**GATE Engineering Sciences Syllabus:**

**1. Engineering Mathematics**

Section 1: Linear Algebra

Algebra of matrices; Inverse and rank of a matrix; System of
linear equations; Symmetric, skew-symmetric and orthogonal matrices;
Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices;
Cayley-Hamilton Theorem.

Section 2: Calculus

*Functions of single variable*: Limit, continuity and differentiability; Mean value theorems; Indeterminate

*forms and L'Hospital's rule; Maxima and minima; Taylor's theorem; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.*

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*Functions of two variables*: Limit, continuity and partial derivatives; Directional derivative; Total

*derivative; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications.*

*Sequence and series:*Convergence of sequence and series; Tests for convergence; Power series; Taylor's

*series; Fourier Series; Half range sine and cosine series.*

Section 3: Vector Calculus

Gradient, divergence and curl;
Line and surface integrals; Green's theorem, Stokes theorem and Gauss
divergence theorem (without proofs).

Section 3: Complex variables

Analytic functions;
Cauchy-Riemann equations; Line integral, Cauchy's integral theorem and integral
formula (without proof); Taylor's series and Laurent series; Residue theorem
(without proof) and its applications.

Section 4: Ordinary Differential Equations

First order equations (linear
and nonlinear); Higher order linear differential equations with constant
coefficients; Second order linear differential equations with variable
coefficients; Method of variation of parameters; Cauchy-Euler equation; Power
series solutions; Legendre polynomials, Bessel functions of the first kind and
their properties.

Section 5: Partial Differential Equations

Classification of second order
linear partial differential equations; Method of separation of variables;
Laplace equation; Solutions of one dimensional heat and wave equations.

Section 6: Probability and Statistics

Axioms of probability; Conditional probability; Bayes'
Theorem; Discrete and continuous random variables: Binomial, Poisson and normal
distributions; Correlation and linear regression.

Section 7: Numerical Methods

Solution of systems of linear equations using LU
decomposition, Gauss elimination and Gauss-Seidel methods; Lagrange and
Newton's interpolations, Solution of polynomial and transcendental equations by
Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson's
rule and Gaussian quadrature rule; Numerical solutions of first order
differential equations by Euler's method and 4th order Runge-Kutta method.

**2. Fluid Mechanics**

Section 1: Flow and Fluid Properties

Viscosity

*,*relationship between stress and strain-rate compressible flows, differences between laminar and manometry, forces on submerged bodies. for Newtonian fluids, incompressible and turbulent flows*.*Hydrostatics: Buoyancy,
Section 2: Kinematics

Eulerian and Lagrangian description of fluids motion,
concept of local and convective accelerations, steady and unsteady flows

*.*
Section 3: Integral analysis

Control
volume analysis for mass, momentum and energy.

Section 4: Differential Analysis

Differential equations of mass and momentum for
incompressible flows: inviscid - Euler equation and viscous flows -
Navier-Stokes equations

*,*concept of fluid rotation, vorticity, stream function, Exact solutions of Navier-Stokes equation for Couette Flow and Poiseuille flow.
Section 5: Inviscid flows

Bernoulli’s equation - assumptions and applications,
potential function, Elementary plane flows - uniform flow, source, sink and
doublet and their superposition for potential flow past simple geometries.

Section 6: Dimensional analysis

Concept of geometric, kinematic and dynamic similarity, some
common non-dimensional parameters and their physical significance: Reynolds
number, Froude number and Mach number.

Section 7: Internal flows

Fully developed pipe flow, empirical relations for laminar
and turbulent flows: friction factor and Darcy-Weisbach relation.

Section 8: Prandtl boundary layer equations

Concept and assumptions

*,*qualitative idea of boundary layer and separation, streamlined and bluff bodies, drag and lift forces. Flow measurements: Basic ideas of flow measurement using venturimeter, pitot-static tube and orifice plate.**3. Materials Science**

Section 1: Processing of Materials:

Powder synthesis, sintering, chemical methods, crystal
growth techniques, zone refining, preparation of nanoparticles and thin films

Section 2: Characterisation Techniques:

X-ray
diffraction, spectroscopic techniques like UV-vis, IR, Raman. Optical and
Electron microscopy

Section 3: Structure and Imperfections:

Crystal symmetry, point groups,
space groups, indices of planes, close packing in solids, bonding in materials,
coordination and radius ratio concepts, point defects, dislocations, grain
boundaries, surface energy and equilibrium shapes of crystals

