This book discusses perturbation methods for solving algebraic and differential equations. The basics of the methods and the classical results are discussed in detail. Recent developments in the methods for solving algebraic and differential equations are also included. Classical perturbation methods depend on the smallness of a perturbation parameter for which the solutions are not valid for large parameters. Recent methods to increase the range of validity of perturbation solutions are given in the book. The new methods produce valid solutions for strongly nonlinear systems in addition to weakly nonlinear systems. The book will be beneficial for applied mathematicians, engineers, and physicists who are in search of approximate solutions for their specific problems. It can be adopted as a graduate textbook for courses on perturbation methods.
Mehmet Pakdemirli received a PhD degree from the Engineering Science and Mechanics Department, Istanbul Technical University, Turkey in 1991. He was a Post-doctorate Associate at Virginia Tech, USA (1991-1993), Visiting Scholar at the University of Michigan, USA (1996), and Visiting Professor at King Fahd University of Petroleum and Minerals, Saudi Arabia (2002-2003). His permanent position was Professor in the Department of Mechanical Engineering, Manisa Celal Bayar University, Turkey from 1993 to 2016 and he is currently Professor Emeritus in the same department. His research interests include applied mathematics, differential equations and their solution techniques, nonlinear dynamics, fluid mechanics, aerodynamics, biomimetics and mathematical education. He has authored/co-authored over 210 journal papers and received more than 5000 citations of his work from others.hsan Timuçin Dolapci graduated from Dokuz Eylül University, Turkey in 1992. He received his PhD degree on Mathematics from the Institute of Science in Osmangazi University, Turkey. His permanent position was Assistant Professor in the Department of Mechanical Engineering, Manisa Celal Bayar University from 2008 to 2016 and he is currently Assistant Professor Emeritus in the same department. His research interests include applied mathematics, differential equations and fluid mechanics.
