**Detailed syllabus for GATE 2018 CSE **

**Engineering Mathematics:**

**Discrete Mathematics **

- Propositional and first-order logic.
- Sets, relations, functions, partial orders and lattices.
- Groups.
- Graphs: connectivity, matching, colouring.
- Combinatorics: counting, recurrence relations, generating functions.
- Linear Algebra
- Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition
- Calculus,Limits, continuity and differentiability.
- Maxima and minima.
- Mean value theorem.
- Integration
- Probability Random variables.
- Uniform, normal, exponential, poisson and binomial distributions.
- Mean, median, mode and standard deviation.
- Conditional probability and Bayes theorem

**Digital Logic:**

- Boolean algebra.
- Combinational and sequential circuits.
- Minimization.
- Number representations and computer arithmetic (fixed and floating point).

**Computer Organization and Architecture:**

- Machine instructions and addressing modes.
- ALU, data-path and control unit. Instruction pipelining.
- Memory hierarchy: cache, main memory, and secondary storage; I/O, interface (Interrupt and DMA mode).

**Programming and Data Structures:**

- Programming in C.
- Recursion.
- Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.
- Algorithms
- Searching, sorting, hashing.
- Asymptotic worst-case time and space complexity.
- Algorithm design techniques: greedy, dynamic programming and divide-and-conquer.
- Graph search, minimum spanning trees, shortest paths.

**Theory of Computation:**

- Regular expressions and finite automata.
- Context-free grammars and pushdown automata.
- Regular and context-free languages, pumping lemma.
- Turing machines and undecidability.

**Compiler Design:**

- Lexical analysis, parsing, syntax-directed translation.
- Runtime environments.
- Intermediate code generation.

**Operating System:**

- Processes, threads, inter-process communication, concurrency, and synchronization.
- Deadlock.
- CPU scheduling.
- Memory management and virtual memory.
- File systems.

**Databases:**

- ER-model.
- Relational model: relational algebra, tuple calculus, SQL.
- Integrity constraints, normal forms.
- File organization, indexing (e.g., B and B+ trees).
- Transactions and concurrency control.

**Computer Networks:**

- The concept of layering.
- LAN technologies (Ethernet).
- Flow and error control techniques, switching.
- IPv4/IPv6, routers and routing algorithms (distance vector, link state).
- TCP/UDP and sockets, congestion control.
- Application layer protocols (DNS, SMTP, POP, FTP, HTTP).
- Basics of Wi-Fi.
- Network security: authentication, basics of a public key and private key cryptography, digital signatures and certificates, firewalls.

**GATE 2018 Civil Syllabus**

**Section 1: Engineering Mathematics**

- Linear Algebra
- Matrix algebra
- Systems of linear equations
- Eigenvalues and Eigenvectors.

**Calculus:**

- Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, 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.

**Complex variables:**

- Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series.

**Probability and Statistics:**

- Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

**Numerical Methods: **

- Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods for differential equations.

**Section 2: Structural Engineering:**

**Mechanics:**

- Bending moment and shear force in statically determinate beams.

**Simple stress and strain relationship:**

- Stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle. Simple bending theory, flexural and shear stresses, unsymmetrical bending, shear center.
- Thin walled pressure vessels, uniform torsion, buckling of column, combined and direct bending stresses.

**Structural Analysis:**

- Analysis of statically determinate trusses, arches, beams, cables and frames, displacements in statically determinate structures and analysis of statically indeterminate structures by force/ energy methods, analysis by displacement methods (slope deflection and moment distribution methods), influence lines for determinate and indeterminate structures.
- Basic concepts of matrix methods of structural analysis.

**Concrete Structures:**

- Concrete Technology- properties of concrete, basics of mix design.

**Steel Structures: **

- Analysis and design of tension and compression members, beams and beam-columns, column bases.
- Connections- simple and eccentric, beam–column connections, plate girders and trusses.
- Plastic analysis of beams and frames.

**Section 3: Geotechnical Engineering**

**Soil Mechanics:**

- Origin of soils, soil classification, three-phase system, fundamental definitions, relationship and interrelationships, permeability & seepage, effective stress principle, consolidation, compaction, shear strength.

**Foundation Engineering: **

- Sub-surface investigations- scope, drilling bore holes, sampling, penetration tests, plate load test. Earth pressure theories, the effect of water table, layered soils.
- Stability of slopes-infinite slopes, finite slopes.
- Foundation types-foundation design requirements.
- Shallow foundations-bearing capacity, the effect of shape, water table, and other factors, stress distribution, settlement analysis in sands & clays.
- Deep foundations–pile types, dynamic & static formulae, the load capacity of piles in sands & clays, negative skin friction.

