Index Gymnastics !

A Black Board Snapshot of My Lecture On Vector Calculus Using Succinct Index Notation Usually Called "Index Gymnastics" . 

SYLLABUS - CLASSICAL AND STATISTICAL MECHANICS - CORE COURSE - CODE: 22BPH5C3

UNIT - I

MECHANICS OF A SYSTEM OF PARTICLES : External and Internal Forces – Centre of Mass - Conservation of Linear Momentum – Conservation of Angular Momentum – Conservation of Energy – Work-Energy Theorem - Conservative Forces – Examples – Constraints – Types of Constraints – Examples – Degrees of Freedom – Generalized Coordinates – Generalized Velocities – Generalized  Momentum.

UNIT - II

LAGRANGIAN FORMULATION : Principle of Virtual Work – D’Alembert’s Principle, Lagrange Equation of Motion for Conservative and Non Conservative Systems - Applications – Simple Pendulum – Atwood Machine – Hamilton Principle – Deduction of Lagrange  Equation of Motion from Hamilton's Principle.

UNIT - III

HAMILTONIAN FORMULATION : Phase Space – The Hamiltonian Function H – Hamilton Canonical Equations of Motion - Physical Significance of H – Deduction of Canonical Equation from a Variational Principle – Applications – Compound Pendulum 

UNIT - IV

CLASSICAL STATISTICS : Micro and Macro States – The Mu Space and Gamma Space - Fundamental Postulates of Statistical Mechanics - Ensembles – Different Types –Thermodynamical Probability – Entropy and Probability - Boltzmann Theorem – Maxwell-Boltzmann Statistics – Maxwell-Boltzmann Energy Distributive Law – Maxwell-Boltzmann Velocity Distributive Law.

UNIT - V

QUANTUM STATISTICS : Development of Quantum Statistics – Bose-Einstein and Fermi-Dirac Statistics – Derivation of Planck Radiation Formula from Bose–Einstein Statistics – Free electrons in Metal- Fermi Gas – Difference between Classical and Quantum Statistics 

REFERENCE AND TEXT BOOKS:

Brijlal & Subramaniam, Reprint 1998, Heat & Thermodynamics. New Delhi: S. Chand & Company.

Gupta, Kumar, Sharma.(2005). Classical Mechanics, Meerut: Pragati Prakashan Publishers.

Gupta,B.D., Satyaprakash. (1991). Classical Mechanics. Meerut: 9th ed., Kadernath Ramnath Publishers.

Murray R.Siegal (1981). Theoretical Mechanics. New Delhi: Tata Mcgraw Hill Publishing Company.

Upadhyaya J.C. (2005). Classical Mechanics, Mumbai : Himalya Publishing House

SYLLABUS - MECHANICS - CORE COURSE - CODE: 23BPH3C1

UNIT - I

LAWS OF MOTION: Newton Laws of Motion – Forces – Equations of Motion – Frictional Force – Motion of a Particle in a Uniform Gravitational Field – Types of Everyday Forces in Physics. Gravitation: Classical Theory of Gravitation – Kepler Laws, Newton Law of Gravitation – Determination of G by Boys method – Earth-Moon System – Weightlessness – Earth Satellites – Parking Orbit – Earth Density – Mass of the Sun – Gravitational Potential – Velocity of Escape – Satellite Potential and Kinetic Energy – Einstein Theory of Gravitation – Introduction – Principle of Equivalence – Experimental Tests of General Theory of Relativity – Gravitational Red Shift – Bending of Light – Perihelion of Mercury.

UNIT - II

CONSERVATION LAWS OF LINEAR AND  ANGULAR MOMENTUM: Conservation of Linear and Angular Momentum – Internal Forces and Momentum Conservation – Center of Mass – Examples – General Elastic Collision of Particles of Different Masses – System with Variable Mass – Examples – Conservation of Angular Momentum – Torque Due to Internal Forces – Torque Due to Gravity – Angular Momentum about Center of Mass – Proton Scattering by Heavy Nucleus.

UNIT - III

CONSERVATION LAWS OF ENERGY: Introduction – Significance of Conservation Laws – Law of Conservation of Energy Concepts of Work - Power – Energy – Conservative Forces – Potential Energy and Conservation of Energy in Gravitational and Electric Field – Examples – Non-Conservative Forces – General Law of Conservation of Energy.

UNIT - IV

RIGID BODY DYNAMICS: Translational and Rotational Motion – Angular Momentum – Moment of Inertia – General Theorems of Moment of Inertia – Examples – Rotation about Fixed Axis – Kinetic Energy of Rotation – Examples – Body Rolling Along a Plane Surface – Body Rolling Down an Inclined Plane – Gyroscopic Precession – Gyrostatic Applications.

UNIT - V

LAGRANGIAN MECHANICS: Generalized Coordinates – Degrees of Freedom – Constraints - Principle of Virtual Work and D’Alembert’s Principle – Lagrange’s Equation from D’ Alembert’s Principle – Application –Simple Pendulum – Atwood’s Machine.

UNIT - VI

PROFESSIONAL COMPONENTS: Expert Lectures – Seminars – Webinars – Industry Inputs – Social Accountability – Patriotism

TEXT BOOKS:

1. J.C.Upadhyaya, 2019, Classical Mechanics, Himalaya Publishing house, Mumbai.

2. P.DuraiPandian, LaxmiDuraiPandian, MuthamizhJayapragasam,2005, Mechanics, 6threvised edition, S.Chandand Co.

3. D. S.Mathur and P. S.Hemne, 2000, Mechanics, Revised Edition, S.Chandand Co.

4. Narayanamurthi, M.and Nagarathnam. N, 1998, Dynamics. The National Publishing,Chennai.

5. Narayanamurthi, M. and Nagarathnam, N, 1982, Statics, Hydrostatics and Hydrodynamics, The National Publishers, Chennai.

REFERENCE BOOKS:

1. Goldstein Herbert, 1980, Classical Mechanics. U.S.A: Addison and Wesely.

2. Halliday, David and Robert, Resnick, 1995, Physics Vol.I. New Age, International, Chennai.

3. Halliday, David Robert Resnick and Walker Jearl, 2001, Fundamentals of Physics, John Wiley, New Delhi