Ordinary Differential Equations

A First Course
1. Auflage 2001
ISBN: 978-0-8493-0988-5
Verlag: Taylor & Francis

Buch, Englisch, 291 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 653 g

Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique. Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations. Relevant motivation for different concepts in each chapter and discussion of theory and problems-without the omission of steps-sets Ordinary Differential Equations: A First Course apart from other texts on ODEs. Full of distinguishing examples and containing exercises at the end of each chapter, this lucid course book will promote self-study among students.

Zielgruppe

Third- and fourth-year undergraduates in the sciences enrolled in differential equations courses

Autoren/Hrsg.

Somasundaram, D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONSIntroductionPreliminariesInitial Value ProblemsBoundary Value ProblemsSuperposition PrincipleThe Wronskian and Its PropertiesLinear Dependence of SolutionsReduction of OrderMethod of Variation of ParametersThe Method of Variation of Parameters for the Non-Homogeneous Equation of n-th orderA Formula for the WronskianHomogeneous Linear Differential Equations with constant Coefficientsn-th Order Homogeneous Differential Equations with Constant CoefficientsExamples IExercises IPOWER SERIES SOLUTIONSIntroductionThe Taylor Series MethodSecond Order Equations with Ordinary PointsSecond Order Linear Equations with Regular Singular PointsTwo Exceptional CasesGauss Hypergeometric SeriesThe Point at Infinity as a Singular PointExamples IIExercises IIFUNCTIONS OF DIFFERENTIAL EQUATIONSIntroductionLegendre FunctionsLegendre Series ExpansionSome Properties of Legendre PolynomialsHermite PolynomialsProperties of Laguerre PolynomialsProperties of Bessel FunctionsBessel Series ExpansionExamples IIIExercises IIIEXISTENCE AND UNIQUENESS OF SOLUTIONSIntroductionLipschitz Condition and Gronwall inequalitySuccessive Approximations and Picard TheoremDependence of Solutions on the Initial ConditionsDependence of Solutions on the FunctionsContinuations of the SolutionsNon-Local Existence of SolutionsExamples IVExercises IVSYSTEMS OF LINEAR DIFFERENTIAL EQUATIONSIntroductionSystems of First Order EquationsMatrix PreliminariesRepresentation of n-th Order Equations as a SystemExistence and Uniqueness of Solutions of System of EquationsWronskian of Vector FunctionsThe Fundamental Matrix and its PropertiesNon-Homogeneous Linear SystemsLinear Systems with Constant CoefficientsLinear Systems with Periodic CoefficientsExistence and Uniqueness of Solutions of systemsExamples VExercises VREFERENCESSOLUTIONS TO EXERCISESINDEX