GATE 2014 Syllabus Download for all Branches

GATE 2014 Syllabus will be available in this page after official announcement of GATE 2014 Syllabus from the GATE 2014 organizing institute until you may refer these GATE Exam 2013 Syllabus Since few thing in some exams won’t change frequently like syllabus, marking system and rules, that why you can refer GATE Exam Syllabus. The reason for this post is to help students with gate syllabus 2013 and notify the changes, if any, given by the GATE 2014 organizing institute. We will update this post if there are changes declared by the organizing institute. As of now there is no news of any change. If we look into GATE organizing institutes we can easily figure out which institute is going to organize GATE 2014. A constant pattern is followed by the institutes to conduct GATE exam and following that pattern, if nothing strange happen, IIT Bombay conducted the GATE 2013. The GATE 2014 syllabus is available for all branches including major GATE branches like ECE, CSE, IT, EEE, ME, CE and CH. As requested by many of the GATE 2014 aspirants, we are trying to provide you the syllabus in pdf format for free download. We hope you all are enjoy our site.

GATE 2014 Syllabus for Aerospace Engineering – AE Syllabus

GATE Paper Code for Aerospace Engineering is AE and the GATE AE syllabus summery is ENGINEERING MATHEMATICS :  Linear Algebra,  Calculus,  Differential Equations,    Numerical methods, FLIGHT MECHANICS:  Atmosphere,  Airplane performance,  Static stability, Dynamic stability, SPACE DYNAMICS,  AERODYNAMICS: Basic Fluid Mechanics,  Airfoils and wings,  Viscous Flows, Compressible Flows, Wind Tunnel Testing, STRUCTURES:  Stress and Strain, Flight Vehicle Structures,  Structural Dynamics, PROPULSION: Turbomachinery,  Aerothermodynamics of non rotating propulsion components. Detailed GATE 2014 Aerospace Engineering Syllabus

GATE 2014 Syllabus for Agricultural Engineering – AG Syllabus

GATE Paper Code for Aerospace Engineering is AG and the GATE AG syllabus summery is ENGINEERING MATHEMATICS:  Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical methods, FARM MACHINERY AND POWER: SOIL AND WATER CONSERVATION ENGINEERING: AGRICULTURAL PROCESSING AND FOOD ENGINEERING. Detailed GATE 2014 Agricultural Engineering Syllabus

GATE 2014 Syllabus for Architecture and Planning – AR Syllabus

GATE Paper Code for Architecture and Planning is AR and the GATE AR syllabus summery is City planning, Housing, Landscape Design, Computer Aided Design, Environmental Studies in Building Science, Visual and Urban Design, History of Architecture, Development of Contemporary Architecture, Building Services, Building Construction and Management, Materials and Structural Systems, Planning Theory, Techniques of Planning, Traffic and Transportation Planning, Infrastructure, Services and Amenities, Development Administration and Management. Detailed GATE 2014 Architecture and Planning Syllabus

GATE 2014 Syllabus for Biotechnology – BT Syllabus

GATE Paper Code for Biotechnology is BT and the GATE BT syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra,  Calculus,  Differential Equations,  Probability and Statistics,  Numerical Methods,  BIOTECHNOLOGY: Microbiology,  Biochemistry,  Molecular Biology and Genetics,  Process Biotechnology,  Bioprocess Engineering,  Plant and Animal Biotechnology,  Characteristics of animal cells,  Immunology,  Recombinant DNA Technology,  Bioinformatics. Detailed GATE 2014 Biotechnology Syllabus

GATE 2014 Syllabus for Civil Engineering – CE Syllabus

GATE Paper Code for Civil Engineering is CE and the GATE CE syllabus summery is  ENGINEERING MATHEMATICS: Linear Algebra,  Calculus,  Differential equations,  Complex variables,  Probability and Statistics,  Numerical Methods,  STRUCTURAL ENGINEERING: Mechanics,  Structural Analysis,  Concrete Structures,  Steel Structures,  GEOTECHNICAL ENGINEERING: Soil Mechanics,  Foundation Engineering,  WATER RESOURCES ENGINEERING: Fluid Mechanics and Hydraulics,  Hydrology,  Irrigation,  ENVIRONMENTAL ENGINEERING: Water requirements,  Air Pollution,  Municipal Solid Wastes,  Noise Pollution,  TRANSPORTATION ENGINEERING: Highway Planning,  Traffic Engineering,  SURVEYING. Detailed GATE 2014 Civil Engineering Syllabus

GATE 2014 Syllabus for Chemical Engineering – CH Syllabus

GATE Paper Code for Chemical Engineering is CH and the GATE CH syllabus summery is  ENGINEERING MATHEMATICS: Linear Algebra,  Calculus,  Differential equations,  Complex variables,  Probability and Statistics,  Numerical Methods,  CHEMICAL ENGINEERING: Process Calculations and Thermodynamics,  Fluid Mechanics and Mechanical Operations,  Heat Transfer,  Mass Transfer,  Chemical Reaction Engineering,  Instrumentation and Process Control,  Plant Design and Economics,  Chemical Technology.  Detailed GATE 2014 Chemical Engineering Syllabus

