GATE 2015 Engineering Science Syllabus:
(a)Engineering Mathematics (Compulsory):
Linear Algebra: Matrices and Determinants; Systems of linear equations; Eigen Values and eigen vectors
Calculus: Limit; Continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes Gauss and Green’s theorems
Differential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs – Laplace, heat and wave equations
Probability and Statistics: Mean, Median, Mode and standard deviation; Random variables; Poisson; normal and binomial distributions; Correlation and regression analysis.
Numerical Methods: Solutions of system of linear equations by L-U decomposition, Gauss-Jordan and Gauss-Jordan and Gauss-Seidel Methods, Newton 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 equations by Euler’s method and 4th order Runge-Kutta method.
Section B: Fluid Mechanics:
Fluid Properties: Relations 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 functional
Potential flow: elementary flow fields and principles 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, pilot-static 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: Solids solutions; solubility limit; phase rule; binary diagrams; intermediate phases; intermediate compounds; iron iron carbide phase diagram; heat treatment of steels; cold; hot working of metals; recovery; re crystallization and grain growth. Micro structure, 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 Material and Tools: Smart materials, exhibiting ferroelectric, piezoelectric; optoelectric; semiconducting behavior; lasers and optical fibres; photoconductivity and superconductivity; nanomaterials- synthesis; properties and applications; bio materials; super alloys; shapes memory alloys. Material characterization techniques such as scanning electron microscopy; transmission electron microscopy; atomic force microscopy; scanning tunneling microscopy; atomic absorption spectroscopy; differentia scanning calorimetry.
Mechanical Properties: stress-strain diagram for materials – conductors; semiconductors and insulators; electrical conductivity- effect of temperature on conductivity; 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 the 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.
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 equilibrim; 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 entropy; availability and irreversibility
Properties of Pure substances: Thermodynamics properties of pure substances in solids, liquid and vapour phases, P-V-T behavior of simple compressible substances; phase rule; thermodynamic property tables and charts, ideal and real gases, equation of state, compressibility chart.
Thermodynamic cycles: Carnot vapor power cycle; Ideal Rankine cycle; Rankine Reheat cycle; Air standard Otto Cycle, air Diesel cycle; Air-standard Brayton cycle; Vapor-compression refrigeration cycles.
Ideal Gas Mixtures: Dalton’s and Amagat’s laws; calculation of properties; air-water vapor mixtures and simple thermodynamics processes involving them.
Section F: Polymer Science and Engineering:
Chemistry of high polymer: Monomers; functionality; degree of polymerizations; classifications 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 form 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 transistions. 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; rubbing curing in parallel plate viscometer; ODR and MDR.
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 Flavors: Terpenes, esters, ketone and quinines:
Enzymes: Specificity; Kinetics and inhibition; Coenzymes; Enzymatic and non-enzymatic browing; Nutrition: Balanced diet; Essential amino acids and fatty acids, PER, Water soluble and fate soluble vitamins; Role of minerals in nutrition; Antinutrients; Nutrition deficiency diseases.
Food Microbiology: Characteristics of mircrorganisms: 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 diseases: Toxins produced by Staphylococcus; Clostridium and Aspergillus; Bacteria pathogens: Salmonella, Bacillus, Listeria, Escherichia coli; Shigella; Campylobacter; Fermented food: Buttermilk, Yogurt, 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, marmalade, squash, candies, and pickles, pectim 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 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 continous sterilization; evaporation of liquid foods, hot air drying in solids; spray and freeze drying, freezing and crystallization; mass transfer operations: Properties of air water vapour mixture; Humidification and dehumidification operations.