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
Radioisotopes and Their Applications
RADIO ISOTOPES
A radioisotope is a type of isotope, which is an atom of a chemical element with the same number of protons but a different number of neutrons in its nucleus than the most abundant variety. The term "radioisotope" specifically refers to isotopes of an element that are unstable and undergo radioactive decay, emitting radiation in the process.
APPLICATIONS OF RADIO ISOTOPES
Radioisotopes have a wide range of applications across various fields.
Medicine: Radioisotopes are extensively used in medicine for diagnosis and treatment. Examples include Technetium-99m for imaging in nuclear medicine procedures like bone scans and thyroid scans, Iodine-131 for thyroid cancer treatment, and cobalt-60 for radiation therapy in cancer treatment.
Industry: Radioisotopes are used in industrial processes for thickness gauging, level gauging, and flow rate measurements. For instance, radioactive isotopes like Americium-241 and Cobalt-60 are used in industrial radiography for non-destructive testing of materials.
Agriculture: Radioisotopes play a crucial role in agricultural research, particularly in studies related to plant nutrition, soil erosion, and pest control. For example, Phosphorus-32 is used to study phosphorus metabolism in plants.
Food Preservation: Radioisotopes such as Cobalt-60 are used for food irradiation to extend the shelf life of certain food products by killing bacteria and pests and inhibiting sprouting.
Carbon Dating: Radioisotopes like Carbon-14 are used in archaeology and geology for carbon dating, which helps determine the age of organic materials and geological formations.
Smoke Detectors: Americium-241, a radioisotope, is used in smoke detectors to ionize air particles, which triggers an alarm when smoke enters the detector.
Environmental Studies: Radioisotopes are utilized in environmental studies to trace the movement of pollutants, study ocean currents, and monitor air and water quality. Examples include tritium for tracing water movement and Cesium-137 for studying soil erosion.
Power Generation: Radioisotopes are used in the generation of electricity in radioisotope thermoelectric generators (RTGs) commonly used in spacecraft and remote locations where traditional power sources are impractical.
Oil Exploration: Radioisotopes like Iodine-131 are used in oil well logging to measure the porosity and density of rock formations, aiding in the exploration and extraction of oil and gas reserves.
Biological Research: Radioisotopes are widely used in biological research for labeling and tracing biological molecules, studying metabolic pathways, and conducting molecular imaging studies. Examples include using tritiated thymidine to study DNA replication and Fluorine-18 in positron emission tomography (PET) scans for imaging biological processes in living organisms.
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