Description

This book presents a comprehensive and practical survey of averaging methods for differential equations. Combining rigorous theory with applied perspectives, this book serves as both a study text and a reference for mathematicians and scientists in fields such as engineering, physics, and biology.

Divided into two complementary parts, the book begins with Part I, the Toolbox of Averaging Theorems, providing clear definitions, theorem formulations, and foundational results. While mathematicians may be content with existence proofs and qualitative analyses, applied scientists require tools that link theory to real-world problems--an essential motivation for Part II.

Part II explores applications in physics and engineering, blending theory with practice and incorporating numerical bifurcation analysis using tools such as AUTO, Mathematica, and MatCont. Interspersed theoretical interludes provide the background necessary for understanding and applying these methods.

Highlights include:

Hamiltonian systems

Fermi-Pasta-Ulam chains

Parametric excitation

dissipation-induced instability

Coupled oscillators and chaos

Diffusion and waves

Whether as a reference, teaching aid, or bridge between theory and application, Averaging for Nonlinear Dynamics equips readers with the tools to analyze, approximate, and apply nonlinear systems across a wide range of scientific disciplines.