**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 | FREE | 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 | FREE | 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 | FREE | 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 | FREE | 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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