Oscillations and waves

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Over thirty years of research and teaching in various fields of physics revealed a lack of an introductory, comprehensive resource on the mathematics of linear and nonlinear oscillations and waves, tailored for physicists and engineers. Oscillations and waves, while fundamentally mathematical, serve as a crucial area for scientists. However, the interests of experimentalists and engineers often diverge from those of mathematicians. The latter focus on proving fundamental laws regarding the existence and behavior of solutions to differential equations, while the former require explicit analytical and numerical solutions, along with relevant computer programs and graphical displays. This divergence has created a communication gap between the two groups. This book aims to bridge that gap, drawing from lecture notes and a previous work published in 1995. The content has been significantly expanded and revised, benefiting from feedback from colleagues. Notable additions include a first classification of two-dimensional autonomous systems, enhancing the understanding of oscillatory behavior in various scientific contexts. This resource is designed to facilitate better communication and understanding between mathematicians and practitioners in the physical sciences.