Week-1: Introduction to waves and oscillations, Normal modes of linear vibrating systems with finite degrees of freedom, Eigenmodes (shapes of oscillation) and frequencies, continuum limit
Week-2: Normal modes of a string with fixed ends, a clamped rectangular and circular membrane, Introduction to elliptic functions
Week-3: Nonlinear pendulum: exact solution using elliptic integrals, amplitude dependence of frequency, intro. to perturbation methods, non-dimensionalisation
Week-4: Perturbative solution to projectile equation, regular perturbative solution to the non-linear pendulum, Lindstedt Poincare technique, Damped harmonic oscillator, regular perturbation, method of multiple scales
Week-5: Multiple scales solution (contd..), Duffing equation, Parametric instability and the Kapitza Pendulum, Introduction to Floquet theory
Week-6: Mathieu equation stability tongues, Introduction to inviscid, irrotational surface gravity waves in deep water, boundary conditions, non-dimensionalisation and linearisation, dispersion relation
Week-7: General solution for surface gravity waves, linearised standing and travelling waves, phase and group velocity, Cauchy-Poisson problem for surface waves in deep water: rectilinear geometry, waves in cylindrical geometry
Week-8: Cauchy Poisson problem in cylindrical geometry, Cauchy-Poisson problem for delta function at origin and group velocity, similarity solution, stationary phase approximation, capillary-gravity waves
Week-9: Waves on finite depth pool, shallow and deep water approx., group velocity and energy propagation, axisymmetric Cauchy-Poisson problem with a Gaussian, engineering applications, Rayleigh-Plateau instability
Week-10: Waves and instability on a coated cylinder, waves and instability on a cylindrical air column, physical
interpretation, shape oscillations of drops and bubbles, physical interpretation of zero frequency
Week-11: Applications of shape oscillations, Faraday instability on a fluid interface, subharmonic response, Floquet
analysis, atomization from Faraday waves, engineering applications, waves on shear flows & Kelvin-Helmholtz
Week-12: Stokes wave in deep water, stability of Stokes wave (sideband instability), comparison of deep and shallow-water theory, non-linear Schrodinger equation and KdV equation, Resonant interactions among water waves
DOWNLOAD APP
FOLLOW US