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, basic
kinetic laws, order of reactions, rate
constants and rate limiting steps principles
of electro chemistry, aqueous, corrosion and
protection of metals, oxidation and high
temperature corrosion - characterization and
control; momentum transfer - concepts of
viscosity, shell balances, Bernoulli's
equation; heat transfer - conduction,
convection and heat transfer coefficient
relations, radiation, mass transfer -
diffusion and Fick's laws.
Extractive Metallurgy: 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,
blast furnace, direct reduction processes,
primary and secondary steel making,
deoxidation and inclusion in steel; ingot
and continuous casting; stainless steel
making, design of furnaces; fuels and
refractories.
Physical Metallurgy: Crystal structure and
bonding characteristics of metals, alloys,
ceramics and polymers; solid solutions;
solidification; phase transformation and
binary phase diagrams; principles of heat
treatment of steels, aluminum alloys and
cast irons; 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; elements of ceramics, composites
and electronic materials; electronic basis
of thermal, optical, electrical and magnetic
properties of materials.
Mechanical Metallurgy: Elements of
elasticity and plasticity; defects in
crystals; elements of dislocation theory -
types of dislocations, slip and twinning,
stress fields of dislocations, dislocation
interactions and reactions, methods of
seeing dislocations; strengthening
mechanisms; tensile, fatigue and creep
behaviour; superplasticity; fracture -
Griffith theory, ductile to brittle
transition, fracture toughness; failure
analysis; mechanical testing - tension,
compression, torsion, hardness, impact,
creep, fatigue, fracture toughness and
formability tests.
Manufacturing Processes: Metal casting -
patterns, moulds, melting, gating, feeding
and casting processes, defects and castings,
hot and cold working of metals; Metal
forming - fundamentals of metal forming,
rolling wire drawing, extrusion, forming,
sheet metal forming processes, defects in
forming; Metal joining - soldering, brazing
and welding, common welding processes,
welding metallurgy, problems associated with
welding of steels and aluminium alloys,
defects in welding, powder metallurgy; NDT
methods - ultrasonic, radiography, eddy
current, acoustic emission and magnetic.
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