An accessible and concrete introduction to the main principles of ordinary differential equations. The study of differential equations is approached from a dynamical systems perspective, so there is an emphasis on qualitative questions and the evolution of solutions. Important principles are sectioned off to present a coherent picture of the study of differential equations, and the questions driving the theory are discussed.

Principles of Differential Equations:

• Exposes the roots of modern dynamical systems in order to help readers gain a solid foundation of ordinary differential equations.
• Sticks strictly to core ideas and firmly adheres to the principle that any result that is part of the core is worth carefully developing and proving.
• Provides an excellent foundation for most of the sub-disciplines of differential equations and dynamical systems.