One Stop GATE Forum: GATE SYLLABUS

Message


   

SECTION A. ENGINEERING MATHEMATICS
                                    (Compulsory)

                                    

                                    Linear Algebra : Determinates, algebra of
                                    matrices, rank, inverse, system of linear
                                    equations, symmetric, skew-symmetric and
                                    orthogonal matrices. Hermitian, skew-hermitian
                                    and unitary matrices. eigenvalues and
                                    eigenvectors, diagonalisation of matrices,
Cayley-Hamiltonian, quadratic forms.

                                    

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

                                    

                                    Complex variable: Analytic functions,
                                    Cauchy's integral theorem and integral
                                    formula without proof. Taylor's and Laurent'
                                    series, Residue theorem (without proof) with
                                    application to the evaluation of real
integarls.

                                    

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

                                    

                                    Ordinary Differential Equations: First order
                                    equation (linear and nonlinear), higher
                                    order linear differential equations with
                                    constant coefficients, method of variation
                                    of paramaters, Cauchy's and Euler's
                                    equations, initial and boundary value
                                    problems, power series solutions, Legendre
                                    polynomials and Bessel's functions of the
                                    first kind.

                                    

                                    Partial Differential Equations: Variables
                                    separable method, solutions of one
                                    dimensional heat, wave and Laplace
                                    equations.

                                    

                                    Probability and Statistics: Definitions of
                                    probability and simple theorems, conditional
                                    probability, mean, mode and standard
                                    deviation, random variables, discrete and
                                    continuous distributions, Poisson, normal
                                    and Binomial distribution, correlation and
                                    regression

                                    

                                    Numerical Methods: L-U decomposition for
                                    systems of linear equations,Newton-Raphson
                                    method, numerical integration(trapezoidal
                                    and Simpson's rule), numerical methods for
                                    first order differential equation (Euler
                                    method)

                                    

                                    SECTION B. COMPUTATIONAL SCIENCE

                                    

                                    Numerical Methods: Truncation errors, round
                                    off errors and their propagation;
                                    Interpolation; Lagrange, Newton's forward,
                                    backward and divided difference formulas,
                                    least square curve fitting, solution of
                                    non-linear equations of one variables using
                                    bisection, false position, secant and Newton
                                    Raphson methods; Rate of convergence of
                                    these methods, general iterative methods.
                                    Simple and multiple roots of polynomials.
                                    Solutions of system of linear algebraic
                                    equations using Gauss elimination methods,
                                    Jacobi and Gauss-Seidel iterative methods
                                    and their rate of convergence; ill
                                    conditioned and well conditioned system.
                                    eigen values and eigen vectors using power
                                    methods. Numerical integration using
                                    trapezoidal, Simpson's rule and other
                                    quadrature formulas. Numerical
                                    Differentiation. Solution of boundary value
                                    problems. Solution of initial value problems
                                    of ordinary differential equations using
                                    Euler's method, predictor corrector and
                                    Runge Kutta method.

                                    

                                    Programming : Elementary concepts and
                                    terminology of a computer system and system
                                    software, Fortran77 and C programming.

                                    

                                    Fortran : Program organization, arithmetic
                                    statements, transfer of control, Do loops,
                                    subscripted variables, functions and
                                    subroutines.

                                    

                                    C language : Basic data types and
                                    declarations, flow of control- iterative
                                    statement, conditional statement,
                                    unconditional branching, arrays, functions
                                    and procedures.

                                    

                                    SECTION C. ELECTRICAL SCIENCES

                                    

                                    Electric Circuits: Ideal voltage and current
                                    sources; RLC circuits, steady state and
                                    transient analysis of DC circuits, network
                                    theorems; alternating currents and voltages,
                                    single-phase AC circuits, resonance;
                                    three-phase circuits.

                                    

                                    Magnetic circuits: Mmf and flux, and their
                                    relationship with voltage and current;
                                    transformer, equivalent circuit of a
                                    practical transformer, three-phase
                                    transformer connections.

                                    

                                    Electrical machines: Principle of operation,
                                    characteristics, efficiency and regulation
                                    of DC and synchronous machines; equivalent
                                    circuit and performance of three-phase and
                                    single-phase induction motors.

                                    

                                    Electronic Circuits: Characteristics of p-n
                                    junction diodes, zener diodes, bipolar
                                    junction transistors (BJT) and junction
                                    field effect transistors (JFET); MOSFET's
                                    structure, characteristics, and operations;
                                    rectifiers, filters, and regulated power
                                    supplies; biasing circuits, different
                                    configurations of transistor amplifiers,
                                    class A, B and C of power amplifiers; linear
                                    applications of operational amplifiers;
                                    oscillators; tuned and phase shift types.

