Ordinary Differential Equations with Applications: Introduction; CH:2 Ordinary Differential Equations; CH:3 First Order Equations; CH:4 Stability of Linear System; CH:5 Linear Systems and Stability inOrdinary Differential Equations; CH:6 System Applications ofOrdinary Differential Equations; CH:7 First Degree PartialDifferential Equations; CH:8 Differential Equations inSpace and Disk; CH:9 Continuation of PeriodicSolutions; CH:10 Global Bifurcation Theorems

Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations.