Toolbox of Averaging Theorems

Ferdinand Verhulst was born in Amsterdam and studied astrophysicist with a specialisation in numerical analysis. He spent five years at the Technical University of Delft, which stimulated his interest in theoretical engineering. Verhulst obtained his PhD from the University of Utrecht and became a Professor of Dynamical Systems there in 1990. He has been a visiting professor in prestigious universities worldwide and has completed five trips to Indonesia to teach mathematics, leading to three successful PhDs. Verhulst has authored numerous research papers and books, including five in English and two in Dutch, as well as edited two Springer Lecture Notes publications. Additionally, he founded Epsilon Uitgaven, a publishing house aimed at supporting teachers and students with Dutch language mathematics books, eventually contributing himself to a couple of their books, one on mathematical proofs and the other on chaos, both aimed at secondary school students.

“This book is a nice and interesting result of the vast expertise ... . It presents a concise survey of averaging theorems as a toolbox for applied mathematicians, and especially also physicists and engineers. … the book can also be useful for a mathematics seminar on averaging as the references to proofs of the theorems can be used to master the technique.” (Adriana Buic˘a, Mathematical Reviews, April, 2025) “The book is intended to present a concise survey of averaging theorems as a toolbox for applied mathematicians, physicists and engineers, with emphasis on the practical use. ... this is an enjoyable and very clear textbook for scientists, engineers, students and practitioners, which reflects the author’s vast expertise on the subject.” (Pablo Amster, zbMATH 1528.34001, 2024)

• - 1. Introduction. - 2. First Order Periodic Averaging. - 3. Periodic Solutions. - 4. Second Order Periodic Averaging. - 5. First Order General Averaging. - 6. Approximations on Timescales Longer than 1/ε. - 7. Averaging over Spatial Variables. - 8. Hamiltonian Resonances. - 9. Quasi-Periodic Solutions and Tori. - 10. Averaging for Partial Differential Equations.