GATE 2014 Syllabus for Computer Science – CS Syllabus

GATE Paper Code for Computer Science Engineering is CS and the GATE CS syllabus summery is  ENGINEERING MATHEMATICS: Mathematical Logic,  Probability,  Set Theory & Algebra,  Combinatorics, Graph Theory,  Linear Algebra, Numerical Methods, Calculus,  COMPUTER SCIENCE AND INFORMATION TECHNOLOGY: Digital Logic,  Computer Organization and Architecture,  Programming and Data Structures,  Algorithms,  Theory of Computation,  Compiler Design,  Operating System,  Databases,  Information Systems and Software Engineering,  Computer Networks,  Web technologies. Detailed GATE 2014 Computer Science Syllabus

GATE 2014 Syllabus for Information Technology

GATE Information Technology syllabus is same as  GATE Computer Science Engineering syllabus. So IT students have to appear GATE CS paper.

GATE 2014 Syllabus for Chemistry – CY Syllabus

GATE Paper Code for Chemistry Engineering is CY and the GATE CY syllabus summery is PHYSICAL CHEMISTRY: Structure, Equilibrium, Kinetics, INORGANIC CHEMISTRY:  Main group elements, Transition Elements, Solids: Instrumental methods of analysis, ORGANIC CHEMISTRY: Stereochemistry, Reaction mechanism, Organic synthesis, Pericyclic reactions, Photochemistry, Heterocyclic compounds, Biomolecules, Spectroscopy. Detailed GATE 2014 Chemistry Syllabus

GATE 2014 Syllabus for Electronics and Communication – EC Syllabus

GATE Paper Code for Electronics and Communication Engineering is EC and the GATE EC syllabus summery is  ENGINEERING MATHEMATICS: Linear Algebra,  Calculus,  Differential equations,  Complex variables, Probability and Statistics,  Numerical Methods, Transform Theory, ELECTRONICS AND COMMUNICATION ENGINEERING: Networks, Electronic Devices, Analog Circuits, Digital circuits, Signals and Systems, Control Systems, Communications, Electromagnetics. Detailed GATE 2014 Electronics and Communication Syllabus

GATE 2014 Syllabus for Electrical Engineering – EE Syllabus

GATE Paper Code for Electrical Engineering is EE and the GATE EE syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra,  Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods Transform Theory, ELECTRICAL ENGINEERING: Electric Circuits and Fields, Signals and Systems, Electrical Machines, Power Systems, Control Systems, Electrical and Electronic Measurements, Analog and Digital Electronics, Power Electronics and Drives. Detailed GATE 2014 Electrical Engineering Syllabus

GATE 2014 Syllabus for Geology and Geophysics – GG Syllabus

GATE Paper Code for Geology and Geophysics is GG and the Detailed GATE 2014 Geology and Geophysics Syllabus

GATE 2014 Syllabus for Instrumentation Engineering – IN Syllabus

GATE Paper Code for Instrumentation Engineering is IN and the GATE IN syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, Transform Theory, INSTRUMENTATION ENGINEERING: Basics of Circuits and Measurement Systems, Transducers, Mechanical Measurement and Industrial Instrumentation, Analog Electronics, Digital Electronics, Signals, Systems and Communications, Electrical and Electronic Measurements, Control Systems and Process Control, Analytical, Optical and Biomedical Instrumentation. Detailed GATE 2014 Instrumentation Engineering Syllabus

GATE 2014 Syllabus for Mathematics – MA Syllabus

GATE Paper Code for Mathematics is MA and the GATE MA syllabus summery is Linear Algebra, Complex Analysis, Real Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Mechanics, Topology, Probability and Statistics, Linear programming, Calculus of Variation and Integral Equations. Detailed GATE 2014 Mathematics Syllabus

GATE 2014 Syllabus for Mechanical Engineering – ME Syllabus

GATE Paper Code for Mechanical Engineering is ME and the GATE ME syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, APPLIED MECHANICS AND DESIGN: Engineering Mechanics: Strength of Materials, Theory of Machines, Vibrations, Design, FLUID MECHANICS AND THERMAL SCIENCES: Fluid Mechanics, Heat-Transfer, Thermodynamics, Applications, MANUFACTURING AND INDUSTRIAL ENGINEERING: Engineering Materials, Metal Casting, Forming, Joining, Machining and Machine Tool Operations, Metrology and Inspection, Computer Integrated Manufacturing, Production Planning and Control, Inventory Control, Operations Research. Detailed GATE 2014 Mechanical Engineering Syllabus

GATE 2014 Syllabus for Mining Engineering – MN Syllabus

GATE Paper Code for Mining Engineering is MN and the GATE MN syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical Methods, MINING ENGINEERING: Mechanics, Mine Development, Geomechanics and Ground Control, Mining Methods and Machinery, Ventilation, Underground Hazards and Surface Environment, Surveying, Mine Planning and Systems Engineering, Principles of planning. Detailed GATE 2014 Mining Engineering Syllabus

