Gate Metallurgical Engineering Syllabus
GATE Metallurgy (MT) Complete Syllabus Guide
Every Topic Covered in Detail | Official Syllabus
Detailed Table of Contents
Section 1: Engineering Mathematics
Linear Algebra
Matrices and Determinants
Matrix operations, types of matrices (symmetric, skew-symmetric, orthogonal), properties of determinants, calculation of determinants, adjoint and inverse of matrices.
Systems of Linear Equations
Solution methods (Gaussian elimination, matrix inversion), consistency of systems, rank of a matrix.
Eigenvalues and Eigenvectors
Characteristic equation, calculation of eigenvalues and eigenvectors, properties, diagonalization.
Calculus
Limit, Continuity and Differentiability
ε-δ definition, L'Hôpital's rule, partial derivatives, chain rule.
Maxima and Minima
Critical points, second derivative test, Lagrange multipliers.
Sequences and Series
Convergence tests (ratio, root, comparison, integral), Taylor and Maclaurin series.
Fourier Series
Periodic functions, Fourier coefficients, Dirichlet conditions.
Vector Calculus
Gradient, Divergence and Curl
Definitions, physical interpretations, vector identities.
Line, Surface and Volume Integrals
Evaluation methods, applications.
Stokes, Gauss and Green's Theorems
Statement, proof and applications of each theorem.
Differential Equations
First Order ODEs
Linear and non-linear equations, exact equations, integrating factors.
Higher Order Linear ODEs
Constant coefficients, complementary function, particular integral.
Cauchy's and Euler's Equations
Solution methods, transformation techniques.
Laplace Transforms
Definition, properties, solution of ODEs.
Partial Differential Equations
Laplace, heat and wave equations, separation of variables.
Probability and Statistics
Basic Probability
Definitions, conditional probability, Bayes' theorem.
Random Variables
Discrete and continuous, probability distributions.
Statistical Distributions
Poisson, normal, binomial distributions.
Data Analysis
Mean, median, mode, standard deviation, linear least squares.
Numerical Methods
Root Finding
Bisection, Secant, Newton-Raphson methods.
Numerical Integration
Trapezoidal rule, Simpson's rule.
Differential Equations
Single and multi-step methods for ODEs.
Section 2: Metallurgical Thermodynamics
Laws of Thermodynamics
First Law
Energy conservation, internal energy, enthalpy.
Second Law
Entropy, Carnot cycle, thermodynamic temperature.
Thermodynamic Potentials
Gibbs and Helmholtz free energy, chemical potential.
Solutions and Phase Equilibria
Ideal and Regular Solutions
Raoult's law, Henry's law, activity coefficients.
Phase Diagrams
Gibbs phase rule, binary systems, lever rule.
Thermodynamic Diagrams
Ellingham diagrams, phase stability diagrams.
Defects and Interfaces
Point Defects
Vacancies, interstitials, thermodynamics of defects.
Surfaces and Interfaces
Surface energy, adsorption, segregation.
Electrochemistry
Electrode Potential
Single electrode potential, standard hydrogen electrode.
Electrochemical Cells
Galvanic and electrolytic cells, cell notation.
Nernst Equation
Derivation and applications.
Potential-pH Diagrams
Pourbaix diagrams, corrosion prediction.
Section 3: Transport Phenomena and Rate Processes
Momentum Transfer
Viscosity
Newtonian fluids, shell balances.
Fluid Flow
Bernoulli's equation, mechanical energy balance.
Heat Transfer
Conduction
Fourier's law, 1-D steady state conduction.
Convection
Forced convection, heat transfer coefficients.
Radiation
Black body radiation, Stefan-Boltzmann law.
Mass Transfer
Diffusion
Fick's laws, mass transfer coefficients.
Dimensional Analysis
Buckingham Pi theorem, dimensionless numbers.
Chemical Kinetics
Reaction Kinetics
First order reactions, Arrhenius equation.
Heterogeneous Reactions
Oxidation kinetics, rate controlling steps.
Electrochemical Kinetics
Polarization, overpotential, Butler-Volmer equation.
Section 4: Mineral Processing and Extractive Metallurgy
Mineral Beneficiation
Comminution
Crushing, grinding, size classification.
Separation Methods
Flotation, gravity separation, magnetic separation.
Agglomeration
Sintering, pelletizing, briquetting.
Extractive Metallurgy
Non-Ferrous Metals
Aluminum (Bayer process, Hall-Héroult), copper (smelting, refining), titanium (Kroll process).
Material and Energy Balances
Stoichiometry, heat balances in metallurgical processes.
Iron and Steel Making
Blast Furnace
Material and heat balance, reactions, slag properties.
Alternative Iron Making
COREX, MIDREX processes.
Steel Making
Basic oxygen furnace, electric arc furnace.
Secondary Steel Making
Ladle metallurgy, degassing, inclusion control.
Continuous Casting
Fluid flow, heat transfer, segregation control.
Section 5: Physical Metallurgy
Structure of Materials
Chemical Bonding
Ionic, covalent, metallic, secondary bonds.
Crystal Structure
BCC, FCC, HCP, Miller indices, X-ray diffraction.
Crystal Defects
Point defects, dislocations, grain boundaries.
Diffusion
Fick's laws, Kirkendall effect, diffusion mechanisms.
Phase Transformations
Solidification
Nucleation, growth, dendritic solidification.
Solid State Transformations
Precipitation, spinodal decomposition, martensite.
Heat Treatment
Steels
TTT diagrams, CCT diagrams, hardening methods.
Other Alloys
Cast iron, aluminum alloys.
Materials Properties
Electronic, magnetic, optical properties, corrosion.
Section 6: Mechanical Metallurgy
Stress and Strain
Tensors, Mohr's circle, yield criteria.
Dislocation Theory
Types of dislocations, multiplication, stress fields.
Strengthening Mechanisms
Work hardening, grain refinement, precipitation.
Fracture
Griffith theory, fracture toughness, ductile-brittle transition.
Fatigue
S-N curves, crack growth, Paris law.
Creep
Mechanisms, stress rupture, Larson-Miller parameter.
Section 7: Manufacturing Processes
Metal Casting
Mold design, gating, risering, casting defects.
Metal Forming
Rolling, forging, extrusion, sheet metal forming.
Metal Joining
Welding, brazing, soldering, weld defects.
Powder Metallurgy
Powder production, compaction, sintering.
Non-Destructive Testing
Ultrasonic, radiography, dye penetrant, eddy current.