## GATE Syllabus for Engineering Sciences

### SECTION A: ENGINEERING MATHEMATICS (Compulsory)

**Linear Algebra:** Algebra of matrices, inverse, rank, system of
linear equations, symmetric, skew-symmetric and orthogonal matrices.
Hermitian, skew-Hermitian and unitary matrices. eigenvalues and
eigenvectors, diagonalisation of matrices, Cayley-Hamilton Theorem.

**Calculus:** Functions of single variable,
limit, continuity and differentiability, Mean value theorems,
Indeterminate forms and L'Hospital rule, Maxima and minima, Taylor's
series, Fundamental and mean value-theorems of integral calculus.
Evaluation of definite and improper integrals, Beta and Gamma
functions, Functions of two variables, limit, continuity, partial
derivatives, Euler's theorem for homogeneous functions, total
derivatives, maxima and minima, Lagrange method of multipliers, double
and triple integrals and their applications, sequence and series, tests
for convergence, power series, Fourier Series, Half range sine and
cosine series.

**Complex variable:** Analytic functions,
Cauchy-Riemann equations, Application in solving potential problems,
Line integral, Cauchy's integral theorem and integral formula (without
proof), Taylor's and Laurent' series, Residue theorem (without proof)
and its applications.

**Vector Calculus:** Gradient, divergence and
curl, vector identities, directional derivatives, line, surface and
volume integrals, Stokes, Gauss and Green's theorems (without proofs)
applications.

**Ordinary Differential Equations:** First order
equation (linear and nonlinear), Second order linear differential
equations with variable coefficients, Variation of parameters method,
higher order linear differential equations with constant coefficients,
Cauchy- Euler's equations, power series solutions, Legendre polynomials
and Bessel's functions of the first kind and their properties.

**Partial Differential Equations:** Separation of variables method, Laplace equation, solutions of one dimensional heat and wave equations.

**Probability and Statistics:** Definitions of
probability and simple theorems, conditional probability, Bayes
Theorem, random variables, discrete and continuous distributions,
Binomial, Poisson, and normal distributions, correlation and linear
regression.

**Numerical Methods:** Solution of a system of
linear equations by L-U decomposition, Gauss-Jordan and Gauss-Seidel
Methods, Newton?s interpolation formulae, Solution of a polynomial and
a transcendental equation by Newton-Raphson method, numerical
integration by trapezoidal rule, Simpson?s rule and Gaussian
quadrature, numerical solutions of first order differential equation by
Euler?s method and 4th order Runge-Kutta method.

### SECTION B: FLUID MECHANICS

**Fluid Properties:** Relation between stress and strain rate for Newtonian fluids.

**Hydrostatics:** Buoyancy, manometry, forces on submerged bodies.

Eulerian and Lagrangian description of fluid motion,
concept of local and convective accelerations, steady and unsteady
flows, control volume analysis for mass, momentum and energy.

Differential equations of mass and momentum (Euler equation), Bernoulli?s equation and its applications.

Concept of fluid rotation, vorticity, stream function and potential function.

**Potential flow:** elementary flow fields and principle of superposition, potential flow past a circular cylinder.

**Dimensional analysis:** Concept of geometric, kinematic and dynamic similarity, importance of non-dimensional numbers.

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

Qualitative ideas of boundary layer and separation, streamlined and bluff bodies, drag and lift forces.

Basic ideas of flow measurement using venturimeter, pitot-static tube and orifice plate.

### SECTION C: MATERIALS SCIENCE

**Structure:** Atomic structure and bonding in materials. Crystal
structure of materials, crystal systems, unit cells and space lattices,
determination of structures of simple crystals by x-ray diffraction,
miller indices of planes and directions, packing geometry in metallic,
ionic and covalent solids. Concept of amorphous, single and
polycrystalline structures and their effect on properties of materials.
Crystal growth techniques. Imperfections in crystalline solids and
their role in influencing various properties.

