### Lecture Description

Integrable Systems: Periodic, Quasiperiodic, Ergotic, Mixing Motion, Exponential Instability, global exponential instability

Lyapunov Exponent

Intermitency

E.N. Lorenz

### Course Index

- Lecture 1: Mass, Length and Time
- Lecture 2: Classical Dynamics
- Lecture 3: Harmonic Oscillator
- Lecture 4: Harmonic Oscillator
- Lecture 5: Dimensional dynamical systems
- Lecture 6: Dimensional dynamical systems
- Lecture 7: The Principles of the Equations of Motion
- Lecture 8: Maxwell's Equations
- Lecture 9: Lagrangian for a charged particle in a EM field
- Lecture 10: Lagrangian and Hamiltonian Dynamics
- Lecture 11: Hamiltonian Systems
- Lecture 12: Integrability of Hamiltonian Systems
- Lecture 13: Emmy Noether, Symmetry, Invariance and Conservation Laws
- Lecture 14: Isotropic Oscillators, The Kepler Problem, Introduction to Statistical Physics
- Lecture 15: Chaotic Dynamics
- Lecture 16: Exponential Divergencies, Lyapunov Exponent, Bernoulli Map and Frobenius-Perron Equation
- Lecture 17: Lyapunov Exponent, Baker's Map, Arnold's cat map, Gauss continued fraction map
- Lecture 18: Questions & Answers
- Lecture 19: Questions & Answers
- Lecture 20: Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble
- Lecture 21: Microcanonical Ensemble: Stirling's Formula, Poisson Distribution
- Lecture 22: Microstates of particles, Entropy, Density of States, Thermodynamics
- Lecture 23: Euler Relation, Enthalpy, Helmholtz / Gibbs Free Energies, Grand Potential, Field / State Variables, Gas Law
- Lecture 24: Density of States, Boltzmann/Gibbs Factor
- Lecture 25: Thermodynamics of Ideal Gases and its Statistic Mechanics
- Lecture 26: Probability and Maxwellian Distributions, Moment generating function, Excess Kurtosis, Levy distributions
- Lecture 27: Maxwellian distributions, Gunbel, Weibull & Frechet distribution, Phase Diagrams
- Lecture 28: Phase Diagrams, Model of Paramagnetism, dipole moment, Weiss molecular field theory
- Lecture 29: Ferromagnetism, spontaneous magnetization, Landau Theory
- Lecture 30: Landau Theory and critical exponents, Thermodynamic relations, Continuum limit of random walk
- Lecture 31: Questions & Answers
- Lecture 32: Lie Groups, homomorphism, kernel
- Lecture 33: Groups, compact and non-compact groups, Universal covering group
- Lecture 34: Group of proper rotation in 3D, Parametrization by Euler angles, unitary matrices, Noether's theorem
- Symmetry, Invariance and Conservation laws (Noether's theorem), Principles of Relativity
- Lecture 36: Lorentz invariance, Riemannian manifold, metric tensors, d'Alembert operator
- Lecture 37: EM Field tensor, dual tensor, Levi-Civita symbol in 4D, Lorentz transformations, time/space-like vectors
- Lecture 38: Lorentz transformations in EM fields

### Course Description

Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. Among the topics in the lectures are:

- Mass, Length and Time

- Classical Dynamics

- Harmonic Oscillator

- Harmonic Oscillator

- Dimensional dynamical systems

- Dimensional dynamical systems

- The Principles of the Equations of Motion

- Maxwell's Equations

- Lagrangian for a charged particle in a EM field

- Lagrangian and Hamiltonian Dynamics

- Hamiltonian Systems

- Integrability of Hamiltonian Systems

- Emmy Noether, Symmetry, Invariance and Conservation Laws

- 2D Isotropic Oscillators, The Kepler Problem, Introduction to Statistical Physics

- Integrable Systems: Periodic, Quasiperiodic, Ergotic, Mixing Motion, Exponential Instability, global - exponential instability

- Lyapunov Exponent

- Intermitency

- E.N. Lorenz

- Exponential Divergencies, Lyapunov Exponent, Bernoulli Map, Frobenius-Perron Equation

- Lyapunov Exponent, Baker's Map, Arnold's cat map, Gauss continued fraction map

- Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble

- Binomial Distribution

- Relative Fluctuation

- Thermodynamics of Ideal Gases and its Statistic Mechanics

- Boltzmann's Formula

- Probability and Maxwellian Distributions, Moment generating function, Excess Kurtosis, Lévy alpha-stable distributions

- J.A. Shabat and J.D. Tamarkin, "The problem of moments"

- Maxwellian distributions, Gunbel, Weibull & Frechet distribution, Phase Diagrams

- Phase Diagrams, Model of Paramagnetism, dipole moment, Weiss molecular field theory

- Ferromagnetism, spontaneous magnetization, Landau Theory

- Landau Theory and critical exponents, Thermodynamic relations, Continuum limit of random walk

- Lie Groups, homomorphism, kernel

- Group of proper rotation in 3D, Parametrization by Euler angles, unitary matrices, Noether's theorem

- Symmetry, Invariance and Conservation laws (Noether's theorem), Principles of Relativity

- Lorentz invariance, Riemannian manifold, metric tensors, d'Alembertian operator

- EM Field tensor, dual tensor, Levi-Civita symbol in 4D, Lorentz transformations, time-like and space-like vectors

- Lorentz transformations in EM fields

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