This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization.

Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition.

The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

Contains a diverse selection of chapters, ranging from the first and the second order ODEs to bifurcation to modeling Richly illustrates each chapter with a number of examples that don't depend on a particular choice of computer-based methods Emphasizes the importance and benefits of mathematical modeling of physical and engineering objects through ordinary differential equations

Autorentext

Jan Awrejcewicz is the 2011 winner of the Humboldt Prize. This award is granted from the Alexander von Humboldt Foundation in Germany. The award is based on a reasearcher's entire achievements to date, whose fundamental discoveries, new theories or insights have had significant impact on their own discipline and who are expected to continue producing cutting-edge achievements in the future. Prof. Awrejcewicz is also the main author of "Nonsmooth Dynamics of Contacting Thermoelastic Bodies", (c) 2009, Springer (AMMA v. 16), 978-0-387-09562-0. He is also the sole editor of "Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems", (c) 2009 Springer, 978-1-4020-8777-6.

Inhalt

1. Introduction.- 2. First order ODEs.- 3. Second order ODEs.- 4. Linear ODEs.- 5. Higher-order ODEs polynomial form.- 6. Systems.- 7. Theory and criteria of similarity.- 8. Model and modeling.- 9. Phase plane and phase space.- 10. Stability.- 11. Modeling via perturbation methods.- 12. Continualization and discretization.- 13. Bifurcations.- 14. Optimization of systems.- 15. Chaos and synchronization.