Physics JAM 2018 Syllabus

I found the of­fi­cial syl­labus hard to read and print. Do not take the break­down as in­dica­tive of any weigh­tage. It’s sim­ply de­mar­cated by the base­line dot (aka the full stop).

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, con­ser­va­tion 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, Maxwelll’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, Schrodinger equa­tion and its so­lu­tion for one, two and three di­men­sional boxes.
• Solution of Schrodinger equa­tion for the one di­men­sional har­monic os­cil­la­tor.
• Reflection and trans­mis­sion at a step po­ten­tial, Pauli ex­clu­sion prin­ci­ple.
• 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 lev­els.
• 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.