**Diffusion:** Fick's laws and application of diffusion in
sintering, doping of semiconductors and surface hardening of metals.
Metals and Alloys: Solid solutions, solubility limit, phase rule,
binary phase diagrams, intermediate phases, intermetallic compounds,
iron-iron carbide phase diagram, heat treatment of steels, cold, hot
working of metals, recovery, recrystallization and grain growth.
Microstrcture, properties and applications of ferrous and non-ferrous
alloys.

**Ceramics:** Structure, properties, processing and applications of traditional and advanced ceramics.

**Polymers:** Classification, polymerization, structure and properties, additives for polymer products, processing and applications.

**Composites:** Properties and applications of various composites.

**Advanced Materials and Tools:** Smart materials, exhibiting
ferroelectric, piezoelectric, optoelectric, semiconducting behavior,
lasers and optical fibers, photoconductivity and superconductivity,
nanomaterials - synthesis, properties and applications, biomaterials,
superalloys, shape memory alloys. Materials characterization techniques
such as, scanning electron microscopy, transmission electron
microscopy, atomic force microscopy, scanning tunneling microscopy,
atomic absorption spectroscopy, differential scanning calorimetry.

**Mechanical Properties:** stress-strain diagrams of metallic,
ceramic and polymeric materials, modulus of elasticity, yield strength,
tensile strength, toughness, elongation, plastic deformation,
viscoelasticity, hardness, impact strength, creep, fatigue, ductile and
brittle fracture.

**Thermal Properties:** Heat capacity, thermal conductivity, thermal expansion of materials.

**Electronic Properties:** Concept of energy band diagram for
materials - conductors, semiconductors and insulators, electrical
conductivity - effect of temperature on conductility, intrinsic and
extrinsic semiconductors, dielectric properties.

**Optical Properties:** Reflection, refraction, absorption and transmission of electromagnetic radiation in solids.

**Magnetic Properties:** Origin of magnetism in metallic and ceramic
materials, paramagnetism, diamagnetism, antiferro magnetism,
ferromagnetism, ferrimagnetism, magnetic hysterisis.

**Environmental Degradation:** Corrosion and oxidation of materials, prevention.

### SECTION D: SOLID MECHANICS

Equivalent force systems; free-body diagrams;
equilibrium equations; analysis of determinate trusses and frames;
friction; simple relative motion of particles; force as function of
position, time and speed; force acting on a body in motion; laws of
motion; law of conservation of energy; law of conservation of momentum.
Stresses and strains; principal stresses and strains; Mohr's circle;
generalized Hooke's Law; thermal strain; theories of failure. Axial,
shear and bending moment diagrams; axial, shear and bending stresses;
deflection (for symmetric bending); torsion in circular shafts; thin
cylinders; energy methods (Castigliano's Theorems); Euler buckling.

Free vibration of single degree of freedom systems.

### SECTION E: THERMODYNAMICS

**Basic Concepts:** Continuum, macroscopic
approach, thermodynamic system (closed and open or control volume);
thermodynamic properties and equilibrium; state of a system, state
diagram, path and process; different modes of work; Zeroth law of
thermodynamics; concept of temperature; heat.

**First Law of Thermodynamics:** Energy, enthalpy, specific heats, first law applied to systems and control volumes, steady and unsteady flow analysis.

**Second Law of Thermodynamics:** Kelvin-Planck
and Clausius statements, reversible and irreversible processes, Carnot
theorems, thermodynamic temperature scale, Clausius inequality and
concept of entropy, principle of increase of entropy; availability and
irreversibility.

**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, equations of state,
compressibility chart.

**Thermodynamic Relations:** T-ds relations,
Maxwell equations, Joule-Thomson coefficient, coefficient of volume
expansion, adiabatic and isothermal compressibilities, Clapeyron
equation.

**Thermodynamic cycles:** Carnot vapor power
cycle, Ideal Rankine cycle, Rankine Reheat cycle, Air standard Otto
cycle, Air standard Diesel cycle, Air-standard Brayton cycle,
Vapor-compression refrigeration cycle.

**Ideal Gas Mixtures:** Dalton's and Amagat?s
laws, calculations of properties, air-water vapor mixtures and simple
thermodynamic processes involving them.

