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September 23, 2023

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Description

Special Topics in Classical Mechanics. Instructor: Professor P.C. Deshmukh, Department of Physics, IIT Madras.

This course has grown out of the first course in Physics taught to engineering students at IIT-Madras. However, the contents are expanded to include the interests of students of basic sciences and a strong emphasis on the foundations of classical mechanics is aimed at.

Essentially, foundations of 'classical mechanics' would include a comprehensive introduction to Newtonian, Lagrangian and Hamiltonian Mechanics, and include an introduction to mechanics of a system of particles, fluid mechanics, introduction to 'chaos', to the special theory of relativity and also to electrodynamics.

The course is designed as the first course students would take after high school, and the scope of some of the advanced topics that are introduced is therefore restricted. A comfortable introduction, adequately rigorous but not overly involved, to advanced applications is attempted. In this course, we emphasize that 'observation' and 'measurements' play a fundamental role in Physics.

We introduce mathematical methods as and where needed, but keep the focus on physical principles. The course aims, even as it will provide a rigorous introduction to the foundations of classical mechanics, at discovering the romance in physics, beauty in its simplicity, and rigor in its formulation. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Course Overview Unlimited
  • Lecture 02 – Equations of Motion; Galileo’s Experiments; Principle of Causality and Newton’s Laws Unlimited
  • Lecture 03 – Equations of Motion (ii): Newton’s Third Law Unlimited
  • Lecture 04 – Equations of Motion (iii): Principle of Least Action Unlimited
  • Lecture 05 – Equations of Motion (iv): Lagrange’s Equation, Hamilton’s Principle Function Unlimited
  • Lecture 06 – Equations of Motion (v): Applications of Lagrange’s/Hamilton’s Equations Unlimited
  • Lecture 07 – Oscillators, Resonances, Waves (i) Unlimited
  • Lecture 08 – Oscillators, Resonances, Waves (ii): Damped Harmonic Oscillator Unlimited
  • Lecture 09 – Oscillators, Resonances, Waves (iii): Forced Oscillations Unlimited
  • Lecture 10 – Oscillators, Resonances, Waves (iv): Aspects of Resonances and Waves Unlimited
  • Lecture 11 – Polar Coordinates (i) Unlimited
  • Lecture 12 – Polar Coordinates (ii) Unlimited
  • Lecture 13 – Dynamical Symmetry in the Kepler Problem (i) Unlimited
  • Lecture 14 – Dynamical Symmetry in the Kepler Problem (ii) Unlimited
  • Lecture 15 – Real Effects of Pseudo-Forces: Inertial and Noninertial Reference Frames Unlimited
  • Lecture 16 – Real Effects of Pseudo-Forces (ii): Noninertial Frame of Reference Unlimited
  • Lecture 17 – Real Effects of Pseudo-Forces (iii): Noninertial Frame of Reference Unlimited
  • Lecture 18 – Real Effects of Pseudo-Forces (iv): The Foucault Pendulum; The Coriolis Effect Unlimited
  • Lecture 19 – Special Theory of Relativity (i): Introduction Unlimited
  • Lecture 20 – Special Theory of Relativity (ii): Length Contraction and Time Dilation Unlimited
  • Lecture 21 – Special Theory of Relativity (iii): Twin Paradox Unlimited
  • Lecture 22 – Special Theory of Relativity (iv): Conclusion Unlimited
  • Lecture 23 – Potentials, Gradients, Fields (i): Potentials, Vector Fields, Directional Derivative Unlimited
  • Lecture 24 – Potentials, Gradients, Fields (ii): Directional Derivative (cont.), Gradients Unlimited
  • Lecture 25 – Potentials, Gradients, Fields (iii): Connections between Potential Gradients and Fields Unlimited
  • Lecture 26 – Gauss’ Law: Equation of Continuity (i) Unlimited
  • Lecture 27 – Gauss’ Law: Equation of Continuity (ii): Gauss’ Divergence Theorem Unlimited
  • Lecture 28 – Gauss’ Law: Equation of Continuity (iii): Application Examples Unlimited
  • Lecture 29 – Fluid Flow, Bernoulli’s Principle (i) Unlimited
  • Lecture 30 – Fluid Flow, Bernoulli’s Principle (ii) Unlimited
  • Lecture 31 – Classical Electrodynamics (i): Gauss’ Law Unlimited
  • Lecture 32 – Classical Electrodynamics (ii): Maxwell’s Equations Unlimited
  • Lecture 33 – Classical Electrodynamics (iii): The Special Theory of Relativity Unlimited
  • Lecture 34 – Classical Electrodynamics (iv): The Special Theory of Relativity Unlimited
  • Lecture 35 – Chaotic Dynamical Systems (i): Complex Behavior of Simple Systems Unlimited
  • Lecture 36 – Chaotic Dynamical Systems (ii): Bifurcations, Chaos Unlimited
  • Lecture 37 – Chaotic Dynamical Systems (iii): Chaos, Fractal Dimensions Unlimited
  • Lecture 38 – Chaotic Dynamical Systems (iv): Fractal Dimensions/ Mandelbrot Sets Unlimited
  • Lecture 39 – Chaotic Dynamical Systems (v): Mandelbrot Sets Unlimited
  • Lecture 40 – The Scope and Limitations of Classical Mechanics Unlimited

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