This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched.

This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Presents a unified view of nonlinear properties in several models from different scientific fields

Includes a review of the theoretical state of the art in the study of dynamical systems

Analyzes several currently topical issues in nonlinear science involving, e.g., gravitational waves, laser dynamics, and cellular automata