Lecture 1 - Introduction
Lecture 2 - Coupled, linear, spring-mass systems
Lecture 3 - Coupled, linear, spring-mass systems (Continued...)
Lecture 4 - Coupled, linear, spring-mass systems (Continued...)
Lecture 5 - Coupled, linear, spring-mass system: continuum limit
Lecture 6 - Normal modes of a string fixed at both ends
Lecture 7 - Vibrations of clamped membranes
Lecture 8 - Vibrations of clamped membranes (Continued...)
Lecture 9 - Introduction to Jacobian elliptic functions
Lecture 10 - The non-linear pendulum
Lecture 11 - The non-linear pendulum (Continued...)
Lecture 12 - Time period of the non-linear pendulum
Lecture 13 - Introduction to perturbation methods
Lecture 14 - Perturbation methods (Continued...)
Lecture 15 - Non-dimensionalisation
Lecture 16 - Perturbative solution to the projectile equation
Lecture 17 - Perturbative solution to the nonlinear pendulum
Lecture 18 - Lindstedt-Poincare technique
Lecture 19 - Method of multiple scales
Lecture 20 - Method of multiple scales (Continued...)
Lecture 21 - Multiple scale analysis for damped-harmonic oscillator
Lecture 22 - Duffing equation using multiple scales
Lecture 23 - Duffing equation (Continued...)
Lecture 24 - Kapitza pendulum
Lecture 25 - Introduction to Floquet theory
Lecture 26 - Floquet theorem (Continued...)
Lecture 27 - Floquet analysis of the Mathieu equation
Lecture 28 - Introduction to waves on an interface
Lecture 29 - Linearized wave equations in deep water
Lecture 30 - Linearized wave equations in deep water: dispersion relation
Lecture 31 - Linearised deep-water surface gravity waves (Continued...)
Lecture 32 - Standing and travelling waves in deep water
Lecture 33 - Cauchy-Poisson initial value problem for surface-gravity waves in deep water
Lecture 34 - Cauchy-Poisson problem (Continued...)
Lecture 35 - Cauchy-Poisson problem in cylindrical geometry
Lecture 36 - Cauchy-Poisson problem in cylindrical geometry (Continued...)
Lecture 37 - Group-velocity and the Cauchy-Poisson problem
Lecture 38 - Cauchy-Poisson problem for delta function initial condition
Lecture 39 - Cauchy-Poisson problem for delta function initial condition (Continued...)
Lecture 40 - Capillary-gravity waves
Lecture 41 - Waves on a pool of finite depth
Lecture 42 - Axisymmetric Cauchy-Poisson problem visualisation: the pebble in the deep pond problem
Lecture 43 - Rayleigh-Plateau capillary instability
Lecture 44 - Rayleigh-Plateau capillary instability (Continued...)
Lecture 45 - Rayleigh-Plateau capillary instability on thin film coating a rod
Lecture 46 - Rayleigh-Plateau capillary instability of a cylindrical air column in a liquid
Lecture 47 - Mechanism of the Rayleigh-Plateau instability
Lecture 48 - Shape oscillations of a spherical interface
Lecture 49 - Shape oscillations of a spherical interface (Continued...)
Lecture 50 - Shape oscillations of a spherical interface (Continued...)
Lecture 51 - Analysis of l=0 and l=1 modes for a spherical drop
Lecture 52 - Faraday waves on an interface - stability of time dependent base states
Lecture 53 - Mathieu equation for Faraday waves
Lecture 54 - Applications of Faraday waves - atomisation and spray formation
Lecture 55 - Waves and instability on density stratified shear flows - the KH model
Lecture 56 - Limits of KH dispersion relation: Rayleigh-Taylor instability
Lecture 57 - KH dispersion relation : model of wind wave generation
Lecture 58 - Helmholtz instability of a vortex sheet and summary
Lecture 59 - Derivation of the Stokes travelling wave
Lecture 60 - Derivation of the Stokes travelling wave (Continued...)
Lecture 61 - Derivation of the Stokes travelling wave (Continued...)
