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Mathematical Methods: Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. First order equations and linear second order differential equations with constant coefficients. Matrices and determinants, Algebra of complex numbers.

Mechanics and General Properties of Matter: Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and non-conservative forces. System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, con-servation of energy, variable mass systems. Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem. Principal moments and axes. Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem.

Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general solution. Superposition of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, resonance. Wave equation, traveling and standing waves in one-dimension. Energy density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media. Doppler Effect. Fermat’s Principle. General theory of image formation. Thick lens, thin lens and lens combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double refraction and optical rotation.

Electricity and Magnetism: Coulomb’s law, Gauss’s law. Electric field and potential. Electrostatic boundary conditions, Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Biot-Savart law, Ampere’s law, Faraday’s law of electromagnetic induction, Self and mutual inductance. Alternating currents. Simple DC and AC circuits with R, L and C components. Displacement current, Maxwell’s equations and plane electromagnetic waves, Poynting’s theorem, reflection and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only). Lorentz Force and motion of charged particles in electric and magnetic fields.

Kinetic theory, Thermodynamics: Elements of Kinetic theory of gases. Velocity distribution and Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas and equation of state. Mean free path. Laws of thermodynamics. Zeroth law and concept of thermal equilibrium. First law and its consequences. Isothermal and adiabatic processes. Reversible, irreversible and quasi-static processes. Second law and entropy. Carnot cycle. Maxwell’s thermodynamic relations and simple applications. Thermodynamic potentials and their applications. Phase transitions and Clausius-Clapeyron equation. Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac and Bose Einstein distributions.

Modern Physics: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy equivalence. Blackbody radiation, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays. Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation values, Schrödinger equation and its solution for one, two and three dimensional boxes. Solution of Schrödinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion prin-ciple. Structure of atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay.

Solid State Physics, Devices and Electronics: Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg’s law Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. p-n junction diode, I-V characteristics, Zener diode and its applications, BJT: characteristics in CB, CE, CC modes. Single stage amplifier, two stage R-C coupled amplifiers. Simple Oscillators: Barkhausen condition, sinusoidal oscillators. OPAMP and applications: Inverting and non-inverting amplifier. Boolean algebra: Binary number systems; conversion from one system to another system; binary addition and subtraction. Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth tables; combination of gates; de Morgan’s theorem.