### SECTION F: POLYMER SCIENCE AND ENGINEERING

**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.

**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.

**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.

**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.

**Polymer Technology:** Polymer compounding-need
and significance, different compounding ingredients for rubber and
plastics, crosslinking and vulcanization, vulcanization kinetics.

**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.
viscoelasticity-creep and stress relaxations, mechanical models,
control of rheological characteristics through compounding, rubber
curing in parallel plate viscometer, ODR and MDR.

**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.

**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.

### SECTION G: FOOD TECHNOLOGY

**Food Chemistry and Nutrition:**
Carbohydrates: Structure and functional properties of mono-
oligo-polysaccharides including starch, cellulose, pectic substances
and dietary fibre; Proteins: Classification and structure of proteins
in food; Lipids: Classification and structure of lipids, Rancidity of
fats, Polymerization and polymorphism; Pigments: Carotenoids,
chlorophylls, anthocyanins, tannins and myoglobin; Food flavours:
Terpenes, esters, ketones and quinones; Enzymes: Specificity, Kinetics
and inhibition, Coenzymes, Enzymatic and non-enzymatic browning;
Nutrition: Balanced diet, Essential amino acids and fatty acids, PER,
Water soluble and fat soluble vitamins, Role of minerals in nutrition,
Antinutrients, Nutrition deficiency diseases.

**Food Microbiology:**
Characteristics of microorganisms: Morphology, structure and detection
of bacteria, yeast and mold in food, Spores and vegetative cells;
Microbial growth in food: Intrinsic and extrinsic factors, Growth and
death kinetics, serial dilution method for quantification; Food
spoilage: Contributing factors, Spoilage bacteria, Microbial spoilage
of milk and milk products, meat and meat products; Foodborne disease:
Toxins produced by Staphylococcus, Clostridium and Aspergillus;
Bacterial pathogens: Salmonella, Bacillus, Listeria, Escherichia coli,
Shigella, Campylobacter; Fermented food: Buttermilk, yoghurt, cheese,
sausage, alcoholic beverage, vinegar, sauerkraut and soya sauce.

**Food Products Technology:**
Processing principles: Canning, chilling, freezing, dehydration,
control of water activity, CA and MA storage, fermentation, hurdle
technology, addition of preservatives and food additives, Food
packaging, cleaning in place and food laws.; Grain products processing:
Milling of rice, wheat, and maize, parboiling of paddy, production of
bread, biscuits, extruded products and breakfast cereals, Solvent
extraction, refining and hydrogenation of oil; Fruits, vegetables and
plantation products processing: Extraction, clarification concentration
and packaging of fruit juice, Production of jam, jelly, marmalade,
squash, candies, and pickles, pectin from fruit waste, tea, coffee,
chocolate and essential oils from spices; Milk and milk products
processing: Pasteurized and sterilized milk, cream, butter, ghee,
ice-cream, cheese and milk powder; Animal products processing: Drying
and canning of fish, post mortem changes, tenderization and freezing of
meat, egg powder.

**Food Engineering:** Mass and energy balance;
Momentum transfer: Flow rate and pressure drop relationships for
Newtonian fluids flowing through pipe, Characteristics of non-Newtonian
fluids - generalized viscosity coefficient and Reynolds number, Flow of
compressible fluid, Flow measurement, Pumps and compressors; Heat
transfer: Heat transfer by conduction, convection, radiation, boiling
and condensation, Unsteady state heat transfer in simple geometry, NTU-
effectiveness relationship of co-current and counter current double
pipe heat exchanger; Mass transfer: Molecular diffusion and Ficks Law,
Steady state mass transfer, Convective mass transfer, Permeability of
films and laminates; Mechanical operations: Energy requirement and rate
of operations involved in size reduction of solids, high pressure
homogenization, filtration, centrifugation, settling, sieving, flow
through porous bed, agitation of liquid, solid-solid mixing, and single
screw extrusion; Thermal operations: Energy requirement and rate of
operations involved in process time evaluation in batch and continuous
sterilization, evaporation of liquid foods, hot air drying of solids,
spray and freeze-drying, freezing and crystallization; Mass transfer
operations: Properties of air-water vapor mixture; Humidification and
dehumidification operations.