GATE 2014 Syllabus for Metallurgical Engineering – MT Syllabus

GATE Paper Code for Metallurgical Engineering is MT and the GATE MT syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical Methods, METALLURGICAL ENGINEERING: Thermodynamics and Rate Processes, Extractive Metallurgy, Physical Metallurgy, Mechanical Metallurgy, Manufacturing Processes. Detailed GATE 2014 Metallurgical Engineering Syllabus

GATE 2014 Syllabus for Physics – PH Syllabus

GATE Paper Code for Physics is PH and the GATE PH syllabus summery is Mathematical Physics, Classical Mechanics, Electromagnetic Theory, Quantum Mechanics, Thermodynamics and Statistical Physics, Atomic and Molecular Physics, Solid State Physics, Nuclear and Particle Physics: Electronics. Detailed GATE 2014 Physics Syllabus

GATE 2014 Syllabus for Production and Industrial Engineering  – PI Syllabus

GATE Paper Code for Production and Industrial Engineering is PI and the GATE PI syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, GENERAL ENGINEERING: Engineering Materials, Applied Mechanics, Theory of Machines and Design, Thermal Engineering, PRODUCTION ENGINEERING: Metal Casting, Metal Forming, Metal Joining Processes, Machining and Machine Tool Operations, Tool Engineering, Metrology and Inspection, Powder Metallurgy, Polymers and Composites, Manufacturing Analysis, Computer Integrated Manufacturing, INDUSTRIAL ENGINEERING: Product Design and Development, Engineering Economy and Costing, Work System Design, Facility Design, Production Planning and Inventory Control, Operation Research, Quality Management, Reliability and Maintenance, Management Information System, Intellectual Property System. Detailed GATE 2014 Production and Industrial Engineering Syllabus

GATE 2014 Syllabus for Textile Engineering and Fibre Science – TF Syllabus

GATE Paper Code for Textile Engineering and Fibre Science is TF and the GATE TF syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical Methods, TEXTILE ENGINEERING AND FIBRE SCIENCE: Textile Fibres, Yarn manufacture and yarn structure and properties, Fabric manufacture and Fabric Structure, Textile Testing, Preparatory Processes, Dyeing, Printing, Finishing, Energy Conservation, Pollution. Detailed GATE 2014 Textile Engineering and Fibre Science Syllabus

GATE 2014 Syllabus for Engineering Sciences – XE Syllabus

Get day to day updates on GATE 2014 Exam

GATE Exam 2010 Syllabus

GTAE Aerospace Engineering Syllabus

GTAE Agricultural Engineering Syllabus

GTAE Architecture and Planning Syllabus

GTAE Biotechnology Syllabus

GTAE Civil Engineering Syllabus

GTAE Chemical Engineering Syllabus

GTAE Computer Science Syllabus

GTAE Information Technology Syllabus

GATE Chemistry Syllabus

GATE Electronics and Communication Syllabus

GATE Electrical Engineering Syllabus

GATE Geology and Geophysics Syllabus

GATE Instrumentation Engineering Syllabus

GATE Mathematics Syllabus

GATE Mechanical Engineering Syllabus

GATE Mining Engineering Syllabus

GATE Metallurgical Engineering Syllabus

GATE Physics Syllabus

GATE Production and Industrial Engineering Syllabus

GATE Textile Engineering and Fibre Science Syllabus

GATE Textile Engineering and Fibre Science Syllabus

GATE Paper Code for Textile Engineering and Fibre Science is TF and the GATE TF syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical Methods, TEXTILE ENGINEERING AND FIBRE SCIENCE: Textile Fibres, Yarn manufacture and yarn structure and properties, Fabric manufacture and Fabric Structure, Textile Testing, Preparatory Processes, Dyeing, Printing, Finishing, Energy Conservation, Pollution. Detailed syllabus for GATE 2013 Textile Engineering and Fibre Science is as follows

GATE 2013 Syllabus for Textile Engineering and Fibre Science (TF)

ENGINEERING MATHEMATICS

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.
Diferential 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 linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

