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.

Differential 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, one-dimensional heat and wave equations.

Probability and Statistics: Definitions of probability and sampling theorems, conditional probability, Mean, median, mode, and standard deviation; Random variables; Poisson, normal and binomial distributions; Analysis of experimental data; linear least-squares method.

Numerical Methods: Solutions of linear and non-linear (Bisection, Secant, Newton- Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

Electrochemistry: Single electrode potential, Electrochemical cells, Nernst equation, Potential-pH diagrams.

Heat transfer:

• Conduction: Fourier’s Law, 1-D steady-state conduction.
• Convection: Heat transfer coefficient relations for forced convection.
• Radiation: Black body radiation, Stefan-Boltzmann Law, Kirchhoff’s Law.

Mass transfer: Diffusion and Fick’s laws, mass transfer coefficients.

Dimensional analysis: Buckingham Pi theorem, Significance of dimensionless numbers.

Basic laws of chemical kinetics: First order reactions, the reaction rate constant, Arrhenius relation, heterogeneous reactions, oxidation kinetics.

Electrochemical kinetics: Polarization.

Material and Energy balances in metallurgical processes; Principles and processes for the extraction of non-ferrous metals – aluminum, copper, and titanium.

Iron and steel making: Material and heat balance in blast furnace; Structure and properties of slags and molten salts – basicity of slags – sulphide and phosphate capacity of slags; Production of metallurgical coke. Other methods of iron making (COREX, MIDREX).

Primary steelmaking: Basic oxygen furnace, process dynamics, oxidation reactions, electric arc furnace.

Secondary steelmaking: Ladle process – deoxidation, argon stirring, desulphurization, inclusion shape control, principles of degassing methods; Basics of stainless-steel manufacturing.

Continuous Casting: Fluid flow in the tundish and mould, heat transfer in the mould, segregation

X-ray Diffraction – Bragg’s law, optical metallography, principles of SEM imaging.

Crystal Imperfections: Point, line, and surface defects; Coherent, semi-coherent, and incoherent interfaces.

Diffusion in solids: Diffusion equation, steady-state and error function solutions; Example: homogenization and carburization; Kirkendall effect; Uphill diffusion; Atomic models for interstitial and substitutional diffusion; Pipe diffusion and grain boundary diffusion.

Phase transformation: Driving force, Homogeneous and heterogeneous nucleation, growth Kinetics Solidification in isomorphous, eutectic and peritectic systems, cast structures and macrosegregation, dendritic solidification and constitutional supercooling, coring and microsegregation.

Solid-state transformations: Precipitation, spinodal decomposition, ordering, massive transformation, discontinuous precipitation, eutectoid transformation, diffusionless transformations; Precipitate coarsening, Gibbs-Thomson effect.

Principles of heat treatment of steels, TTT and CCT diagrams; Surface hardening treatments; Recovery, recrystallization, and grain growth; Heat treatment of cast iron and aluminium alloys.

Electronic, magnetic, and optical properties of materials.

Basic forms of corrosion and its prevention

6. Mechanical Metallurgy

Dislocation theory: Edge, screw, and mixed dislocations, source and multiplication of dislocations, stress fields around dislocations; Partial dislocations, dislocation interactions, and reactions.

Strengthening mechanisms: Work/strain hardening, strengthening due to grain boundaries, solid solution, precipitation, and dispersion.

Fracture behavior, Griffith theory, linear elastic fracture mechanics, fracture toughness, fractography, ductile to brittle transition.

Fatigue: Cyclic stress-strain behaviour – low and high cycle fatigue, crack growth. Mechanisms of high-temperature deformation and failure; creep and stress rupture, stress exponent, and activation energy.

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: Principles of soldering, brazing and welding, welding metallurgy, defects in welded joints in steels and aluminum alloys.

Powder metallurgy: production of powders, compaction, and sintering.

Non-destructive Testing (NDT): Dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission, and magnetic particle inspection methods.