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# Classical Physics

### 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

For more details on NPTEL visit http://nptel.iitm.ac.in

**17**ratings

### Video Lectures & Study Materials

## Comments

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Knut Johnsen wrote 8 years ago.Lecture 4 is missing. Its running lecture 3 again. Please

fix.

Peter Russell wrote 8 years ago.These are very useful lectures. The prof certaintly knows

his stuff.

For me great revision with extra insights.

Peter Russell wrote 8 years ago.These are very useful lectures. The prof certaintly knows

his stuff.

For me great revision with extra insights.

Jennie wrote 9 years ago.Prof. Balakrishnan uses differentials and partial

derivatives throughout as the primary tool to drive the

lecture. He changes variables among thermodynamic potentials

as a first example then defines the Legendre transformation

which changes between the Hamiltonian and the Lagrangian. He

covers constants of motion, understands the Hamiltonian as

steering/driving time changes in a system, defines the

Poisson bracket as a bilinear operation on phase space

variables, gives the Jacobi identity and briefly introduces

the definition of a Lie algebra. He writes a Hamiltonian

system in matrix form using the so-called symplectic

gradient. He shows that the Poisson bracket is precisely the

symplectic dot product of gradients, and hence shows the

importance of symplectic geometry in phase space. He defines

conjugate pairs of phase space variables using the Poisson

bracket. Finally, he summarizes via examples of a simple

harmonic oscillator and a charged particle in an

electromagnetic field.

Jennie wrote 9 years ago.Prof. Balakrishnan uses differentials and partial

derivatives throughout as the primary tool to drive the

lecture. He changes variables among thermodynamic potentials

as a first example then defines the Legendre transformation

which changes between the Hamiltonian and the Lagrangian. He

covers constants of motion, understands the Hamiltonian as

steering/driving time changes in a system, defines the

Poisson bracket as a bilinear operation on phase space

variables, gives the Jacobi identity and briefly introduces

the definition of a Lie algebra. He writes a Hamiltonian

system in matrix form using the so-called symplectic

gradient. He shows that the Poisson bracket is precisely the

symplectic dot product of gradients, and hence shows the

importance of symplectic geometry in phase space. He defines

conjugate pairs of phase space variables using the Poisson

bracket. Finally, he summarizes via examples of a simple

harmonic oscillator and a charged particle in an

electromagnetic field.

Jennie wrote 9 years ago.Prof. Balakrishnan uses differentials and partial

derivatives throughout as the primary tool to drive the

lecture. He changes variables among thermodynamic potentials

as a first example then defines the Legendre transformation

which changes between the Hamiltonian and the Lagrangian. He

covers constants of motion, understands the Hamiltonian as

steering/driving time changes in a system, defines the

Poisson bracket as a bilinear operation on phase space

variables, gives the Jacobi identity and briefly introduces

the definition of a Lie algebra. He writes a Hamiltonian

system in matrix form using the so-called symplectic

gradient. He shows that the Poisson bracket is precisely the

symplectic dot product of gradients, and hence shows the

importance of symplectic geometry in phase space. He defines

conjugate pairs of phase space variables using the Poisson

bracket. Finally, he summarizes via examples of a simple

harmonic oscillator and a charged particle in an

electromagnetic field.

Jennie wrote 9 years ago.Prof. Balakrishnan uses differentials and partial

derivatives throughout as the primary tool to drive the

lecture. He changes variables among thermodynamic potentials

as a first example then defines the Legendre transformation

which changes between the Hamiltonian and the Lagrangian. He

covers constants of motion, understands the Hamiltonian as

steering/driving time changes in a system, defines the

Poisson bracket as a bilinear operation on phase space

variables, gives the Jacobi identity and briefly introduces

the definition of a Lie algebra. He writes a Hamiltonian

system in matrix form using the so-called symplectic

gradient. He shows that the Poisson bracket is precisely the

symplectic dot product of gradients, and hence shows the

importance of symplectic geometry in phase space. He defines

conjugate pairs of phase space variables using the Poisson

bracket. Finally, he summarizes via examples of a simple

harmonic oscillator and a charged particle in an

electromagnetic field.

sergiokapone wrote 9 years ago.I with pleasure have started to look lectures. It is

interesting, where it is possible to take the literature on

the questions considered in lectures?

sergiokapone wrote 9 years ago.I with pleasure have started to look lectures. It is

interesting, where it is possible to take the literature on

the questions considered in lectures?

indian wrote 9 years ago.excellent videos! talks about everything you need to know

about classical physics before jumping to quantum mechanics.

Has a lot to teach.