GATE 2015 Instrumentation Engineering Syllabus:
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier Series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential Equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Methods of variation of parameters, Cauchy’s and Euler’s equation, Initial and boundary value problems, Partial Differential Equations and variable separable method.
Complex Variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Transform Theory: Fourier transform, laplace transform, Z-transform
Basics of Circuits and Measurement systems: Kirchoff’s laws, mesh and nodal Analysis. Circuit theorems, One-port and two port Network Functions. Static and dynamic characteristics of Measurement Systems. Error and uncertainity analysis. Statistical analysis of data and curve fitting.
Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET. Diode circuits.Transistors at low and high frequencies, Amplifiers, single and multi-stage. Feedback amplifiers. Operational amplifiers, characteristics and circuit configurations. Instrumentation amplifier. Precision rectifier. V-to-I and I-to-V converter. Op-Amp based active filters. Oscillators and signal generators.
Digital Electronics: Combinational logic circuits, minimization of Boolean functions. IC families, TTL, MOS and CMOS. Arithmetic circuits. Comparators, Schmitt trigger, timers and mono-stable multi vibrator. Sequential circuits, flip-flops, counters, shift registers. Multiplexer, S/H Circuit. Analog-to-Digital and Digital-to-analog converters. Basics of number system. Microprocessor applications, memory and input-output interfacing. Microcontrollers.
Signals, Systems and Communications: Periodic and aperiodic signals. Impulse response, transfer function and frequency response of first and second order systems. Convolution, correlation and characteristics of linear time invariant systems. Discrete time system, impulse and frequency response. Pulse transfer function. IIR and FIR filters. Amplitude and frequency modulation and demodulation. Sampling theorem, pulse code modulation. Frequency and time division multiplexing. Amplitude shift keying, frequency shift keying and pulse shift keying for digital modulation.
Electrical and Electronic Measurement: Bridges and potientiometers, measurement of R,L and C. Measurement of voltage, current, power, power factor and energy. AC & DC current probes. Extension of instrument ranges. Q-meter and waveform analyzer. Digital voltmeter and multi-meter. Time, phrase, and frequency measurements. Cathode ray oscilloscope. Serial and parallel communication. Shielding and grounding.
Control Systems and Process Control: Feedback principles. Signal flow graphs. Transient Response, steady state errors. Routh and Nyquist criteria. Bode plot, root loci. Time delay systems. Phase and gain margin. State space representation of systems. Mechanical, hydraulic and pneumatic system components. Synchro pair, servo and step motors. On-off, cascade, P,P-I, P-I-D, feed forward and derivative controller, Fuzzy controllers.
Analytical Optical and Biomedical Instrumentation: Mass spectrometry. UV, visible and IR spectrometry. X-Ray and nuclear radiation measurements. Optical sources and detectors, LED, laser, Photo-diode, photo-diode, photo resistor and their characteristics. Interferometers, applications in metrology. Basics of fiber optics. Biomedical instruments, EEG, ECG and EMG. Clinical measurements. Ultrasonic transducers and Ultrasonography. Principles of Computer Assisted Tomography.