معادلات دیفرانسیل معمولی غیرخطی

This text has been especially written for advanced undergraduate students in mathematics, applied mathematics, engineering and, to a lesser extent, chemistry and physics. In writing the text, the author recognises and attempts to bridge the gap which exists between standard elementary courses on differential equations and advanced graduate courses on dynamical systems and chaotic motion. The text is concerned wih nonlinear differential equations and the use of perturbation methods to reveal the subtle effects that even small nonlinear terms can produce. The emphasis of the text is on stability, nonlinearity and perturbation methods Volume I provides a comprehensive account of the mathematical study and self-contained analysis of vibration and damping in systems governed by partial differential equations. It presents partial differential equations techniques for the mathematical study of this subject. A special objective of establishing the stability theory to treat many distributed vibration models containing damping is discussed. The book presents the theory and methods of functional analysis, energy identities, and strongly continuous and holomorphic semigroups. Many mechanical designs provide concrete examples of damping devices. Numerical examples also confirm the strong agreements between the theoretical estimates and numerical computations of damping rates of eigenmodes. The author has recognised and tried to bridge the gap which exists between standard elementary courses on differential equations and advanced graduate courses on dynamical systems and chaotic motion.