Summary of Topics in GATE ECE Exam Syllabus

1. Engineering Mathematics:
- Linear Algebra: Matrix algebra, Eigenvalues and eigenvectors, Systems of linear equations.
- Calculus: Mean value theorems, Theorems of integral calculus, Maxima and minima, Multiple integrals, Partial derivatives, Vector identities, Line, surface and volume integrals, Stokes, Gauss and Green's theorems.
- Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one-dimensional heat and wave equations and Laplace equation.
- Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

2. Networks, Signals, and Systems:
- Network Solution Methods: Network theorems, Network graphs, KCL and KVL, Node and Mesh analysis, Transient response of networks, Sinusoidal steady state analysis, Resonance, Two-port networks, Network functions.
- Signals and Systems: Representation of continuous and discrete-time signals, Shifting and scaling operations, Linear Time Invariant and Causal systems, Fourier series representation, Fourier and Laplace transform analysis of signals and systems, Convolution and correlation.

3. Electronic Devices and Circuits:
- Semiconductors: Energy bands in silicon, Intrinsic and extrinsic silicon, Carrier transport mechanisms, P-N junction diode, Zener diode, BJT, MOS capacitor, MOSFET, LED, and Photodiode.
- Analog Circuits: Small Signal Equivalent circuits of diodes, BJT, and MOSFETs, Simple diode circuits, Amplifiers, Biasing and Bias stability of transistor and FET amplifiers, Feedback amplifiers, Oscillators, Operational amplifiers and applications, Simple active filters.
- Digital Circuits: Boolean algebra, Combinational and sequential circuits, Number representation and computer arithmetic (fixed and floating-point).

4. Control Systems:
- Basic control system components, Feedback principle, Transfer function, Block diagram representation, Signal flow graph, Transient and steady-state analysis of LTI systems, Frequency response, Routh-Hurwitz and Nyquist stability criteria, Bode and Root-Locus plots, Lag, Lead and Lead-Lag compensators, State variable model and solution of state equation of LTI control systems.

5. Communications:
- Analog Communication Systems: Random processes, Amplitude modulation, Angle modulation, Noise in analog communication systems, Performance of AM and FM systems, Superheterodyne receivers, Analog-to-digital and digital-to-analog converters.
- Digital Communication Systems: Digital modulation schemes, Bandwidth efficiency, Signal-to-noise ratio, Error probability, Pulse code modulation (PCM), Differential pulse code modulation (DPCM), Digital modulation techniques: ASK, FSK, PSK, QPSK, CPM, Error control coding, Convolutional coding.

6. Electromagnetics:
- Electro