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Engineering Mathematics__

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Linear Algebra***:
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Matrices and Determinants, Systems of linear equations,
Eigen values and Eigen vectors.

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Calculus**:
Limit, continuity and differentiability; Partial
Derivatives; Maxima and minima; Sequences and series; Test
for convergence; Fourier series.

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Vector Calculus**:
Gradient; Divergence and Curl; Line; surface and volume
integrals; Stokes, Gauss and Green’s theorems.

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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.

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Probability and Statistics**:
Mean, median, mode and standard deviation; Random variables;
Poisson, normal and binomial distributions; Correlation and
regression analysis.

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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.

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Metallurgical Engineering:__

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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.

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Extractive Metallurgy: **
Minerals of economic importance, comminution techniques,
size classification, Flotation, gravity and other methods of
mineral processing; agglomeration, pyrohydro- 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.

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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.

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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.

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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.