                                    

                                    Digital circuits: Number systems, Boolean
                                    algebra; logic gates, combinational
                                    circuits, flip-flops (RS, JK, D and T)
                                    counters.

                                    

                                    Measuring instruments: Moving coil, moving
                                    iron, and dynamometer type instruments;
                                    shunts, instrument transformers, cathode ray
                                    oscilloscopes; D/A and A/D converters.

                                    

                                    SECTION D. FLUID MECHANICS

                                    

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

                                    

                                    Hydrostatics, buoyancy, manometry

                                    

                                    Concept of local and convective
                                    accelerations; control volume analysis for
                                    mass, momentum and energy conservation.

                                    

                                    Differential equations of continuity and
                                    momentum (Euler's equation of motion);
                                    concept of fluid rotation, stream function,
                                    potential function; Bernoulli's equation and
                                    its applications.

                                    

                                    Qualitative ideas of boundary layers and its
                                    separation; streamlined and bluff bodies;
                                    drag and lift forces.

                                    

                                    Fully-developed pipe flow; laminar and
                                    turbulent flows; friction factor; Darcy
                                    Weisbach relation; Moody's friction chart;
                                    losses in pipe fittings; flow measurements
                                    using venturimeter and orifice plates.

                                    

                                    Dimensional analysis; similitude and concept
                                    of dynamic similarity; importance of
                                    dimensionless numbers in model studies.

                                    

                                    SECTION E. MATERIALS SCIENCE

                                    

                                    Atomic structure and bonding in materials:
                                    metals, ceramics and polymers.

                                    

                                    Structure of materials: Crystal systems,
                                    unit cells and space lattice; determination
                                    of structures of simple crystals by X-ray
                                    diffraction; Miller indices for planes and
                                    directions. Packing geometry in metallic,
                                    ionic and covalent solids.

                                    

                                    Concept of amorphous, single and
                                    polycrystalline structures and their effects
                                    on properties of materials.

                                    

                                    Imperfections in crystalline solids and
                                    their role in influencing various
                                    properties.

                                    

                                    Fick´s laws of diffusion and applications
                                    of diffusion in sintering, doping of
                                    semiconductors and surface hardening of
                                    metals.

                                    

                                    Alloys: solid solution and solubility limit.
                                    Binary phase diagram, intermediate phases
                                    and intermetallic compounds; iron-iron
                                    carbide phase diagram. Phase transformation
                                    in steels. Cold and hot working of metals,
                                    recovery, recrystallization and grain
                                    growth.

                                    

                                    Properties and applications of ferrous and
                                    nonferrous alloys.

                                    

                                    Structure, properties, processing and
                                    applications of traditional and advanced
                                    ceramics.

                                    

                                    Polymers: classification, polymerization,
                                    structure and properties, additives for
                                    polymer products, processing and
                                    application.

                                    

                                    Composites: properties and application of
                                    various composites.

                                    

                                    Corrosion and environmental degradation of
                                    materials (metals, ceramics and polymers).

                                    

                                    Mechanical properties of materials:
                                    Stress-strain diagrams of metallic, ceramic
                                    and polymeric materials, modulus of
                                    elasticity, yield strength, plastic
                                    deformation and toughness, tensile strength
                                    and elongation at break; viscoelasticity,
                                    hardness, impact strength. ductile and
                                    brittle fracture. creep and fatigue
                                    properties of materials.

                                    

                                    Heat capacity, thermal conductivity, thermal
                                    expansion of materials.

                                    

                                    Concept of energy band diagram for
                                    materials; conductors, semiconductors and
                                    insulators in terms of energy bands.
                                    Electrical conductivity, effect of
                                    temperature on conductivity in materials,
                                    intrinsic and extrinsic semiconductors,
                                    dielectric properties of materials.

                                    

                                    Refraction, reflection, absorption and
                                    transmission of electromagnetic radiation in
                                    solids.

                                    

                                    Origin of magnetism in metallic and ceramic
                                    materials, paramagnetism, diamagnetism,
antiferromagnetism, ferromagnetism,
                                    ferrimagnetism in materials and magnetic
hysteresis.

                                    

                                    Advanced materials: Smart materials
                                    exhibiting ferroelectric, piezoelectric,
optoelectronic, semiconducting behaviour;
                                    lasers and optical fibers; photoconductivity
                                    and superconductivity in materials.

                                    

                                    SECTION F. SOLID MECHANICS

                                    

                                    Equivalent force systems; free-body
                                    diagrams; equilibrium equations; analysis of
                                    determinate and indeterminate 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; equilibrium equations; compatibility
                                    conditions; yield criteria.

                                    

                                    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.

