Wigging S. Ordinary Differential Equations

School of Mathematics, University of Bristol, 2017. — 146 p.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.Getting Started: The Language of ODEs
Special Structure and Solutions of ODEs
Behavior Near Trajectories and Invariant Sets: Stability
Behavior Near Trajectories: Linearization
Behavior Near Equilbria: Linearization
Stable and Unstable Manifolds of Equilibria
Lyapunov’s Method and the LaSalle Invariance Principle
Bifurcation of Equilibria, I
Bifurcation of Equilibria, II
Center Manifold Theory
Appendixes
Jacobians, Inverses of Matrices, and Eigenvalues
Integration of Some Basic Linear ODEs
Finding Lyapunov Functions
Center Manifolds Depending on Parameters
Dynamics of Hamilton’s Equations
A Brief Introduction to the Characteristics