Course Curriculum

Section 1: MECHANICS
NEWTON LAWS OF MOTION
Introduction to Mechanics 01:02:00
Normal Reaction FREE 00:36:00
Tension 00:35:00
Pseudo Forces 01:01:00
FRICTION
Friction 00:51:00
VELOCITY AND ACCELERATION
Velocity and Acceleration 00:29:00
CENTRAL FORCES
Equivalent One Body Problem 00:49:00
Conservation laws in Central Force Motion FREE 00:37:00
Trajectory of Particle Undergoing Central Force Motion 00:43:00
Types of Central Force Motion 02:19:00
Problems on Central Forces 01:44:00
Gravitation 00:25:00
Gravitational Field 01:42:00
Gravitational Potential 00:52:00
Gravitational Potential Energy 01:41:00
Previous Year Problems on Central Forces in IISc 00:36:00
Previous Year Problems on Central Forces in TIFR 00:34:00
Previous Year Problems on Central Forces in JEST 01:49:00
UNIFORMLY ROTATING FRAME- CENTRIFUGAL AND CORIOLIS FORCES
Uniformly Rotating Frame 00:57:00
Circular Motion FREE 01:43:00
Coriolis Force 00:27:00
Previous Years Questions on Coriolis forces FREE 00:42:00
CONSERVATION LAWS
Law of Conservation of Linear Momentum 00:47:00
Law of Conservation of Energy 00:39:00
Collision 01:35:00
CENTRE OF MASS AND VRIABLE MASS SYSTEMS
Centre of Mass 02:10:00
Variable Mass Systems 00:25:00
RIGID BODY DYNAMICS
Rotation about Fixed Axis 01:48:00
Translation + Rotation FREE 01:07:00
Angular Momentum 01:25:00
Moment of Inertia Tensor 00:48:00
Previous Year Problems on Rigid Body Dynamics in IISc 00:56:00
Previous Year Problems on Rigid Body Dynamics in TIFR 00:46:00
Previous Year Problems on Rigid Body Dynamics in JEST 00:15:00
FLUID DYNAMICS
Fluid Statics 01:46:00
Fluid Dynamics 01:28:00
Euler Equations and Its Applications 00:35:00
Section 2: ELECTRICITY AND MAGNETISM
COULOMB LAW AND ELECTRIC FIELD
Coulombs Law 00:35:00
Electric Field 00:56:00
Electric Flux 01:26:00
GAUSS LAW OF ELECTROSTATICS AND APPLICATIONS
Gauss Law of Electrostatics 02:03:00
Determination of Charge Distribution on Conductors using Gauss Law 00:59:00
Electrostatic Potential 00:51:00
Capacitance 00:32:00
Force on Charged Surface 00:17:00
POLARIZATION OF DIELECTRICS
Polarization of Dielectrics 01:04:00
Problems on Field Calculation 00:35:00
Boundary Condition of Polarization 00:17:00
Problems on Calculation of Bound Charges 00:35:00
Boundary Condition of D and E 00:47:00
Capacitors 01:01:00
Effect of Polarization on Capacitance 01:20:00
WORK AND ENERGY IN ELECTROSTATICS
Electrostatic Energy 00:52:00
Problems on Electrostatic Energy 00:33:00
Problems on Work and Energy 00:53:00
Electrostatic Energy in Dielectrics 00:31:00
BOUNDARY VALUE PROBLEMS
Boundary Value Problems 00:51:00
Uniqueness Theorems 00:31:00
Laplace Equation in Spherical Polar Coordinates 01:18:00
CURRENT ELECTRICITY
Electric Current and Resistance 00:52:00
Combination of Resistors and Cells 00:51:00
Ammeter and Voltmeter 00:17:00
Problems on Current Electricity 00:39:00
MAGNETOSTATICS
Motion of Charged Particle in Magnetic Field 00:37:00
Biot Savart Law 00:48:00
Gauss law of Magnetostatics 00:14:00
Ampere Law 01:19:00
Magnetic Dipoles and Force on Current Carrying Conductor 01:04:00
FARADAY LAW OF ELECTROMAGNETIC INDUCTION
Faraday Law and Induced EMF 00:39:00
Problems on Faraday Law 01:15:00
MAGNETIC MATERIALS
Magnetisation and H Vector 00:49:00
Boundary Conditions of B and H 00:29:00
Ferromagnetism 00:21:00
Moving Coil Galvanometer 00:10:00
DC CIRCUITS
Introduction to DC Circuit 00:05:00
RC Circuit 02:14:00
LR circuit 00:45:00
LC Circuit 01:20:00
LCR Circuit 00:14:00
AC CIRCUITS
AC Circuit 02:09:00
MAXWELL EQUATIONS
Maxwell Equations 01:13:00
POYNTING VECTOR
Poynting Vector 01:14:00
ELECTROMAGNETIC WAVES
EM Waves in Free Space and Isotropic Dielectric Medium 00:46:00
Problems on EM Waves 00:38:00
REFLECTION AND REFRACTION OF EM WAVES AT THE INTERFACE OF TWO DIELECTRICS
Kinematic Properties 00:36:00
Fresnel Formula 01:41:00
Total Internal Reflection 00:39:00
Section 3: MATHEMATICAL PHYSICS
Beta and Gamma Function 00:33:00
MULTIPLE INTEGRAL
Introduction to Double Integrals 00:12:00
Change of Order 01:50:00
VECTOR CALCULUS
Gradient 01:12:00
Tangent Plane and Normal 00:18:00
Problems on Gradient 00:07:00
Divergence and Curl 00:41:00
Line Integral 00:56:00
Greens Theorem 01:06:00
Surface Integral 01:19:00
Gauss Divergence Theorem 01:36:00