TEXTILE ENGINEERING AND FIBRE SCIENCE

Textile Fibres: Classification of textile fibres; Essential requirements of fibre forming polymers; Gross and fine structure of natural fibres like cotton, wool and silk. Introduction to important bastfibres; properties and uses of natural and man-made fibres; physical and chemical methods of fibre and blend identification and blend analysis. Molecular architecture, amorphous and crystalline phases, glass transition, plasticization, crystallization, melting, factors affecting Tg and Tm; Process of viscose and acetate preparation. Polymerization of nylon-6, nylon-66, poly (ethylene terephthalate), polyacrylonitrile and polypropylene; Melt Spinning processes, characteristic features of PET, polyamide and polypropylene spinning; wet and dry spinning of viscose and acrylic fibres; post spinning operations such as drawing, heat setting, tow-to-top conversion and different texturing methods. Methods of investigating fibre structure e.g., Density, X-ray diffraction, birefringence, optical and electron microscopy, I.R. absorption, thermal methods (DSC, DMA/TMA, TGA); structure and morphology ofman-made fibres, mechanical properties of fibres, moisture sorption in fibres; fibre structure and property correlation.
Yarn manufacture and yarn structure & properties: Principles of opening, cleaning and mixing/blending of fibrous materials, working principle of modern opening and cleaning equipments; the technology of carding, carding of cotton and synthetic fibres; Drafting operation, roller and apron drafting principle, causes of mass irregularity introduced by drafting; roller arrangements in drafting systems; principles of cotton combing, combing cycle, mechanism and function, combing efficiency, lap preparation; recent developments in comber; Roving production, mechanism of bobbin building, roving twist; Principle of ring spinning, forces acting on yarn and traveler; ring & traveler designs; mechanism of cop formation, causes of end breakages; working principle of ring doubler and two for one twister, single and folded yarn twist, properties of double yarns, production of core spun yarn, compact spinning, principle of non conventional methods of yarn production such as rotor spinning, air jet spinning, wrap spinning, twist less spinning and friction spinning. Yarn contraction, yarn diameter, specific volume & packing coefficient; twist strength relationship in spun yarns; fibre configuration and orientation in yarn; cause of fibre migration and its estimation, irregularity index, properties of ring, rotor and air-jet yarns.
Fabric manufacture and Fabric Structure: Principles of cheese and cone winding processes and machines; random and precision winding; package faults and their remedies; yarn clearers and tensioners; different systems of yarn splicing; features of modern cone winding machines; different types of warping creels; features of modern beam and sectional warping machines; different sizing systems, sizing of spun and filament yarns, modern sizing machines; principles of pirn winding processes and machines; primary and secondary motions of loom, effect of their settings and timings on fabric formation, fabric appearance and weaving performance; dobby and jacquard shedding; mechanics of weft insertion with shuttle; warp and weft stop motions, warp protection, weft replenishment; functional principles of weft insertion systems of shuttle-less weaving machines, principles of multiphase and circular looms. Principles of weft and warp knitting; basic weft and warp knitted structures. Classification, production and areas of application of nonwoven fabrics.Basic woven fabric constructions and their derivatives; crepe, cord, terry, gauze, leno and double cloth constructions. Peirce’s equations for fabric geometry; elastica model of plain woven fabrics; thickness, cover and maximum sett of woven fabrics.
Textile Testing: Sampling techniques, sample size and sampling errors. Measurement of fibre length, fineness, crimp, strength and reflectance; measurement of cotton fibre maturity and trash content; HVI and AFIS for fibre testing. Measurement of yarn count, twist and hairiness; tensile testing of fibres, yarns and fabrics; evenness testing of slivers, rovings and yarns; testing equipment for measurement test methods of fabric properties like thickness, compressibility, air permeability, drape, crease recovery, tear strength, bursting strength and abrasion resistance. FAST and Kawabata instruments and systems for objective fabric evaluation.Statistical data analysis of experimental results.Correlation analysis, significance tests and analysis of variance; frequency distributions and control charts.
Preparatory Processes: Chemistry and practice of preparatory processes for cotton, wool and silk. Mercerization of cotton.Preparatory processes for nylon, polyester and acrylic and polyester/cotton blends.
Dyeing: Classification of dyes. Dyeing of cotton, wool, silk, polyester, nylon and acrylic with appropriate dye classes. Dyeing polyester/cotton and polyester/wool blends. Batchwise and continuous dyeing machines. Dyeing of cotton knitted fabrics and machines used. Dye fibre interaction. Introduction to thermodynamics and kinetics of dyeing.Methods for determination of wash, light and rubbing fastness.Evaluation of fastness properties with the help of grey scale.
Printing: Styles of printing. Printing thickeners including synthetic thickeners. Printing auxiliaries. Printing of cotton with reactive dyes. Printing of wool, silk, nylon with acid
and metal complex dyes. Printing of polyester with disperse dyes. Methods of dye fixation after printing. Resist and discharge printing of cotton, silk and polyester. Printing of polyester/cotton blends with disperse/reactive combination. Transfer printing of polyester. Developments in inkjet printing.
Finishing: Mechanical finishing of cotton. Stiff. Soft, wrinkle resistant, water repellent, flame retardant and enzyme (bio-polishing) finishing of cotton.Milling, decatizing and shrink resistant finishing of wool.Antistat finishing of synthetic fibre fabrics. Heat setting of polyester.
Energy Conservation: Minimum application techniques.
Pollution: Environment pollution during chemical processing of textiles. Treatment of textile effluents.

