Desjardins, Steven J. and Remi Vaillancourt. 2011. Ordinary Differential Equations, Laplace Transforms, and Numerical Methods for Engineers, Notes for the Course MAT 2384 3X. Departement de mathematiques et de statistique/Department of Mathematics and Statistics, Universite d’Ottawa /University of Ottawa Ottawa, ON, Canada K1N 6N5. http://www.site.uottawa.ca/~remi/ode.pdf. Accessed 17 October 2016.
This text is jam packed with thoroughly worked out presentations, problems, and exercises (with solutions) as well as MatLab code in support of the by-hand analyses. The text covers the usual firs- and second-order ordinary differential equations with suitable applications to reinforce the subject and to introduce new concepts, e.g., two mass spring systems are used to motivate the conversion from two second-order equations into a linear system of four differential equations.
After such introductions and motivations the Laplace Transform approach is given a chapter as are series method. Finally, the next hundred page (pp. 153-252) of the text is devoted to Numerical Methods. The text rounds out with solutions to "starred" exercises from all chapters and an extensive list of formulae and tables.
There is sufficient detail and attention to topics to more than address interests/needs in an introductory course, e.g., the existence and uniqueness theorems are stated nicely, but not proven, rather applied to show just that - the existence and uniqueness.
While the applications are not up front in motivating the study of differential equations, nor that rich in number, they are nicely done with diagrams using French and English(!) labels. There are no modeling activities assigned here.
The notes read smoothly and there is ample conversational style in which students will see the details. There is no attempt to hide anything and the flow is smooth in presentation.
This book could be the source and resource for a course which otherwise might concentrate on modeling.
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