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. This book consists of 10 chapters, a...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Bristol, England
Stephen Wiggins
[2017]
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| Series: | Open textbook library.
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| Subjects: | |
| Online Access: | Access online version |
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Table of Contents:
- Preface
- 1 Getting Started: The Language of ODEs
- 2 Special Structure and Solutions of ODEs
- 3 Behavior Near Trajectories and Invariant Sets: Stability
- 4 Behavior Near Trajectories: Linearization
- 5 Behavior Near Equilbria: Linearization
- 6 Stable and Unstable Manifolds of Equilibria
- 7 Lyapunov's Method and the LaSalle Invariance Principle
- 8 Bifurcation of Equilibria, I
- 9 Bifurcation of Equilibria, II
- 10 Center Manifold Theory
- A Jacobians, Inverses of Matrices, and Eigenvalues
- B Integration of Some Basic Linear ODEs
- C Finding Lyapunov Functions
- D Center Manifolds Depending on Parameters
- E Dynamics of Hamilton's Equations
- F A Brief Introduction to the Characteristics of Chaos
- Bibliography
- Index