**Section 4: Water Resources Engineering**

**Fluid Mechanics and Hydraulics: **

- Properties of fluids, the principle of conservation of mass, momentum, energy and corresponding equations, potential flow, applications of momentum and Bernoulli’s equation, laminar and turbulent flow, flow in pipes, pipe networks.
- The concept of the boundary layer and its growth.
- Uniform flow, critical flow, and gradually varied flow in channels, specific energy concept, hydraulic jump.
- Forces on immersed bodies, flow measurements in channels, tanks, and pipes.
- Dimensional analysis and hydraulic modeling.
- Kinematics of flow, velocity triangles and specific speed of pumps and turbines.

**Hydrology: **

- Hydrologic cycle, rainfall, evaporation, infiltration, stage discharge relationships, unit hydrographs, flood estimation, reservoir capacity, reservoir and channel routing. Well, hydraulics.

**Irrigation: **

- Duty, delta, estimation of evapotranspiration and Crop water requirements.
- Design of lined and unlined canals, waterways, head works, gravity dams, and spillways.
- Design of weirs on permeable foundation.
- Types of the irrigation system, irrigation methods.
- Waterlogging and drainage, sodic soils.

**Section 5: Environmental Engineering**

**Water requirements: **

- Quality standards, basic unit processes, and operations for water treatment.
- Drinking water standards, water requirements, basic unit operations and unit processes for surface water treatment, distribution of water.
- Sewage and sewerage treatment, quantity and characteristics of wastewater.
- Primary, secondary and tertiary treatment of wastewater, sludge disposal, effluent discharge standards.
- Domestic wastewater treatment, the quantity of characteristics of domestic wastewater, primary and secondary treatment Unit operations and unit processes of domestic wastewater, sludge disposal.

**Air Pollution: **

- Types of pollutants, their sources and impacts, air pollution meteorology, air pollution control, air quality standards and limits.
- Municipal Solid Wastes: Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment, and disposal).

**Noise Pollution: **

- Impacts of noise, permissible limits of noise pollution, measurement of noise and control of noise pollution.

**Section 6: Transportation Engineering**

**Highway Planning: **

- The geometric design of highways, testing, and specifications of paving materials, the design of flexible and rigid pavements.

**Traffic Engineering: **

- Traffic characteristics, the theory of traffic flow, intersection design, traffic signs and signal design, highway capacity.

**Section 7: Geomatics Engineering**

- Principles of surveying; Errors and their adjustment; Maps – scale, coordinate system; Distance and angle measurement – Levelling and trigonometric leveling; Traversing and triangulation survey; Total station; Horizontal and vertical curves.
- Photogrammetry – scale, flying height; remote sensing – basics, platform and sensors, visual image interpretation; Basics of Geographical information system (GIS) and Geographical Positioning system (GPS)
- The importance of surveying, principles and classifications, mapping concepts, coordinate system, map projections, measurements of distance and directions, leveling, theodolite traversing, plane table surveying, errors and adjustments, curves.

**GATE 2018 Engineering Mathematics Syllabus**

- Linear Algebra, Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
- Calculus, Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.
- Differential equations, First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace’s equations.
- Complex variables Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series.
- Probability and Statistics: Definitions of probability, sampling theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.
- Numerical Methods Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.

**GATE 2018 syllabus for Applied Mechanics & Design**

- Engineering Mechanics Free-body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations, collisions.
- Mechanics of Materials Stress and strain, elastic constants, Poisson’s ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength.
- Theory of Machines Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope.
- Vibrations Free and forced vibration of single degree of freedom systems, the effect of damping; vibration isolation; resonance; critical speeds of shafts.
- Machine Design Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.

**GATE 2018 syllabus for Fluid Mechanics and Thermal Sciences**

- Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy, forces on submerged bodies, stability of floating bodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends and fittings.
- Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept and electrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system, Heisler’s charts; thermal boundary layer, dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, Stefan-Boltzmann law, Wien’s displacement law, black and grey surfaces, view factors, radiation network analysis.
- Thermodynamics: Thermodynamic systems and processes; properties of pure substances, behaviour of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in various processes; second law of thermodynamics; thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations.
- Applications Power Engineering: Air and gas compressors; vapour and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles. Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes
- Turbomachinery Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines.
- Materials, Manufacturing and Industrial Engineering
- Engineering Materials Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials.
- Casting, Forming and Joining Processes Different types of castings, design of patterns, moulds and cores; solidification and cooling; riser and gating design.
- Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy
- Principles of welding, brazing, soldering and adhesive bonding.
- Machining and Machine Tool Operations: Mechanics of machining; basic machine tools; single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, design of jigs and fixtures.
- Metrology and Inspection Limits, fits and tolerances; linear and angular measurements; comparators; gauge design; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.

