Details
Ordinary Differential Equations and Mechanical Systems
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96,29 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 17.09.2014 |
| ISBN/EAN: | 9783319076591 |
| Sprache: | englisch |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<p>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.</p><p>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.</p><p>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. </p>
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.
<p>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. </p><p>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. </p><p>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. </p>
<p>Contains a diverse selection of chapters, ranging from the first and the second order ODEs to bifurcation to modeling</p><p>Richly illustrates each chapter with a number of examples that don't depend on a particular choice of computer-based methods</p><p>Emphasizes the importance and benefits of mathematical modeling of physical and engineering objects through ordinary differential equations</p>
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