                                    

                                    SECTION G. THERMODYNAMICS

                                    

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

                                    

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

                                    

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

                                    

                                    Properties of Pure Substances: Thermodynamic
                                    properties of pure substances in solid,
                                    liquid and vapour phases, P-V-T behaviour of
                                    simple compressible substances, phase rule,
                                    thermodynamic property tables and charts,
                                    ideal and real gases, equations of state,
                                    compressibility chart.

                                    

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

                                    

                                    Ideal Gas Mixtures: Dalton's and Amagat's
                                    laws, calculations of properties, air-water
                                    vapour mixtures.

Author	Message
Smitha Newbie Joined: 08Feb2007 Online Status: Offline Posts: 14	Topic: GATE SYLLABUS - ENGINEERING SCIENCES........ Posted: 08Feb2007 at 6:07pm
	SECTION A. ENGINEERING MATHEMATICS (Compulsory) Linear Algebra : Determinates, algebra of matrices, rank, inverse, system of linear equations, symmetric, skew-symmetric and orthogonal matrices. Hermitian, skew-hermitian and unitary matrices. eigenvalues and eigenvectors, diagonalisation of matrices, Cayley-Hamiltonian, quadratic forms. Calculus : Functions of single variables, limit, continuity and differentiability, Mean value theorems, Intermediate forms and L'Hospital rule, Maxima and minima, Taylor's series, Fundamental and mean value-theorems of integral calculus. Evaluation of definite and improper integrals, Beta and Gamma functions, Functions of two variables, limit, continuity, partial derivatives, Euler's theorem for homogeneous functions, total derivatives, maxima and minima, Lagrange method of multipliers, double and triple integrals and their applications, sequence and series, tests for convergence, power series, Fourier Series, Fourier integrals. Complex variable: Analytic functions, Cauchy's integral theorem and integral formula without proof. Taylor's and Laurent' series, Residue theorem (without proof) with application to the evaluation of real integarls. Vector Calculus: Gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green's theorems (without proofs) with applications. Ordinary Differential Equations: First order equation (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of paramaters, Cauchy's and Euler's equations, initial and boundary value problems, power series solutions, Legendre polynomials and Bessel's functions of the first kind. Partial Differential Equations: Variables separable method, solutions of one dimensional heat, wave and Laplace equations. Probability and Statistics: Definitions of probability and simple theorems, conditional probability, mean, mode and standard deviation, random variables, discrete and continuous distributions, Poisson, normal and Binomial distribution, correlation and regression Numerical Methods: L-U decomposition for systems of linear equations,Newton-Raphson method, numerical integration(trapezoidal and Simpson's rule), numerical methods for first order differential equation (Euler method) SECTION B. COMPUTATIONAL SCIENCE Numerical Methods: Truncation errors, round off errors and their propagation; Interpolation; Lagrange, Newton's forward, backward and divided difference formulas, least square curve fitting, solution of non-linear equations of one variables using bisection, false position, secant and Newton Raphson methods; Rate of convergence of these methods, general iterative methods. Simple and multiple roots of polynomials. Solutions of system of linear algebraic equations using Gauss elimination methods, Jacobi and Gauss-Seidel iterative methods and their rate of convergence; ill conditioned and well conditioned system. eigen values and eigen vectors using power methods. Numerical integration using trapezoidal, Simpson's rule and other quadrature formulas. Numerical Differentiation. Solution of boundary value problems. Solution of initial value problems of ordinary differential equations using Euler's method, predictor corrector and Runge Kutta method. Programming : Elementary concepts and terminology of a computer system and system software, Fortran77 and C programming. Fortran : Program organization, arithmetic statements, transfer of control, Do loops, subscripted variables, functions and subroutines. C language : Basic data types and declarations, flow of control- iterative statement, conditional statement, unconditional branching, arrays, functions and procedures. SECTION C. ELECTRICAL SCIENCES Electric Circuits: Ideal voltage and current sources; RLC circuits, steady state and transient analysis of DC circuits, network theorems; alternating currents and voltages, single-phase AC circuits, resonance; three-phase circuits. Magnetic circuits: Mmf and flux, and their relationship with voltage and current; transformer, equivalent circuit of a practical transformer, three-phase transformer connections. Electrical machines: Principle of operation, characteristics, efficiency and regulation of DC and synchronous machines; equivalent circuit and performance of three-phase and single-phase induction motors. Electronic Circuits: Characteristics of p-n junction diodes, zener