GATE 2027 ECE — Complete Syllabus

Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and eigenvectors, rank, solution of linear equations, existence and uniqueness.
Calculus: Mean value theorems, integral calculus, definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line/surface/volume integrals, Taylor series.
Differential Equations: Linear differential equations, Euler-Cauchy equation, nonhomogeneous equations, variation of parameters, complementary function, particular integral, partial differential equations, variable separable method, initial and boundary value problems.
Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence, curl, Gauss's theorem, Green's theorem, Stokes' theorem.
Complex Analysis: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula, sequences and series, convergence tests, Taylor and Laurent series, residue theorem.
Probability & Statistics: Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial, Poisson, exponential and normal distributions, joint and conditional probability, correlation and regression.

Circuit Analysis: Node and mesh analysis, superposition, Thevenin's theorem, Norton's theorem, reciprocity.
Sinusoidal Steady-State Analysis: Phasors, complex power, maximum power transfer.
Linear Circuits: RL, RC and RLC circuits, Laplace transform, two-port network parameters, wye-delta transformation.
LTI Systems: Definition and properties, causality, stability, impulse response, convolution, poles and zeros, frequency response, group delay, phase delay.
Continuous-Time Signals: Fourier series, Fourier transform, Nyquist sampling theorem, sampling and reconstruction.
Discrete-Time Signals: DTFT, DFT, Z-transform, FIR and IIR filter design.

Semiconductor Fundamentals: Energy bands, intrinsic and extrinsic semiconductors, equilibrium carrier concentration, direct and indirect band-gap semiconductors.
Carrier Transport: Diffusion current, drift current, mobility, resistivity, generation and recombination, Poisson equation, continuity equation.
Electronic Devices: P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, MOSFET scaling, LED, photodiode and solar cell.

Diode Circuits: Clipping, clamping and rectifiers.
BJT & MOSFET Amplifiers: Biasing, AC coupling, small-signal analysis, frequency response, current mirrors, differential amplifiers.
Op-Amp Circuits: Amplifiers, summers, differentiators, integrators, active filters, Schmitt trigger, oscillators, dominant-pole/Miller compensation, phase margin.

Number Representation: Binary, integer and floating-point numbers.
Combinational Circuits: Boolean algebra, Boolean minimization, Karnaugh maps, logic gates, static CMOS implementation, arithmetic circuits, code converters, multiplexers and decoders.
Sequential Circuits: Latches, flip-flops, counters, shift registers, finite-state machines, propagation delay, setup and hold time, critical path delay.
Data Converters: Sample-and-hold circuits, ADCs and DACs.
Semiconductor Memories: ROM, SRAM and DRAM.
Computer Organization: Machine instructions, addressing modes, ALU, datapath, control unit and instruction pipelining.

Random Processes: Autocorrelation, power spectral density, white noise, filtering of random signals through LTI systems.
Analog Communications: AM and demodulation, angle modulation and demodulation, AM/FM spectra, superheterodyne receivers.
Information Theory: Entropy, source coding, mutual information, channel capacity theorem.
Digital Communications: PCM, DPCM, ASK, PSK, FSK, QAM, bandwidth, inter-symbol interference, MAP detection, ML detection, matched-filter receiver, SNR and BER.
Error Correction: Fundamentals of error correction, Hamming codes and CRC.

Maxwell's Equations: Differential and integral forms, interpretation, boundary conditions, wave equation, Poynting vector.
Plane Waves: Reflection and refraction, polarization, phase velocity, group velocity, propagation through different media, skin depth.
Transmission Lines: Transmission-line equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart.
Waveguides: Rectangular and circular waveguides.
Optical Fibers: Light propagation through optical fibers.
Antennas: Dipole and monopole antennas, linear antenna arrays.

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