GATE Production and Industrial Engineering Syllabus

GATE Paper Code for Production and Industrial Engineering is PI and the GATE PI syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, GENERAL ENGINEERING: Engineering Materials, Applied Mechanics, Theory of Machines and Design, Thermal Engineering, PRODUCTION ENGINEERING: Metal Casting, Metal Forming, Metal Joining Processes, Machining and Machine Tool Operations, Tool Engineering, Metrology and Inspection, Powder Metallurgy, Polymers and Composites, Manufacturing Analysis, Computer Integrated Manufacturing, INDUSTRIAL ENGINEERING: Product Design and Development, Engineering Economy and Costing, Work System Design, Facility Design, Production Planning and Inventory Control, Operation Research, Quality Management, Reliability and Maintenance, Management Information System, Intellectual Property System. Detailed Syllabus for GATE Production and Industrial Engineering is as follows

GATE 2013 Syllabus for Production and Industrial Engineering (PI)

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
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.

GENERAL ENGINEERING

Engineering Materials: Structure and properties of engineering materials and their applications; effect of strain, strain rate and temperature on mechanical properties of metals and alloys; heat treatment of metals and alloys, its influence on mechanical properties.
Applied Mechanics: Engineering mechanics – equivalent force systems, free body concepts, equations of equilibrium; strength of materials – stress, strain and their relationship, Mohr’s circle, deflection of beams, bending and shear stress, Euler’s theory of columns.
Theory of Machines and Design: Analysis of planar mechanisms, cams and followers; governers and fly wheels; design of elements – failure theories; design of bolted, riveted and welded joints; design of shafts, keys, spur gears, belt drives, brakes and clutches.
Thermal Engineering: Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, equations of continuity and momentum; thermodynamics – zeroth, first and second law of thermodynamics, thermodynamic system and processes, calculation of work and heat for systems and control volumes; air standard cycles; basics of internal combustion engines and steam turbines; heat transfer – fundamentals of conduction, convection and radiation, heat exchangers.

PRODUCTION ENGINEERING

Metal Casting: Casting processes – types and applications; patterns – types and materials; allowances; moulds and cores – materials, making, and testing; casting techniques of cast iron, steels and nonferrous metals and alloys; solidification; design of casting, gating and risering; casting inspection, defects and remedies.
Metal Forming: Stress-strain relations in elastic and plastic deformation; concept of flow stress, deformation mechanisms; hot and cold working – forging, rolling, extrusion, wire and tube drawing; sheet metal working processes such as blanking, piercing, bending, deep drawing, coining and embossing; analysis of rolling, forging, extrusion and wire /rod drawing; metal working defects.
Metal Joining Processes: Welding processes – manual metal arc, MIG, TIG, plasma arc, submerged arc, electroslag, thermit, resistance, forge, friction, and explosive welding;other joining processes – soldering, brazing, braze welding; inspection of welded joints, defects and remedies; introduction to advanced welding processes – ultrasonic, electron beam, laser beam; thermal cutting.
Machining and Machine Tool Operations: Basic machine tools; machining processes-turning, drilling, boring, milling, shaping, planing, gear cutting, thread production, broaching, grinding, lapping, honing, super finishing; mechanics of machining – geometry of cutting tools, chip formation, cutting forces and power requirements, Merchant’s analysis; selection of machining parameters; tool materials, tool wear and tool life, economics of machining, thermal aspects of machining, cutting fluids, machinability; principles and applications of nontraditional machining processes – USM, AJM, WJM, EDM and Wire cut EDM, LBM, EBM, PAM, CHM, ECM.
Tool Engineering: Jigs and fixtures – principles, applications, and design; press tools – configuration, design of die and punch; principles of forging die design.
Metrology and Inspection: Limits, fits, and tolerances, interchangeability, selective assembly; linear and angular measurements by mechanical and optical methods, comparators; design of limit gauges; interferometry; measurement of straightness, flatness, roundness, squareness and symmetry; surface finish measurement; inspection of screw threads and gears; alignment testing of machine tools.
Powder Metallurgy: Production of metal powders, compaction and sintering.
Polymers and Composites: Introduction to polymers and composites; plastic processing – injection, compression and blow molding, extrusion, calendaring and thermoforming; molding of composites.
Manufacturing Analysis: Sources of errors in manufacturing; process capability; tolerance analysis in manufacturing and assembly; process planning; parameter selection and comparison of production alternatives; time and cost analysis; manufacturing technologies – strategies and selection.
Computer Integrated Manufacturing: Basic concepts of CAD,CAM, CAPP, cellular manufacturing, NC, CNC, DNC, Robotics, FMS, and CIM.

