This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included.The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations.

Autorentext

Dr. Belkacem Said-Houari received his Ph.D degree in partial differential equations (hyperbolic problems and nonclassical thermoelasticity) from Annaba University (Algeria) in 2005.His research interests focus on analysis of hyperbolic PDE (e.g. in thermoelasticity, Timoshenko systems, nonlinear wave equations), integro-differential equations, parabolic and hyperbolic-parabolic PDE.

He is the author or co-author of 45 research papers published in refereed international journals.

He is the winner of the Abdul Hameed Shoman Award for Young Arab Researchers, Mathematics (2012).

Inhalt

Preface.-1. Modelling and definitions.- 2. First-order differential equations.- 3. Linear second-order equations.- 4. Laplace Transforms.- 5. Power series solution.- 6. Systems of differential equations.- 7. Qualitative theory.- Index.