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