INDUSTRIAL ENGINEERING

Product Design and Development: Principles of good
product design, tolerance design; quality and cost considerations;product life cycle; standardization, simplification, diversification, value engineering and analysis, concurrent engineering.
Engineering Economy and Costing: Elementary cost accounting and methods of depreciation; break-even analysis, techniques for evaluation of capital investments, financial statements.
Work System Design: Taylor’s scientific management, Gilbreths’s contributions; productivity – concepts and measurements;methodstudy, micro-motion study, principles of motion economy; work measurement – stop watch time study, work sampling, standard data, PMTS; ergonomics; job evaluation, merit rating, incentive schemes, and wage administration; business process reengineering.
Facility Design: Facility location factors and evaluation of alternate locations; types of plant layout and their evaluation; computer aided layout design techniques; assembly line balancing; materials handling systems.
Production Planning and Inventory Control: Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; aggregate production planning; master production scheduling; MRP and MRP-II; order control and flow control; routing, scheduling and priority dispatching; push and pull production systems, concept of JIT manufacturing system; logistics, distribution, and supply chain management; Inventory – functions, costs, classifications, deterministic and probabilistic inventory models, quantity discount; perpetual and periodic inventory control systems.
Operation Research: Linear programming – problem formulation, simplex method, duality and sensitivity analysis; transportation and assignment models; network flow models, constrained optimization and Lagrange multipliers; simple queuing models; dynamic programming; simulation – manufacturing applications; PERT and CPM, time-cost trade-off, resource leveling.
Quality Management: Quality – concept and costs, quality circles, quality assurance; statistical quality control, acceptance sampling, zero defects, six sigma; total quality management; ISO 9000; design of experiments – Taguchi method.
Reliability and Maintenance: Reliability, availability and maintainability; distribution of failure and repair times; determination of MTBF and MTTR, reliability models; system reliability determination; preventive maintenance and replacement, total productive maintenance – concept and applications.
Management Information System: Value of information; information storage and retrieval system – database and data structures; knowledge based systems.
Intellectual Property System: Definition ofintellectual property, importance of IPR; TRIPS and its implications, patent, copyright, industrial design and trademark.

GATE Physics Syllabus

GATE Paper Code for Physics is PH and the GATE PH syllabus summery is Mathematical Physics, Classical Mechanics, Electromagnetic Theory, Quantum Mechanics, Thermodynamics and Statistical Physics, Atomic and Molecular Physics, Solid State Physics, Nuclear and Particle Physics: Electronics. Detailed syllabus for GATE Physics is as follows

GATE 2013 Syllabus for Physics (PH)

Mathematical Physics: Linear vector space; matrices; vector calculus; linear differential equations; elements of complex analysis; Laplace transforms, Fourier analysis, elementary ideas about tensors.
Classical Mechanics: Conservation laws; central forces, Kepler problem and planetary motion; collisions and scattering in laboratory and centre of mass frames; mechanics of system of particles; rigid body dynamics; moment of inertia tensor; noninertial frames and pseudo forces; variational principle; Lagrange’s and Hamilton’s formalisms; equation of motion, cyclic coordinates, Poisson bracket; periodic motion, small oscillations, normal modes; special theory of relativity – Lorentz transformations, relativistic kinematics, mass-energy equivalence.
Electromagnetic Theory: Solution of electrostatic and magnetostatic problems includingboundary value problems;dielectrics andconductors; Biot-Savart’s and Ampere’s laws; Faraday’s law; Maxwell’s equations; scalar and vector potentials; Coulomb and Lorentz gauges; Electromagnetic waves and their reflection, refraction, interference, diffraction and polarization. Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation from a moving charge.
Quantum Mechanics: Physical basis of quantum mechanics; uncertainty principle; Schrodinger equation; one, two and three dimensional potential problems; particle in a box, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and spin; addition of angular momenta; time independent perturbation theory; elementary scattering theory.
Thermodynamics and Statistical Physics: Laws of thermodynamics; macrostates and microstates; phase space; probability ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body radiation and Planck’s distribution law; Bose-Einstein condensation; first and second order phase transitions, critical point.
Atomic and Molecular Physics: Spectra of one- and many-electron atoms; LS and jj coupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; X-ray spectra; rotational and vibrational spectra of diatomic molecules; electronic transition in diatomic molecules, Franck-Condon principle; Raman effect; NMR and ESR; lasers.
Solid State Physics: Elements of crystallography; diffraction methods for structure determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors and insulators; transport properties; optical, dielectric and magnetic properties of solids; elements of superconductivity.
Nuclear and Particle Physics: Nuclear radii and charge distributions, nuclear binding energy, Electric and magnetic moments; nuclear models, liquid drop model – semi-empirical mass formula, Fermi gas model of nucleus, nuclear shell model; nuclear force and two nucleon problem; Alpha decay, Beta-decay, electromagnetic transitions in nuclei;Rutherford scattering,nuclear reactions, conservation laws; fission and fusion;particle accelerators and detectors; elementary particles, photons, baryons, mesons and leptons; quark model.
Electronics: Network analysis; semiconductor devices; Bipolar Junction Transistors, Field Effect Transistors, amplifier and oscillator circuits; operational amplifier, negative feedback circuits ,active filters and oscillators; rectifier circuits, regulated power supplies; basic digital logic circuits, sequential circuits, flip-flops, counters, registers, A/D and D/A conversion.

