I'm currently taking a course on Vibrations and Waves. Starting the course we studied the classical book by French (a good text for physics students new to the topic). However my teacher is now using Mathematical Methods of Classical Mechanics which has something like $3$ pages of theory about the oscillations we have studied (but these $3$ pages are very juicy and compact). I would like to know if any of you know a text in which the tools for linear analysis of oscillations are developed rigorously.
I appreciate your help.