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# GATE 2020 Syllabus for Engineering Sciences (XE)

Last Updated - July 19th 2019

GATE syllabus is different for each discipline. The question paper consists of 65 questions which are divided into three sections worth 100 marks and the duration of the exam is three hours. The questions are mostly fundamental, concept based and thought-provoking. GATE 2020 is scheduled to take place in the month of February i.e. 01, 02, 08 and 09 February 2020.

GATE Engineering Sciences (XE)syllabus comprises 3 sections namely- General Aptitude, Engineering Mathematics and Engineering Sciences. The weightage of General Aptitude and Engineering Mathematics is 30% and rest 70% is reserved for the chosen specialization i.e. XE in this case.

• GATE Syllabus for Engineering Sciences mostly covers the graduation level topics.
• Engineering sciences section comprises the following subjects:
1. Engineering Mathematics
2. Fluid mechanics
3. Polymer Science and Engineering
4. Solid mechanics
5. Material Science
6. Thermodynamics
7. Food technology
8. Atmospheric and Oceanic Sciences
• Participants have to choose any 2 of the above-mentioned subjects.
• Each subject (chosen ones) will carry 35 marks.

GATE is a national level exam which is held for admission to M.Tech/ Ph.D. in the field of engineering and technology. It is conducted on a rotational basis by zonal IITs and IISc Bangalore. To ace GATE 2020, one must have a clear about GATE Exam Pattern and syllabus. Candidates can check engineering sciences section syllabus in this article.

### Engineering Mathematics (Compulsory)

Engineering Mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. It is an interdisciplinary subject motivated by engineers' needs both for practical, theoretical and other considerations out with their specialization, and to deal with constraints to be effective in their work.

TopicsSub Topics
Linear AlgebraAlgebra 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.
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.

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.

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

Ordinary Differential EquationsFirst 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.
Partial Differential EquationsClassification of second order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one dimensional heat and wave equations.
Probability and StatisticsAxioms of probability; Conditional probability; Bayes' Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.
Numerical MethodsSolution 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.

#### Engineering Mathematics Important Books

Book NameAuthorISBN Number
GATE Engineering MathematicsAbhinav Goel, Suraj Singh935203550X, 978-9352035502
Higher Engineering MathematicsB.S. Grewal8174091955, 978-8174091956
GATE 2017: Engineering MathematicsME Team9351471977, 978-9351471974
A Textbook of Engineering MathematicsDr. Sudheer K. Srivastava, Dr. Suyash N. Mishra Dr. Vijai S. Verma9383758465, 978-9383758463
Wiley Acing the Gate: Engineering Mathematics and General AptitudeAnil K. Maini, Varsha Agrawal, Nakul Maini8126567430, 978-8126567430

### Fluid Mechanics

Fluid Mechanics is a branch of physics concerned with the mechanics of fluids and the forces on them. Fluid mechanics has a wide range of applications, including mechanical engineering, civil engineering, chemical engineering, biomedical engineering, geophysics, astrophysics, and biology.

TopicsSub Topics
Flow and Fluid PropertiesViscosity, relationship between stress and strain-rate for Newtonian fluids, incompressible and compressible flows, differences between laminar and turbulent flows. Hydrostatics:Buoyancy, manometry, forces on submerged bodies.

KinematicsEulerian and Lagrangian description of fluids motion, concept of local and convective accelerations, steady and unsteady flows.
Integral analysisControl volume analysis for mass, momentum and energy.
Differential AnalysisDifferential 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.
Inviscid flowsBernoulli’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.
Dimensional analysisConcept of geometric, kinematic and dynamic similarity, some common non-dimensional parameters and their physical significance: Reynolds number, Froude number and Mach number.
Internal flowsFully developed pipe flow, empirical relations for laminar and turbulent flows: friction factor and Darcy-Weisbach relation.
Prandtl boundary layer equationsConcept 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.

#### Fluid Mechanics Important Books

Book NameAuthor
Fluid Mechanics: Fundamentals and ApplicationsYunus A. Cengel, John Cimbala
A Textbook of Fluid Mechanics and Hydraulic MachinesR.K. Bansal
A Textbook of Fluid MechanicsR.K. Bansal
Fundamentals of fluid mechanicsBruce Roy Munson
An Introduction to Fluid DynamicsGeorge Batchelor

### Materials Science

The interdisciplinary field of materials science, also commonly termed materials science and engineering, involves the discovery and design of new materials, with an emphasis on solids.

TopicsSub Topics
StructureAtomic 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.
DiffusionFick’s laws and application of diffusion in sintering, doping of semiconductors and surface hardening of metals.
Metals and AlloysSolid 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.
PolymersClassification, polymerization, structure and properties, additives for polymer products, processing and applications.
CompositesProperties and applications of various composites.
Advanced Materials and ToolsSmart 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 Propertiesstress-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 PropertiesHeat capacity, thermal conductivity, thermal expansion of materials.
Electronic PropertiesConcept of energy band diagram for materials – conductors, semiconductors and insulators, electrical conductivity – effect of temperature on conductility, intrinsic and extrinsic semiconductors, dielectric properties.
Optical PropertiesReflection, refraction, absorption and transmission of electromagnetic radiation in solids.
Magnetic PropertiesOrigin of magnetism in metallic and ceramic materials, paramagnetism, diamagnetism, antiferro magnetism, ferromagnetism, ferrimagnetism, magnetic hysterisis.
Environmental DegradationCorrosion and oxidation of materials, prevention.

