A Toolbox of Averaging Theorems
Ordinary and Partial Differential Equations
Buch in deiner Nähe kaufen
Beschreibung
This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε.
Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs).
In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practicaltools and theoretical insights to help you tackle a range of mathematical problems.
This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε.
Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs).
In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practicaltools and theoretical insights to help you tackle a range of mathematical problems.
Includes numerous hands-on applications of the stated theorems in each chapter The van der Pol, Duffing and Mathieu equations are discussed in detail Provides scientists and engineers with a concise survey of averaging theorems for ODE's and PDE's
Autor*in
Ferdinand Verhulst
Themen in »A Toolbox of Averaging Theorems«
Differential Equations in Engineering Periodic Averaging Mathieu Equation Averaging Methods Van der Pol Equation Verhulst Averaging Duffing Equation Hamiltonian Resonances
Stimmen zu »A Toolbox of Averaging Theorems«
“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)
()