Section 4: Thermodynamics and Kinetics:

Phase rule, phase diagrams,
solid solutions, invariant reactions, lever rule, basic heat treatment of
metals, solidification and phase transformations, Fick’s laws of diffusion,
mechanisms of diffusion, temperature dependence of diffusivity

Section 5: Properties of Materials:

Mechanical
Properties: Stress-strain response of metallic, ceramic
and polymer materials, yield strength, tensile strength and modulus of elasticity, toughness, plastic
deformation, fatigue, creep and fracture

Electronic
Properties: Free electron theory, Fermi energy, density of
states, elements of band theory, semiconductors, Hall effect, dielectric behaviour, piezo, ferro,
pyroelectricmaterials

Magnetic
Properties: Origin of magnetism in metallic and ceramic
materials, paramagnetism, diamagnetism, ferro and ferrimagnetism

Thermal Properties: Specific heat, thermal
conductivity and thermal expansion, thermoelectricity

Optical Properties: Refractive index, absorption and transmission of electromagnetic
radiation in solids, electrooptic and magnetoopticmaterials, spontaneous and stimulated
emission, gas and solid state lasers

Section 6: Material types

Concept of amorphous, single
crystals and polycrystalline materials, crystallinity and its effect on
physical properties, metal, ceramic, polymers, classification of polymers,
polymerization, structure and properties, additives for polymer products,
processing and applications, effect of environment on materials, composites

Section 7: Environmental Degradation

Corrosion,
oxidation and prevention

Section 8: Elements of Quantum Mechanics and Mathematics

Basics of quantum mechanics, quantum mechanical treatment of
electrical, optical and thermal properties of materials, analytical solid
geometry, differentiation and integration, differential equations, vectors and
tensors, matrices, Fourier series, complex analysis, probability and statistics

**4. Solid Mechanics**

Equivalent force systems; free-body diagrams; equilibrium
equations; analysis of determinate trusses and frames; friction; particle
kinematics and dynamics; dynamics of rigid bodies under planar motion; law of
conservation of energy; law of conservation of momentum.

Stresses and strains; principal stresses and strains; Mohr’s
circle for plane stress and plane strain; generalized Hooke’s Law; elastic
constants; thermal stresses; theories of failure.

Axial, shear and bending moment diagrams; axial, shear and
bending stresses; combined stresses; deflection (for symmetric bending);
torsion in circular shafts; thin walled pressure vessels; energy methods
(Castigliano’s Theorems); Euler buckling.

Free
vibration of single degree of freedom systems.

**5. Thermodynamics**

Section 1: Basic Concepts

Continuum and macroscopic approach; thermodynamic systems
(closed and open); thermodynamic properties and equilibrium; state of a system,
state postulate for simple compressible substances, state diagrams, paths and
processes on state diagrams; concepts of heat and work, different modes of
work; zeroth law of thermodynamics; concept of temperature.

Section 2: First Law of Thermodynamics

Concept of energy and various
forms of energy; internal energy, enthalpy; specific heats; first law applied
to elementary processes, closed systems and control volumes, steady and
unsteady flow analysis.

Section 3: Second Law of Thermodynamics

Limitations of the first law of thermodynamics, concepts of
heat engines and heat pumps/refrigerators, Kelvin-Planck and Clausius
statements and their equivalence; reversible and irreversible processes; Carnot
cycle and Carnot principles/theorems; thermodynamic temperature scale; Clausius
inequality and concept of entropy; microscopic interpretation of entropy, the
principle of increase of entropy, T-s diagrams; second law analysis of control
volume; availability and irreversibility; third law of thermodynamics.

Section 4: Properties of Pure Substances

Thermodynamic properties of pure substances in solid, liquid
and vapor phases; P-v- T behaviour of simple compressible substances, phase
rule, thermodynamic property tables and charts, ideal and real gases, ideal gas
equation of state and van der Waals equation of state; law of corresponding
states, compressibility factor and generalized compressibility chart.

Section 5: Thermodynamic Relations

T-ds relations, Helmholtz and Gibbs functions, Gibbs
relations, Maxwell relations, Joule-Thomson coefficient, coefficient of volume
expansion, adiabatic and isothermal compressibilities, Clapeyron and
Clapeyron-Clausius equations.

Section 6: Thermodynamic Cycles

Carnot vapor cycle, ideal Rankine cycle, Rankine reheat
cycle, air-standard Otto cycle, air-standard Diesel cycle, air-standard Brayton
cycle, vapor-compression refrigeration cycle.