Stokes Theorem 00:56:00
Conservative Vector Field 00:23:00
DIFFERENTIAL EQUATIONS
Introduction to Differential Equations 00:25:00
Differential Equation of First order and First Degree 02:01:00
Orthogonal Trajectory 00:27:00
Differential Equation with Constant Coefficient 01:19:00
Homogeneous Linear Differential Equation 00:49:00
Differential Equation of Second Order 01:24:00
MATRICES
Introduction to Matrices 02:17:00
Rank of Matrix 00:54:00
Linear Equations 02:04:00
Determinant 02:14:00
Revision of Matrices 02:03:00
Vector Spaces 01:05:00
Linear Equations – Vector Space Approach 01:43:00
Introduction to Eigenvalues and Eigenvectors 00:36:00
Diagonalisation of Matrices and its Applications 00:59:00
Properties of Eigenvalues 00:18:00
Symmetric Matrices 01:09:00
Cayley Hamilton Equation 00:08:00
Similar Matrices 00:16:00
DIFFERENTIAL CALCULUS
Monotonicity 01:07:00
Critical Points 00:54:00
Maxima and Minima 00:45:00
Rolle Theorem 00:25:00
Lagrange Mean Value Theorem 00:33:00
Taylors Theorem 00:33:00
Function of Two Variables 01:32:00
Jacobian 00:32:00
Maxima and Minima of Function of Several Variables 01:02:00
FOURIER SERIES
Fourier Series 00:14:00
Section 4: MODERN PHYSICS
PARTICLE NATURE OF WAVE
Photoelectric Effect 01:08:00
Compton Effect 00:36:00
Pair Production 00:33:00
Cross-section of Photon Absorption and Scattering 00:22:00
WAVE NATURE OF PARTICLE
Wave Nature of Particle 01:22:00
H ATOM
H atom and X-rays 00:56:00
POSTULATES OF QUANTUM MECHANICS
Postulates of Quantum Mechanics 02:39:00
Problems on Postulates 00:46:00
SCHRONDINGER WAVE WQUATION
Applications of Schrodinger Wave Equation 03:11:00
Linear Harmonic Oscillator 00:29:00
Particle in Three Dimensional Box 00:34:00
NUCLEAR PHYSICS
Basic Nuclear Properties and Radioactive Decay 01:31:00
Problems on Radioactive Decay 00:42:00
SPECIAL THEORY OF RELATIVITY
Einstein postulates 00:25:00
Time Dilation and Length Contraction 00:34:00
Simultanity and Lorentz Transformation 00:25:00
Problems on Relativity 00:54:00
Mass and Energy 00:37:00
IISc Previous Year Problems on Relativity 00:41:00
TIFR Previous Year Problems on Relativity 00:36:00
JEST Previous Year Problems on Relativity 00:34:00
Section 5: OSCILLATION,WAVES AND OPTICS
SIMPLE HARMONIC OSCILLATION
Simple Harmonic Motion 00:43:00
Lissajous Figures 00:39:00
DAMPED AND FORCED OSCILLATION
Damped Oscillation 00:33:00
Forced Oscillation 00:48:00
WAVES
Waves 01:28:00
GEOMETRICAL OPTICS
Fermat Principle 00:12:00
Thin Lens 00:33:00
System of Lens 00:24:00
INTERFERENCE
Young Double Slit Experiment 01:35:00
Thin Films 00:25:00
Newtons Ring FREE 00:29:00
DIFFRACTION
Single Slit 00:46:00
Double Slit 00:36:00
Plane Transmission Grating 00:51:00
Dispersive and Resolving Power FREE 00:59:00
POLARIZATION OF LIGHT
Brewster Law and Double Refraction 00:52:00
Malus Law and Action of Half Wave and Quarter Wave Plate on Plane Polarized Light 00:45:00
Problems on Polarization of light 00:19:00
Section 6: THERMAL PHYSICS
THERMAL EXPANSION
Thermal Expansion 00:59:00
CALORIMETRY
Calorimetry 01:25:00
TRANSMISSION OF HEAT
Thermal Conduction 00:35:00
Convection and Newtons Law of Cooling 00:28:00
Problems on Heat Transfer 01:10:00
FIRST LAW OF THERMODYNAMICS
First Law of Thermodynamics 00:32:00
Thermodynamic Systems 00:42:00
Heat and Work 00:41:00
Thermodynamic Processes 00:43:00
Problems on First Law of Thermodynamics 00:28:00
SECOND LAW OF THERMODYNAMICS
Second Law of Thermodynamics 01:10:00
Thermodynamic Potential 01:09:00
THERMODYNAMIC POTENTIALS
STATISTICAL PHYSICS
Microstates and Macrostates 00:47:00
Statistical Distributions 02:34:00
Problems on Statistical Physics 00:45:00
KINETIC THEORY OF GASES
Kinetic Theory of Gases 01:03:00
Section 7: SOLID STATE PHYSICS AND ELECTRONICS
CRYSTALS
Crystals 01:11:00
SEMICONDUCTORS
Semiconductors 00:55:00
SEMICONDUCTOR DIODE
Semiconductor Diodes and Clippers 00:41:00
Clamper 00:25:00
Zener Diode 00:35:00
BIPOLAR JUNCTION TRANSISTORS
BJT and Its Characteristics 01:54:00
Transistor Biasing 01:52:00
Transistor as a Switch and Role of Capacitors in Transistor Amplifier 00:33:00
SINUSOIDAL OSCILLATOR
Sinusoidal Oscillator 00:33:00
OPERATIONAL AMPLIFIER
Operational Amplifier 00:34:00
NEWTON LAWS OF MOTION-MCQ-LEVEL-1 00:30:00

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