Thinking about Ordinary Differential Equations [Paperback]

This book stresses alternative examples and analyses of finding solutions to ordinary differential equations.Ordinary differential equations are also key elements of disciplines as diverse as engineering and economics. This study stresses alternative examples and analyses by which the student can understand a number of approaches to finding and understanding solutions.Ordinary differential equations are also key elements of disciplines as diverse as engineering and economics. This study stresses alternative examples and analyses by which the student can understand a number of approaches to finding and understanding solutions.While mastery of these equations is essential, adhering to any one method of solving them is not. This book stresses alternative examples and analyses by means of which students can understand a number of approaches to finding solutions and understanding their behavior. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application.1. First-order equations; 2. Linear second-order equations; 3. Power series solutions and special functions; 4. Systems of linear differential equations; 5. Stability concepts; 6. Singular perturbation methods; General references; Index. The distinguishing feature of this text is the last chapter, on singular perturbation theory, which intoduces the notions of both boundary layer and multiple scales. THis text is certainly suitable for an advanced lecture course, particlulary as it contains a wealth of examples and solutions. Journal of Fluid Mechanics ...this volume is a worthy addition to the literature and will be useful as a reference to students, faculty, and practicing scientists. The UMAP Journal