Section 7: Ideal Gas Mixtures

Dalton’s and Amagat’s laws, properties of ideal gas
mixtures, air-water vapor mixtures and simple thermodynamic processes involving
them; specific and relative humidities, dew point and wet bulb temperature,
adiabatic saturation temperature, psychrometric chart.

**6. Polymer Science and Engineering**

Section 1: Chemistry of high polymers

Monomers, functionality, degree of polymerizations,
classification of polymers, glass transition, melting transition, criteria for
rubberiness, polymerization methods: addition and condensation; their kinetics,
metallocene polymers and other newer techniques of polymerization,
copolymerization, monomer reactivity ratios and its significance, kinetics,
different copolymers, random, alternating, azeotropic copolymerization, block
and graft copolymers, techniques for copolymerization- bulk, solution,
suspension, emulsion.

Section 2: Polymer Characterization

Solubility and swelling, concept of average molecular
weight, determination of number average, weight average, viscosity average and
Z-average molecular weights, polymer crystallinity, analysis of polymers using
IR, XRD, thermal (DSC, DMTA, TGA), microscopic (optical and electronic)
techniques.

Section 3: Synthesis and properties

Commodity
and general purpose thermoplastics: PE, PP, PS, PVC, Polyesters, Acrylic, PU
polymers.

Engineering Plastics: Nylon, PC,
PBT, PSU, PPO, ABS, Fluoropolymers Thermosetting polymers: PF, MF, UF, Epoxy,
Unsaturated polyester, Alkyds. Natural and synthetic rubbers: Recovery of NR
hydrocarbon from latex, SBR, Nitrile, CR, CSM, EPDM, IIR, BR, Silicone, TPE.

Section 4: Polymer blends and composites

Difference between blends and composites, their
significance, choice of polymers for blending, blend miscibility-miscible and
immiscible blends, thermodynamics, phase morphology, polymer alloys, polymer
eutectics, plastic-plastic, rubber-plastic and rubber-rubber blends, FRP,
particulate, long and short fibre reinforced composites.

Section 5: Polymer Technology

Polymer compounding-need and
significance, different compounding ingredients for rubber and plastics,
cross-linking and vulcanization, vulcanization kinetics.

Section 6: Polymer rheology

Flow of Newtonian and non-Newtonian fluids, different flow
equations, dependence of shear modulus on temperature, molecular/segmental
deformations at different zones and transitions. Measurements of rheological
parameters by capillary rotating, parallel plate, cone-plate rheometer. Visco-
elasticity-creep and stress
relaxations, mechanical models, control of rheological characteristics through
compounding, rubber curing in parallel plate viscometer, ODR and MDR.

Section 7: Polymer processing

Compression molding, transfer molding, injection molding,
blow molding, reaction injection molding, extrusion, pultrusion, calendaring,
rotational molding, thermoforming, rubber processing in two-roll mill, internal
mixer.

Section 8: Polymer testing

Mechanical-static and dynamic tensile, flexural,
compressive, abrasion, endurance, fatigue, hardness, tear, resilience, impact,
toughness. Conductivity-thermal and electrical, dielectric constant,
dissipation factor, power factor, electric resistance, surface resistivity,
volume resistivity, swelling, ageing resistance, environmental stress cracking
resistance.

**7. Food Technology**

Section 1: Food Chemistry and Nutrition

Carbohydrates: structure and functional properties of mono-,
oligo-, & poly- saccharides including starch, cellulose, pectic substances
and dietary fibre, gelatinization and retrogradation of starch. Proteins:
classification and structure of proteins in food, biochemical changes in post
mortem and tenderization of muscles. Lipids: classification and structure of
lipids, rancidity, polymerization and polymorphism. Pigments: carotenoids,
chlorophylls, anthocyanins, tannins and myoglobin. Food flavours: terpenes,
esters, aldehydes, ketones and quinines. Enzymes: specificity, simple and
inhibition kinetics, coenzymes, enzymatic and non- enzymatic browning.
Nutrition: balanced diet, essential amino acids and essential fatty acids,
protein efficiency ratio, water soluble and fat soluble vitamins, role of
minerals in nutrition, co-factors, anti-nutrients, nutraceuticals, nutrient
deficiency diseases. Chemical and biochemical changes: changes occur in foods
during different processing.

Section 2: Food Microbiology

Characteristics
of microorganisms: morphology of bacteria, yeast, mold and actinomycetes,
spores and vegetative
cells, gram-staining. Microbial growt h: growth and death kinetics, serial
dilution technique.

