the Initial Value Problem y' = f(x,y); y(c) = d 117

4 N-th Order Linear Differential Equations 163

5 The Laplace Transform Method 223

6 Applications of Linear Differential Equations with Constant Coefficients 275

7 Systems of First-Order Differential Equations 313

8 Linear Systems of First-Order Differential Equations 335

9 Applications of Linear Systems with Constant Coefficients 383

10 Applications of Systems of Equations 407

Appendix A CSODE User's Guide 499

Appendix B PORTRAIT User's Guide 525

Appendix C Laplace Transforms 537

Answers to Selected Exercises 539

References 571

Index 575

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