Linear Algebra: Matrix algebra, Systems of linear equations, Eigenvalues and Eigenvectors.
Calculus: Functions of single variable, Limit, Continuity and Differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential Equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms.
Complex Variables: Analytic functions, Cauchy’s integral theorem, Taylor series.
Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, Median, Mode and Standard Deviation, Linear regression, Random variables, Poisson, Normal, Binomial and Exponential distributions.
Numerical Methods: Numerical solutions of linear and nonlinear algebraic equations, Integration by trapezoidal and Simpson’s rules, Single and multi-step methods for differential equations.
Section 2: General Engineering
Core Topics:
Engineering Materials: Structure, Physical and Mechanical properties, Applications of common engineering materials (metals, alloys, semiconductors, ceramics, polymers, and composites), Iron-carbon equilibrium phase diagram, Heat treatment of metals and alloys, Stress-strain behavior of metals and alloys.
Applied Mechanics: Engineering mechanics (equivalent force systems, free body concepts, equations of equilibrium), Trusses, Strength of materials, Failure theories, Mohr’s circle, Deflection of beams, Bending and shear stresses, Euler’s theory of columns, Thick and thin cylinders, Torsion.
Theory of Machines and Design: Analysis of planar mechanisms, Cams and followers, Governors and flywheels, Design of bolted, riveted, and welded joints, Friction and lubrication, Design of shafts, keys, couplings, spur gears, belt drives, brakes and clutches, Pressure vessels.
Thermal and Fluids Engineering: Fluid mechanics (fluid statics, Bernoulli’s equation, flow through pipes, laminar and turbulent flows), Thermodynamics (zeroth, first and second laws, thermodynamic systems and processes), Heat transfer (conduction, convection, radiation).
Section 3: Manufacturing Processes I
Core Topics:
Casting: Types and applications, Sand casting (patterns, molds, and cores), Design of gating system and riser, Other casting techniques, Defects and inspection.
Metal Forming: Stress-strain relations, Bulk and sheet forming processes, Defects and causes.
Joining of Materials: Fusion welding, Solid state welding, Welding defects, Adhesive joining, Brazing, and soldering.
Powder Processing: Metal/ceramic powder production, Compaction and sintering, Isostatic pressing.
Polymers and Composites: Polymer and composite molding techniques.
Section 4: Manufacturing Processes II
Core Topics:
Machining: Orthogonal and oblique machining, Tool wear and tool life, Cutting forces, Economics of machining, Finishing processes.
Machine Tools: Lathe, milling, drilling and shaping machines, Jigs and fixtures.
Advanced Manufacturing: USM, EDM, LBM, and additive manufacturing techniques.
