## GATE Syllabus for Metallurgical Engineering

### 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.