diodes, bipolar junction transistors (BJT) and junction field effect transistors (JFET); MOSFET's structure, characteristics, and operations; rectifiers, filters, and regulated power supplies; biasing circuits, different configurations of transistor amplifiers, class A, B and C of power amplifiers; linear applications of operational amplifiers; oscillators; tuned and phase shift types. Digital circuits: Number systems, Boolean algebra; logic gates, combinational circuits, flip-flops (RS, JK, D and T) counters. Measuring instruments: Moving coil, moving iron, and dynamometer type instruments; shunts, instrument transformers, cathode ray oscilloscopes; D/A and A/D converters. SECTION D. FLUID MECHANICS Fluid Properties: Relation between stress and strain rate for Newtonian fluids Hydrostatics, buoyancy, manometry Concept of local and convective accelerations; control volume analysis for mass, momentum and energy conservation. Differential equations of continuity and momentum (Euler's equation of motion); concept of fluid rotation, stream function, potential function; Bernoulli's equation and its applications. Qualitative ideas of boundary layers and its separation; streamlined and bluff bodies; drag and lift forces. Fully-developed pipe flow; laminar and turbulent flows; friction factor; Darcy Weisbach relation; Moody's friction chart; losses in pipe fittings; flow measurements using venturimeter and orifice plates. Dimensional analysis; similitude and concept of dynamic similarity; importance of dimensionless numbers in model studies. SECTION E. MATERIALS SCIENCE Atomic structure and bonding in materials: metals, ceramics and polymers. Structure of materials: Crystal systems, unit cells and space lattice; determination of structures of simple crystals by X-ray diffraction; Miller indices for planes and directions. Packing geometry in metallic, ionic and covalent solids. Concept of amorphous, single and polycrystalline structures and their effects on properties of materials. Imperfections in crystalline solids and their role in influencing various properties. Fick´s laws of diffusion and applications of diffusion in sintering, doping of semiconductors and surface hardening of metals. Alloys: solid solution and solubility limit. Binary phase diagram, intermediate phases and intermetallic compounds; iron-iron carbide phase diagram. Phase transformation in steels. Cold and hot working of metals, recovery, recrystallization and grain growth. Properties and applications of ferrous and nonferrous alloys. Structure, properties, processing and applications of traditional and advanced ceramics. Polymers: classification, polymerization, structure and properties, additives for polymer products, processing and application. Composites: properties and application of various composites. Corrosion and environmental degradation of materials (metals, ceramics and polymers). Mechanical properties of materials: Stress-strain diagrams of metallic, ceramic and polymeric materials, modulus of elasticity, yield strength, plastic deformation and toughness, tensile strength and elongation at break; viscoelasticity, hardness, impact strength. ductile and brittle fracture. creep and fatigue properties of materials. Heat capacity, thermal conductivity, thermal expansion of materials. Concept of energy band diagram for materials; conductors, semiconductors and insulators in terms of energy bands. Electrical conductivity, effect of temperature on conductivity in materials, intrinsic and extrinsic semiconductors, dielectric properties of materials. Refraction, reflection, absorption and transmission of electromagnetic radiation in solids. Origin of magnetism in metallic and ceramic materials, paramagnetism, diamagnetism, antiferromagnetism, ferromagnetism, ferrimagnetism in materials and magnetic hysteresis. Advanced materials: Smart materials exhibiting ferroelectric, piezoelectric, optoelectronic, semiconducting behaviour; lasers and optical fibers; photoconductivity and superconductivity in materials. SECTION F. SOLID MECHANICS Equivalent force systems; free-body diagrams; equilibrium equations; analysis of determinate and indeterminate 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; equilibrium equations; compatibility conditions; yield criteria. 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. SECTION G. THERMODYNAMICS Basic Concepts: Continuum, macroscopic approach, thermodynamic system (closed and open or control volume); thermodynamic properties and equilibrium; state of a system, state diagram, path and process; different modes of work; Zeroth law of thermodynamics; concept of temperature; heat. First Law of Thermodynamics: Energy, enthalpy, specific heats, first law applied to systems and control volumes, steady and unsteady flow analysis. Second Law of Thermodynamics: Kelvin-Planck and Clausius statements, reversible and irreversible processes, Carnot theorems, thermodynamic temperature scale, Clausius inequality and concept of entropy, principle of increase of entropy; availability and irreversibility. Properties of Pure Substances: Thermodynamic properties of pure substances in solid, liquid and vapour phases, P-V-T behaviour of simple compressible substances, phase rule, thermodynamic property tables and charts, ideal and real gases, equations of state, compressibility chart. Thermodynamic Relations: T-ds relations, Maxwell equations, Joule-Thomson coefficient, coefficient of volume expansion, adiabatic and isothermal compressibilities, Clapeyron equation. Ideal Gas Mixtures: Dalton's and Amagat's laws, calculations of properties, air-water vapour mixtures. Post Resume: Click here to Upload your Resume & Apply for Jobs

	IP Logged


One Stop GATE Forum : GATE AT A GLANCE : Syllabus