Introduction to the Theory of Vibrations and Waves

Prerequisites: undergraduate courses in ordinary differential equations and linear algebra.

Equations of motion, variational principle, symmetries, conservation laws. Oscillations: eigenvalues, stability, resonances. Linear waves: discrete and continuous equations, the spectral method. Nonlinear waves: mathematical models, basic solutions, applications.

References:
ARNOLD, V.I. – Lectures on Partial Differential Equations. Springer, 2004.
ARNOLD, V.I. – Mathematical Methods of Classical Mechanics. Springer, 1989.
LANDAU, L.D. and LIFSHITZ, E.M. – Mechanics. Pergamon Press, 1976.
SEYRANIAN, A.M. and MAILYBAEV, A.A. – Multiparameter Stability Theory with Mechanical Applications. World Scientific, 2004.
WHITHAM, G.B. – Linear and Nonlinear Waves. New York, Wiley, 1974.

Class Notes:
Part 1: http://alexei.impa.br/data/_uploaded/file/courses/ITVO_part1.pdf
Part 2.2: http://alexei.impa.br/data/_uploaded/file/courses/parametric.pdf
Part 3: http://alexei.impa.br/data/_uploaded/file/courses/ondas_eng.pdf