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Viser: Ordinary Differential Equations - Basics and Beyond
Ordinary Differential Equations: Basics and Beyond Vital Source e-bog
David G. Schaeffer
Detaljer Om Varen
- Vital Source E-book
- Udgiver: Springer Nature (November 2016)
- ISBN: 9781493963898
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Detaljer Om Varen
- Udgiver: Springer (November 2016)
- Forfattere: John Cain og David Schaeffer
- ISBN: 9781493963874
A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book).
Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
- Linear Systems with Constant Coefficients. - Nonlinear Systems: Local Theory. - Nonlinear Systems: Global Theory. - Nondimensionalization and Scaling. - Trajectories Near Equilibria. - Oscillations in ODEs. - Bifurcation from Equilibria. - Examples of Global Bifurcation. - Epilogue. - Appendices.