**GATE 2018 syllabus for Computer Integrated Manufacturing**

- Basic concepts of CAD/CAM and their integration tools. Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning.
- Inventory Control: Deterministic models; safety stock inventory control systems.
- Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.
- Linear Algebra, Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and eigenvectors, rank, the solution of linear equations – existence and uniqueness.
- Calculus, Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.
- Differential Equations, First order equations (linear and nonlinear), higher order linear differential equations, Cauchy’s and Euler’s equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems
- Vector Analysis, Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss’s, Green’s and Stoke’s theorems
- Complex Analysis Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula; Taylor’s and Laurent’s series, residue theorem
- Numerical Methods Solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria
- Probability and Statistics Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions – binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis.

**Networks, Signals & Systems:**

- Network solution methods Nodal and mesh analysis; Network theorems: superposition, Thevenin and Norton’s, maximum power transfer; Wye-Delta transformation; Steady state sinusoidal analysis using phasors; Time domain analysis of simple linear circuits; Solution of network equations using Laplace transform; Frequency domain analysis of RLC circuits; Linear 2-port network parameters: driving point and transfer functions; State equations for networks
- Continuous-time signals Fourier series and Fourier transform representations, sampling theorem and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time signals; LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques.
- Electronic Devices Energy bands in intrinsic and extrinsic silicon
- Carrier transport Diffusion current, drift current, mobility and resistivity; Generation and recombination of carriers; Poisson and continuity equations; P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photodiode and solar cell
- Integrated circuit fabrication process Oxidation, diffusion, ion implantation, photolithography and twin-tub CMOS process.

**Analog Circuits:**

- Circuits, Small signal equivalent circuits of diodes, BJTs, and MOSFETs
- Simple diode circuits, Clipping, clamping, and rectifiers
- BJT and MOSFET amplifiers
- Single-stage BJT and MOSFET amplifiers biasing, bias stability, mid-frequency small signal analysis and frequency response; multi-stage, differential, feedback, power and operational; Simple op-amp circuits; Active filters.

**Sinusoidal oscillators: **

- Criterion for oscillation, single-transistor and op-amp configurations; Function generators, wave-shaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation

**Digital Circuits:**

- Combinatorial circuits, Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders and PLAs.
- Sequential circuits latches and flip-flops, counters, shift registers and finite state machines; Data converters: sample and hold circuits, ADCs and DACs
- Semiconductor memories: ROM, SRAM, DRAM
- 8-bit microprocessor (8085)
- Architecture, programming, memory and I/O interfacing.

**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 lag-lead compensation; State variable model and solution of state equation of LTI systems

**Communications:**

- Random processes autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems
- Analog communications amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers, circuits for analog communications
- Information theory entropy, mutual information and channel capacity theorem
- Digital communications,PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of band, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.

**Electromagnets:**

- Electrostatics
- Maxwell’s equations Differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector
- Plane waves and properties
- Reflection and refraction, polarisation, phase and group velocity, propagation through various media, skin depth
- Transmission lines Equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart
- Waveguides Modes, boundary conditions, cut-off frequencies, dispersion relations
- Antenna: Antenna types, radiation pattern, gain and directivity, return loss, antenna arrays; Basics of radar; Light propagation in optical fibers.

**GATE 2018 syllabus for Electrical Engineering**

- Engineering Mathematics Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors. 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 integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.
- Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
- Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals
- Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.
- Numerical Methods: Solutions of non-linear algebraic equations, Single and Multi-step methods for differential equations.
- Transform Theory: Fourier Transform, Laplace Transform, z-Transform.
- Electric Circuits, Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and AC networks, Sinusoidal steady-state analysis, Resonance, Passive filters, Ideal current and voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem, Two-port networks, Three phase circuits, Power and power factor in AC circuits.
- Electromagnetic Fields ,Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot-Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.
- Signals and Systems: Representation of continuous and discrete-time signals, Shifting and scaling operations, Linear Time.

**Note:** In short the syllabi can be consolidated as follows:

**Syllabus for CSE:**Engineering Mathematics, Digital Logic, Programming and Data Structures, Theory of computation and Databases.**Syllabus for Civil:**Engineering Mathematics, Structural Engineering, Geotechnical Engineering, Water Resources Engineering, Environmental Engineering, Transportation Engineering, Geomatics Engineering.**Engineering Mathematics syllabus:**This**section comprises of arithmetical questions and Engineering mathematics. The main aim is to test the applicant’s ability to understand complex concepts of mathematics involved in Engineering with ease and their application to problems.**- Applied Mechanics and Design syllabus