GATE Metallurgical Engineering Syllabus

GATE Paper Code for Metallurgical Engineering is MT and the GATE MT syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical Methods, METALLURGICAL ENGINEERING: Thermodynamics and Rate Processes, Extractive Metallurgy, Physical Metallurgy, Mechanical Metallurgy, Manufacturing Processes. Detailed syllabus for GATE Metallurgical Engineering is as follows

GATE 2013 Syllabus for Metallurgical Engineering (MT)

ENGINEERING MATHEMATICS

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.
Diferential 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 linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

METALLURGICAL ENGINEERING

Thermodynamics and Rate Processes: Laws of thermodynamics, activity, equilibrium constant, applications to metallurgical systems, solutions, phase equilibria, Ellingham and phase stability diagrams, thermodynamics of surfaces, interfaces and defects, adsorption and segregation; basic kinetic laws, order of reactions, rate constants and rate limiting steps; principles of electro chemistry- single electrode potential, electro-chemical cells and polarizations, aqueous corrosion and protection of metals, oxidation and high temperature corrosion – characterization and control; heat transfer – conduction, convection and heat transfer coefficient relations, radiation, mass transfer – diffusion and Fick’s laws, mass transfer coefficients; momentum transfer – concepts of viscosity, shell balances, Bernoulli’s equation, friction factors.
Extractive Metallurgy: Minerals of economic importance, comminution techniques, size classification, Flotation, gravity and other methods of mineral processing; agglomeration, pyro- hydro- and electro-metallurgical processes; material and energy balances; principles and processes for the extraction of non-ferrous metals – aluminium, copper, zinc, lead, magnesium, nickel, titanium and other rare metals; iron and steel making – principles, role structure and properties of slags, metallurgical coke, blast furnace, direct reduction processes, primary and secondary steel making, ladle metallurgy operations including deoxidation, desulphurization, sulphide shape control, inert gas rinsing and vacuum reactors; secondary refining processes including AOD, VAD, VOD, VAR and ESR; ingot and continuous casting; stainless steel making, furnaces and refractories.
Physical Metallurgy: Crystal structure and bonding characteristics of metals, alloys, ceramics and polymers, structure of surfaces and interfaces, nano-crystalline and amorphous structures; solid solutions; solidification; phase transformation and binary phase diagrams; principles of heat treatment of steels, cast iron and aluminum alloys; surface treatments; recovery, recrystallization and grain growth; industrially important ferrous and non-ferrous alloys; elements of X-ray and electron diffraction; principles of scanning and transmission electron microscopy; industrial ceramics, polymers and composites; electronic basis of thermal, optical, electrical and magnetic properties of materials; electronic and opto-electronic materials.
Mechanical Metallurgy: Elasticity, yield criteria and plasticity; defects in crystals; elements of dislocation theory – types of dislocations, slip and twinning, source and multiplication of dislocations, stress fields around dislocations, partial dislocations, dislocation interactions and reactions; strengthening mechanisms; tensile, fatigue and creep behaviour; super-plasticity; fracture – Griffith theory, basic concepts of linear elastic and elasto-plastic fracture mechanics, ductile to brittle transition, fracture toughness; failure analysis; mechanical testing – tension, compression, torsion, hardness, impact, creep, fatigue, fracture toughness and formability.
Manufacturing Processes: Metal casting – patterns and moulds including mould design involving feeding, gating and risering, melting, casting practices in sand casting, permanent mould casting, investment casting and shell moulding, casting defects and repair; hot, warm and cold working of metals, Metal forming – fundamentals of metal forming processes of rolling, forging, extrusion, wire drawing and sheet metal forming, defects in forming; Metal joining – soldering, brazing and welding, common welding processes of shielded metal arc welding, gas metal arc welding, gas tungsten arc welding and submerged arc welding; welding metallurgy, problems associated with welding of steels and aluminium alloys, defects in welded joints; powder metallurgy; NDT using dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle methods.

GATE Mining Engineering Syllabus

GATE Paper Code for Mining Engineering is MN and the GATE MN syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics, Numerical Methods, MINING ENGINEERING: Mechanics, Mine Development, Geomechanics and Ground Control, Mining Methods and Machinery, Ventilation, Underground Hazards and Surface Environment, Surveying, Mine Planning and Systems Engineering, Principles of planning. Detailed syllabus for GATE 2013 Mining Engineering is as follows

GATE 2013 Syllabus for Mining Engineering (MN)

ENGINEERING MATHEMATICS

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.
Diferential 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 linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

