非線形常微分方程式：問題と解答 Nonlinear Ordinary Differential Equations: Problems and Solutions : A Sourcebook for Scientists and Engineers (Oxford Texts in Applied and Engineering Mathematics)

Jordan, Dominic/ Smith, Peter

Oxford University Press（2007/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 594 p.／サイズ 272 illus.
• 言語 ENG
• 商品コード 9780199212033
• DDC分類 515.35

Full Description

An ideal companion to the new 4th Edition of Nonlinear Ordinary Differential Equations by Jordan and Smith (OUP, 2007), this text contains over 500 problems and fully-worked solutions in nonlinear differential equations. With 272 figures and diagrams, subjects covered include phase diagrams in the plane, classification of equilibrium points, geometry of the phase plane, perturbation methods, forced oscillations, stability, Mathieu's equation, Liapunov methods, bifurcations and manifolds, homoclinic bifurcation, and Melnikov's method.

The problems are of variable difficulty; some are routine questions, others are longer and expand on concepts discussed in Nonlinear Ordinary Differential Equations 4th Edition, and in most cases can be adapted for coursework or self-study.

Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Contents

Preface ; 1. Second-order differential equations in the phase plane ; 2. Plane autonomous systems and linearization ; 3. Geometrical aspects of plane autonomous systems ; 4. Periodic solutions; averaging methods ; 5. Perturbation methods ; 6. Singular perturbation methods ; 7. Forced oscillations: harmonic and subharmonic response, stability, entrainment ; 8. Stability ; 9. Stability by solution perturbation: Mathieu's equation ; 10. Liapunov methods for determining stability of the zero equation ; 11. The existence of periodic solutions ; 12. Bifurcations and manifolds ; 13. Poincare sequences, homoclinic bifurcation, and chaos