#### Material Science Important Books

Book NameAuthorISBN Number
Material Science and EngineeringWilliam F. Smith, Javad Hashemi, Ravi Prakash1259062759, 978-1259062759
Materials Science and Engineering - SIEWilliam Smith, Javad Hashemi, Ravi Prakash0070667179, 978-0070667174
Materials Science and EngineeringI P Singh8183600956, 978-8183600958
Materials ScienceSedha R.S.8121901464, 978-8121901468
Basics of Material Science and EngineeringMade Easy Editorial Board9351472078, 978-9351472070

### Solid Mechanics

Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics such as materials science.

TopicsSub Topics
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.

#### Solid Mechanics Important Books

Book NameAuthorISBN Number
Fundamentals of Solid Mechanics: A Treatise on Strength of MaterialsGambhir M.L8120338707, 978-8120338708
Solid Mechanics: Theory, Modeling, and ProblemsAlbrecht Bertram, Rainer Glüge3319360035, 978-3319360034
Strength of Materials (Mechanics of Solids)R.K. Rajput9350144786, 978-9350144787

### Thermodynamics

Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. It applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering.

TopicsSub Topics
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 ThermodynamicsEnergy, enthalpy, specific heats, first law applied to systems and control volumes, steady and unsteady flow analysis.
Second Law of ThermodynamicsKelvin-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 SubstancesThermodynamic 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 RelationsT-ds relations, Maxwell equations, Joule-Thomson coefficient, coefficient of volume expansion, adiabatic and isothermal compressibilities, Clapeyron equation.
Thermodynamic cyclesCarnot vapor power cycle, Ideal Rankine cycle, Rankine Reheat cycle, Air standard Otto cycle, Air standard Diesel cycle, Air-standard Brayton cycle, Vaporcompression refrigeration cycle.
Ideal Gas MixturesDalton’s and Amagat’s laws, calculations of properties, air-water vapor mixtures and simple thermodynamic processes involving them.

#### Thermodynamics Important Books

Book NameAuthorISBN Number
Heat and ThermodynamicsAnandamoy Manna8131754006, 978-8131754009
ThermodynamicsSingh Kumar Ashok9383137967, 978-9383137961
Thermodynamics and An Introduction to ThermostatisticsHerbert B Callen8126508124, 978-8126508129
Engineering ThermodynamicsGupta S.K.8121942705, 978-8121942706

### Polymer Science and Engineering

Polymer science or macromolecular science is a subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics and elastomers. The field of polymer science includes researchers in multiple disciplines including chemistry, physics, and engineering.

TopicsSub Topics
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 CharacterizationSolubility 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 propertiesCommodity 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 compositesDifference 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, rubberplastic and rubber-rubber blends, FRP, particulate, long and short fibre reinforced composites.
Polymer TechnologyPolymer compounding-need and significance, different compounding ingredients for rubber and plastics, crosslinking and vulcanization, vulcanization kinetics.
Polymer rheologyFlow 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 processingCompression 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 testingMechanical-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.

#### Polymer Science and Engineering Important Books

Book NameAuthorISBN Number
Textbook of Polymer ScienceFred W. Billmeyer8126511109, 978-8126511105
Specialty Polymers: Materials and ApplicationsFaiz Mohammad8188237655, 978-8188237654
The Elements of Polymer Science and EngineeringAlfred Rudin Phillip Choi9780123821782, 0123821789
Introduction To Polymer Science And TechnologyN. B. Singh8122430074

### Food Technology

Food technology is a branch of food science that deals with the production processes that make foods.

TopicsSub Topics
Food Chemistry and NutritionCarbohydrates: Structure and functional properties of monooligo-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 MicrobiologyCharacteristics 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 TechnologyProcessing 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 EngineeringMass 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, NTUeffectiveness relationship of co-current and counter current double pipe heat exchanger; Mass transfer: Molecular diffusion and Fick’s 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.

#### Food Technology Important Books

Book NameAuthorISBN Number
Training Manual for Food and Beverage ServicesMahendra Singh Negi9385909185, 978-9385909184
Food ScienceB Srilakshmi8122438091, 978-8122438093
Question Bank on food Science and TechnologyU D Chavan8170358825, 978-8170358824
Foods Facts and PrinciplesN. Shakuntala Mana8122422152, 978-8122422153

### Syllabus Of Other Papers

PaperCodePaperCode
Aerospace EngineeringAEEvolution and EcologyEY
Agricultural EngineeringAGGeology and GeophysicsGG
Architecture and PlanningARInstrumentation EngineeringIN
BiotechnologyBTMetallurgical EngineeringMT
Civil EngineeringCEMechanical EngineeringME
Chemical EngineeringCHMining EngineeringMN
Computer Science and Information TechnologyCSPetroleum EngineeringPE
ChemistryCYProduction and Industrial EngineeringPI
Electronics and CommunicationECTextile Engineering and Fibre ScienceTF
Electrical EngineeringEEPhysicsPH
MathematicsMA--

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