Ordinary Differential Equations

Applications, Models, and Computing
1. Auflage 2018
ISBN: 978-1-138-11821-8
Verlag: Taylor & Francis Ltd

Buch, Englisch, 600 Seiten, Format (B × H): 232 mm x 155 mm, Gewicht: 884 g

Reihe: Textbooks in Mathematics

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.

Zielgruppe

Undergraduate and junior college students in mathematics and engineering; physicists and engineers.

Autoren/Hrsg.

Roberts, Charles

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

IntroductionHistorical PrologueDefinitions and TerminologySolutions and ProblemsA Nobel Prize Winning Application
The Initial Value Problem y' = f (x, y); y(c) =dDirection FieldsFundamental TheoremsSolution of Simple First-Order Differential EquationsNumerical Solution
Applications of the Initial Value Problem y' = f (x, y); y(c) =dCalculus RevisitedLearning Theory ModelsPopulation ModelsSimple Epidemic ModelsFalling BodiesMixture ProblemsCurves of PursuitChemical Reactions
N-th Order Linear Differential EquationsBasic TheoryRoots of PolynomialsHomogeneous Linear Equations with Constant CoefficientsNonhomogeneous Linear Equations with Constant CoefficientsInitial Value Problems
The Laplace Transform MethodThe Laplace Transform and Its PropertiesUsing the Laplace Transform and Its Inverse to Solve Initial Value ProblemsConvolution and the Laplace TransformThe Unit Function and Time-Delay FunctionsImpulse Functions
Applications of Linear Differential Equations with Constant CoefficientsSecond-Order Differential EquationsHigher Order Differential Equations
Systems of First-Order Differential Equations
Linear Systems of First-Order Differential EquationsMatrices and VectorsEigenvalues and EigenvectorsLinear Systems with Constant Coefficients
Applications of Linear Systems with Constant CoefficientsCoupled Spring-Mass SystemsPendulum SystemsThe Path of an ElectronMixture Problems
Applications of Systems of EquationsRichardson’s Arms Race ModelPhase-Plane PortraitsModified Richardson’s Arms Race ModelsLanchester’s Combat ModelsModels for Interacting SpeciesEpidemicsPendulumsDuffing’s EquationVan der Pol’s EquationMixture ProblemsThe Restricted Three-Body Problem
Appendix A: CSODE User’s Guide Appendix B: PORTRAIT User’s GuideAppendix C: Laplace Transforms

Answers to Selected Exercises
References
Index

Über Autor(innen)

Charles E. Roberts, Jr. is a professor in the Department of Mathematics and Computer Science at Indiana State University.