Food spoilage: spoilage microorganisms in different food
products including milk, fish, meat, egg, cereals and their products. Toxins
from microbes: pathogens and non-pathogens including Staphylococcus,
Salmonella, Shigella, Escherichia, Bacillus, Clostridium, and Aspergillus
genera. Fermented foods and beverages: curd, yoghurt, cheese, pickles,
soya-sauce, sauerkraut, idli, dosa, vinegar, alcoholic beverages and sausage.

Section 3: Food Products Technology

Processing principles: thermal processing, chilling,
freezing, dehydration, addition of preservatives and food additives,
irradiation, fermentation, hurdle technology, intermediate moisture foods. Food
pack aging and storage: packaging materials, aseptic packaging, controlled and
modified atmosphere storage. Cereal processing and products: milling of rice,
wheat, and maize, parboiling of paddy, bread, biscuits, extruded products and
ready to eat breakfast cereals. Oil processing: expelling, solvent extraction,
refining and hydrogenation. Fruits and vegetables p processing: extraction, clarification,
concentration and packaging of fruit juice, jam, jelly, marmalade, squash,
candies, tomato sauce, ketchup, and puree, potato chips, pickles. Plantation
crops processing and products: tea, coffee, cocoa, spice, extraction of
essential oils and oleoresins from spices. Milk and milk products processing:
pasteurization and sterilization, cream, butter, ghee, ice- cream, cheese and
milk powder. Processing of animal products: drying, canning, and freezing of
fish and meat; production of egg powder. Waste utilization: pectin from fruit
wastes, uses of by-products from rice milling. Food standards and quality
maintenance: FPO, PFA, A-Mark, ISI, HACCP, food plant sanitation and cleaning
in place (CIP).

Section 4: Food Engineering

Mass
and energy balance; Momentum transfer: Flow rate and pressure drop
relationships for Newtonian fluids
flowing through pipe, Reynolds number. Heat transfer: heat transfer by
conduction, convection, radiation, heat exchangers. Mass
transfer: molecular diffusion and Flick's law, conduction and convective mass
transfer, permeability through single and multilayer films. Mechanical
operations: size reduction of solids, high pressure homogenization, filtration,
centrifugation, settling, sieving, mixing & agitation of liquid. Thermal
operations: thermal sterilization, evaporation of liquid foods, hot air drying
of solids, spray and freeze-drying, freezing and crystallization. Mass transfer
operations: psychometric, humidification and dehumidification operations.

**8. Atmospheric & Ocean Science**

Section A: Atmospheric Science

Fundamental of Meteorology, Thermal structure of the
atmosphere and its composition, Radiation Balance and Laws, Wind Belts,
Monsoon, Climate. Atmospheric Thermodynamics. Hydrostatic equilibrium and:
Hydrostatic equation, variation of pressure with height, geopotential, Tropical
convection. Atmospheric Electricity. Cloud Physics. Observation Techniques of
the Atmosepheric Properties.

Fundamental equations. Pressure,
gravity, centripetal and Corolis forces, continuity equation in Cartesian and
isobaric coordinates, Scale analysis, inertial flow, geostrophic and gradient
winds, thermal wind, vorticity. Atmospheric turbulence, baroclinic instabiltiy.
Atmosphreric Waves.

Tropical meteorology: Trade wind inversion, ITCZ; monsoon
trough tropical cyclones, their structure and development theory; monsoon
depressions; Climate variability and forcings; Madden-Julian oscillation (MJO),
ENSO, QBO (quasi-biennial oscillation) and sunspot cycles. Primitive equations
of Numerical Weather Prediction. General Circulation and Climate Modelling.

Synoptic weather forecasting,
prediction of weather elements such as rain, maximum and minimum temperature
and fog. Data Assimilation.

Section B: Ocean Sciences

Seawater Properties, T-S diagrams, Ocean Observations, Ocean
Tide and Waves and their properties. Coastal processes and Estuary Dynamics.
coastal zone management. Wind Driven Circulation: Ekman, Sverdrup, Stommel and
Munk theories, Inertial currents; geostrophic motion; barotropic and baroclinic
conditions; Oceanic eddies. Global conveyor belt circulation. Subtropical
gyres; Western boundary currents; equatorial current systems; Current System in
the Indian Ocean.

Momentum
equation, mass conservation, vorticity. Ocean and Wave Modeling, Ocean State
Forecasting.

Data
Assimilation. Ocean Turbulence.

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