MINING ENGINEERING

Mechanics: Equivalent force systems; Equations of equilibrium; Two dimensional frames and trusses; Free body diagrams; Friction forces; Particle kinematics and dynamics.
Mine Development, Geomechanics and Ground Control: Methods of access to deposits; Underground drivages; Drilling methods and machines; Explosives, blasting devices and practices.
Geo-technical properties of rocks; Rock mass classification; Ground control, instrumentation and stress measurement techniques; Theories of rock failure; Ground vibrations; Stress distribution around mine openings; Subsidence; Design of supports in roadways and workings; Rock bursts and coal bumps; Slope stability.
Mining Methods and Machinery: Surface mining: layout, development, loading, transportation and mechanization, continuous surface mining systems; Underground coal mining: bord and pillar systems, room and pillar mining, longwall mining, thick seam mining methods; Underground metal mining : open, supported and caved stoping methods, stope mechanization, ore handling systems, mine filling.
Generation and transmission of mechanical, hydraulic and pneumatic power; Materials handling: haulages, conveyors, face and development machinery, hoisting systems, pumps.
Ventilation, Underground Hazards and Surface Environment: Underground atmosphere; Heat load sources and thermal environment, air cooling; Mechanics of air flow, distribution, natural and mechanical ventilation; Mine fans and their usage; Auxiliary ventilation; Ventilation planning.
Subsurface hazards from fires, explosions, gases, dust and inundation; Rescue apparatus and practices; Safety in mines, accident analysis, noise, mine lighting, occupational health and risk.
Air, water and soil pollution : causes, dispersion, quality standards, reclamation and control.
Surveying, Mine Planning and Systems Engineering: Fundamentals of engineering surveying; Levels and leveling, theodolite, tacheometry, triangulation, contouring, errors and adjustments, correlation; Underground surveying; Curves; Photogrammetry; Field astronomy; EDM, total station and GPS fundamentals.
Principles of planning: Sampling methods and practices, reserve estimation techniques, basics of geostatistics and quality control, optimization of facility location, cash flow concepts and mine valuation, open pit design; GIS fundamentals.
Work-study; Concepts of reliability, reliability of series and parallel systems.
Linear programming, transportation and assignment problems, queueing, network analysis, basics of simulation.

GATE Mechanical Engineering Syllabus

GATE Paper Code for Mechanical Engineering is ME and the GATE ME syllabus summery is ENGINEERING MATHEMATICS: Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, APPLIED MECHANICS AND DESIGN: Engineering Mechanics: Strength of Materials, Theory of Machines, Vibrations, Design, FLUID MECHANICS AND THERMAL SCIENCES: Fluid Mechanics, Heat-Transfer, Thermodynamics, Applications, MANUFACTURING AND INDUSTRIAL ENGINEERING: Engineering Materials, Metal Casting, Forming, Joining, Machining and Machine Tool Operations, Metrology and Inspection, Computer Integrated Manufacturing, Production Planning and Control, Inventory Control, Operations Research. Detailed GATE 2013 Mechanical Engineering Syllabus

GATE 2013 Syllabus for Mechanical Engineering (ME)

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
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.

APPLIED MECHANICS AND 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, including impulse and momentum (linear and angular) and energy formulations; impact.
Strength of Materials: Stress and strain, stress-strain relationship and elastic constants, 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; strain energy methods; thermal stresses.
Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains; flywheels.
Vibrations: Free and forced vibration of single degree of freedom systems; effect of damping; vibration isolation; resonance, critical speeds of shafts.
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, spur gears, rolling and sliding contact bearings, brakes and clutches.

FLUID MECHANICS AND THERMAL SCIENCES

Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer, black and grey surfaces, shape factors, network analysis; heat exchanger performance, LMTD and NTU methods.
Thermodynamics:Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle.irreversibility and availability; behaviour of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion.
Applications:Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration and reheat. I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and air-conditioning: Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse Brayton cycle; moist air: psychrometric chart, basic psychrometric processes. Turbomachinery:Pelton-wheel, Francis and Kaplan turbines — impulse and reaction principles, velocity diagrams.

MANUFACTURING AND INDUSTRIAL ENGINEERING

Engineering Materials: Structure and properties of engineering materials, heat treatment, stress-strain diagrams for engineering materials.
Metal Casting: Design of patterns, moulds and cores; solidification and cooling; riser and gating design, design considerations.
Forming: 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.
Joining: Physics of welding, brazing and soldering; adhesive bonding; design considerations in welding.
Machining and Machine Tool Operations: Mechanics of machining, 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, principles of 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.
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 and probabilistic m
odels; safety stock inventory control systems.
Operations Research: Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

GATE Mathematics Syllabus

GATE Paper Code for Mathematics is MA and the GATE MA syllabus summery is Linear Algebra, Complex Analysis, Real Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Mechanics, Topology, Probability and Statistics, Linear programming, Calculus of Variation and Integral Equations. Detailed GATE 2013 Mathematics Syllabus

GATE Syllabus for Mathematics (MA)

Linear Algebra: Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.
Complex Analysis: Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.
Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.
Ordinary Differential Equations: First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality.
Algebra:Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow’s theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.
Functional Analysis:Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.
Numerical Analysis: Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss Legendrequadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.
Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
Mechanics: Virtual work, Lagrange’s equations for holonomic systems, Hamiltonian equations.
Topology: Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Probability and Statistics: Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.
Linear programming: Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, u -u method for solving transportation problems; Hungarian method for solving assignment problems.
Calculus of Variation and Integral Equations: Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.