Ordinary Differential Equations: Basics and Beyond. 1st ed. 2016

種類:

電子ブック

責任表示:

by David G. Schaeffer, John W. Cain

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2016

著者名:

• Schaeffer, David G.
• Cain, John W.
• SpringerLink (Online service)

シリーズ名:

Texts in Applied Mathematics ; 65

ISBN:

9781493963898 [1493963899]    

注記:

Introduction -- 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.
This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. 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. Given its many applications, the book may be used comfortably in sc

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