GATE PH study plan

Evaluate contour integrals with Cauchy's theorem and the residue theorem, including real integrals of rational and trigonometric functions.

Solve second-order linear ODEs by Frobenius series and identify Legendre, Bessel, and Hermite solutions with their recurrence relations.

Formulate Lagrangians for constrained mechanical systems and derive Euler-Lagrange equations for pendulum, bead-on-wire, and rolling-without-slipping setups.

Linearise a two-degree-of-freedom system about equilibrium and extract normal-mode frequencies and eigenvectors.

Derive Hamilton's equations from a Legendre transform and evaluate Poisson brackets to test conserved quantities.

Solve central-force orbit problems using the effective potential, including Kepler orbits and Rutherford scattering cross-sections.

Apply Gauss's law and Laplace's equation with boundary conditions to compute fields, potentials, and induced charges in dielectric media.

Compute capacitance, electrostatic energy, and forces in parallel-plate and coaxial configurations containing layered dielectrics.

Apply the Biot-Savart law and Ampere's law to symmetric current distributions such as solenoids, toroids, and rotating charged shells.

Derive Maxwell's equations from scalar and vector potentials and verify gauge invariance under the Lorenz gauge.

Solve plane-wave propagation in conductors and dielectrics to obtain skin depth, phase velocity, and attenuation constant.

Compute the Poynting vector and total radiated power for an oscillating electric dipole.

Solve the Schrodinger equation for step, barrier, and finite square-well potentials and calculate transmission and reflection coefficients.

Apply raising and lowering operators to angular momentum to compute eigenvalues, commutators, and matrix elements.

Calculate expectation values and uncertainties for harmonic-oscillator and hydrogen-atom states.

Apply first-order non-degenerate perturbation theory to compute energy shifts for a perturbed oscillator and the Stark effect in hydrogen.

Derive the four thermodynamic potentials and generate Maxwell relations from them.

Compute partition functions for ideal gases and harmonic oscillators and extract internal energy, entropy, and specific heat.

Apply Fermi-Dirac and Bose-Einstein distributions to electron gas and blackbody radiation problems.

Calculate fine-structure splittings, selection rules, and Zeeman shifts for one-electron atoms.

Compute rotational and vibrational energy levels and transition frequencies for diatomic molecules.

Construct reciprocal lattices and apply Bragg and Laue conditions to determine diffraction angles and structure factors.

Use free-electron and Kronig-Penney models to explain band gaps and calculate Fermi energy and density of states.

Compute nuclear binding energies, Q-values, and decay kinematics for alpha, beta, and gamma processes.

Classify elementary particles and test conservation of charge, baryon number, lepton number, and strangeness in reactions.

Analyse BJT and MOSFET DC biasing and draw small-signal equivalent circuits to compute voltage gain and input/output impedance.

Design inverting, non-inverting, integrator, and comparator op-amp circuits with specified gains and bandwidths.

Simplify Boolean expressions using Karnaugh maps and implement them with NAND/NOR gates.

Re-derive quantum-mechanical selection rules and solve one two-state perturbation problem under timed conditions.

Complete two full-length timed mock tests under GATE conditions, including the virtual calculator and on-screen aptitude section.

Revise the personal error log and re-solve every previously missed problem without notes.

Drill general aptitude quantitative and verbal items at 90 seconds per question to build speed.

Memorise the consolidated formula sheet and reproduce it from blank paper within 20 minutes.