Nguồn ngoài
Ordinary Differential Equations
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take.
- Tác giả
- Stephen Wiggins
- Nhà xuất bản
- University of Bristol
- Nguồn
- LibreTexts
- Giấy phép
- CC BY
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 30 mục
- 01: Getting Started - The Language of ODEs
- 1.01: Problem Set
- 02: Special Structure and Solutions of ODEs
- 2.01: Problem Set
- 03: Behavior Near Trajectories and Invariant Sets - Stability
- 3.01: Problem Set
- 04: Behavior Near Trajectories - Linearization
- 4.01: Problem Set
- 05: Behavior Near Equilbria - Linearization
- 5.01: Problem Set
- 06: Stable and Unstable Manifolds of Equilibria
- 6.01: Problem Set
- 07: Lyapunovs Method and the LaSalle Invariance Principle
- 7.01: Lyapunov’s Method and the LaSalle Invariance Principle
- 7.02: Problem Set
- 08: 8. Bifurcation of Equilibria I
- 8.01: Bifurcation of Equilibria I
- 8.02: Problem Set
- 09: Bifurcation of Equilibria II
- 9.01: Bifurcation of Equilibria II
- 9.02: Problem Set
- 10: Center Manifold Theory
- 10.01: Center Manifold Theory
- 10.E: Center Manifold Theory (Exericses)
- 11: Appendices
- 11.01: A- Jacobians Inverses of Matrices and Eigenvalues
- 11.02: B- Integration of Some Basic Linear ODEs
- 11.03: C- Finding Lyapunov Functions
- 11.04: D- Center Manifolds Depending on Parameters
- 11.05: E- Dynamics of Hamiltons Equations