From Scaling and Perturbation to Stability

1. Auflage 2026
ISBN: 978-1-041-37684-2
Verlag: Taylor & Francis Ltd

Buch, Englisch, 448 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Textbooks in Mathematics

This book aims not only to teach technical methods, but also to cultivate an “asymptotic way of thinking” that emphasizes scaling, dominant balances, approximation, and physical insight as essential tools in mathematical modeling. The book is designed to help students extract meaningful approximations from complex mathematical models before seeking exact solutions.

The author takes a modeling-first, intuition-driven approach. The book begins with dimensional analysis to emphasize physical reasoning before formal solution techniques are introduced. The development proceeds from simple to complex: from scalar problems to systems, from regular to singular perturbations, and from linear to nonlinear stability.

The presentation is unified and systematic. Methods are introduced in a coherent framework, repeatedly connected to physical interpretation and to the limitations of approximations. The text reflects extensive classroom testing through a two-semester sequence, and its structure is shaped by what has proven most effective for student learning.

Distinguishing Features

- Extensive, carefully graded exercises, ranging from introductory to challenging.

- Strong emphasis on physical intuition and modeling, not merely formal manipulation.

- Unified treatment of perturbation methods, asymptotic analysis, integrals, and dynamical systems.

- Integration of stability and bifurcation theory into an asymptotic framework.

- Clear connection between theory and applications, with numerous worked examples drawn from science and engineering.  This text provides a coherent, example-driven introduction to asymptotic and perturbation methods for students in applied mathematics, science, and engineering.  Other books by Youssef N. Raffoul, published by CRC Press: Fourier Series and Boundary Value Problems with Engineering Applications (2025) and Applied Mathematics for Scientists and Engineers (2023).

Zielgruppe

Postgraduate

Autoren/Hrsg.

Raffoul, Youssef N.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1. Dimensional Analysis 2. Scaling in Differential Equations 3. Perturbation in Differential Equations 4. Boundary Layers in Singularly Perturbed Ordinary Differential Equations 5. Asymptotic Expansions in Integrals 6. Systems of Ordinary Differential Equations 7. Stability of Linear Systems 8. Stability and Bifurcations in Non-linear Systems

Über Autor(innen)

Youssef N. Raffoul is Professor and Graduate Program Director at the University of Dayton. He holds a Ph.D. from Southern Illinois University. He is the recipient of the University of Dayton College of Arts and Sciences’ Award for Outstanding Scholarship (twice), and the University of Dayton Alumni Award in Scholarship. Professor Raffoul has published over one hundred and sixty articles in prestigious journals in the area of functional differential equations, difference equations, and dynamical systems on time scales. He was honored by the Lebanese government with the Career in Science Award. The Archbishop of Lebanon awarded him the Lifetime Achievement Award. Most notably, he is the recipient of the Order of Merit, Silver Medal with Distinction and awarded by the president of Lebanon, General Aoun.