Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.
Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.
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.
Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.
Mechanics: Equivalent force systems; Equations of equilibrium; Two dimensional frames and trusses; Free body diagrams; Friction forces; Particle kinematics and dynamics.
Mine Development, Geomechanics and Ground Control:
Methods of access to deposits; Underground drivages; Drilling methods and machines; Explosives, blasting devices and practices.
Geo-technical properties of rocks; Rock mass classification; Ground control, instrumentation and stress measurement techniques; Theories of rock failure; Ground vibrations; Stress distribution around mine openings; Subsidence; Design of supports in roadways and workings; Rock bursts and coal bumps; Slope stability.
Mining Methods and Machinery:
Layout, development, loading, transportation and mechanization, continuous surface mining systems; Underground coal mining: bord and pillar systems, room and pillar mining, longwall mining, thick seam mining methods; Underground metal mining : open, supported and caved stoping methods, stope mechanization, ore handling systems, mine filling.
Generation and transmission of mechanical, hydraulic and pneumatic power; Materials handling:
Haulages, conveyors, face and development machinery, hoisting systems, pumps.
Ventilation, Underground Hazards and Surface Environment: Underground atmosphere; Heat load sources and thermal environment, air cooling; Mechanics of air flow, distribution, natural and mechanical ventilation; Mine fans and their usage; Auxiliary ventilation; Ventilation planning.
Subsurface hazards from fires, explosions, gases, dust and inundation; Rescue apparatus and practices; Safety in mines, accident analysis, noise, mine lighting, occupational health and risk.
Air, water and soil pollution : causes, dispersion, quality standards, reclamation and control.
Surveying, Mine Planning and Systems Engineering:
Fundamentals of engineering surveying; Levels and leveling, theodolite, tacheometry, triangulation, contouring, errors and adjustments, correlation; Underground surveying; Curves; Photogrammetry; Field astronomy; EDM, total station and GPS fundamentals.
Principles of planning:
Sampling methods and practices, reserve estimation techniques, basics of geostatistics and quality control, optimization of facility location, cash flow concepts and mine valuation, open pit design; GIS fundamentals.
Work-study; Concepts of reliability, reliability of series and parallel systems.
Linear programming, transportation and assignment problems, queueing, network analysis, basics of simulation