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

Classical Physics
Professor Balakrishnan in Lecture 22
17 ratings

Video Lectures & Study Materials

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

Comments

Displaying 15 comments:

Knut Johnsen wrote 7 years ago.
Lecture 4 is missing. Its running lecture 3 again. Please
fix.


Peter Russell wrote 7 years ago.
These are very useful lectures. The prof certaintly knows
his stuff.
For me great revision with extra insights.


Peter Russell wrote 7 years ago.
These are very useful lectures. The prof certaintly knows
his stuff.
For me great revision with extra insights.


Jennie wrote 7 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 7 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 7 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 7 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 7 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 7 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 8 years ago.
excellent videos! talks about everything you need to know
about classical physics before jumping to quantum mechanics.
Has a lot to teach.


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