CE - Civil Engineering
Linear Algebra: Determinants, algebra of matrices, systems of linear equations, eigen values and eigen vectors.
Calculus: Functions of single variable: limit, continuity and differentiability, mean value theorems, theorems "'of integral calculus; evaluation of definite and improper integrals. Functions of two variables: limit, continuity, partial derivatives, total derivative and directional derivative, maxima and minima, multiple integrals and their applications, sequences and series, test for convergence, Fourier series.
Ordinary Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy's or Euler's equations, initial and boundary value problems, Laplace transform.
Statistics: Basic concepts of Probability and Statistics.
Mechanics: Bending moments and. shear forces in statically determinate beams; simple stress and strain: relationship; stress and strain in two dimensions, principal stresses, stress transformation, Mohr's circle; v-srrrTple1)ending theory; flexural shear stress; thin-walled pressure vessels; uniform torsion.
Structural Analysis: Analysis of statically determinate trusses, arches and frames; displacements in statically determinate structures and analysis of statically indeterminate structures by force/energy methods; .-o"analysis by displacement methods (slope-deflection and moment-distribution methods); influence lines for determinate and indeterminate structures; basic concepts of matrix methods of structural analysis.
Concrete Structures: Basic working stress and limit states design concepts; analysis of ultimate load capacity and design of members subject to flexure, shear, compression and torsion (beams, columns and isolated footings); basic elements of prestressed concrete: analysis of beam sections at transfer and service loads.
Steel Structures: Analysis and design of tension and compression members, beams and beam-columns, column bases; connections - simple and eccentric, beam-column connections, plate girders and trusses; plastic analysis of beams and frames.
Soil Mechanics: Origin of soils; soil classification; three-phase system, fundamental definitions, relationship and inter-relationships; permeability and seepage; effective stress principle: consolidation, compaction; shear strength.
Foundation Engineering: Sub-surface investigation - scope, drilling bore holes, sampling, penetrometer tests, plate load test; earth pressure theories, effect of water table, layered soils; stability of slopes - infinite slopes, finite slopes; foundation types - foundation design requirements; shallow foundations; bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays; deep foundations - pile types, dynamic and static formulae, load capacity of piles in sands and clays.
Water Resources Engineering
Fluid Mechanics and Hydraulics: Hydrostatics, applications of Bernoulli equation, laminar and turbulent flow in pipes, pipe networks; concept of boundary layer and its growth; uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump; forces on immersed bodies; flow measurement in channels; tanks and pipes; dimensional analysis and hydraulic modeling. Applications of momentum equation, potential flow, kinematics of flow; velocity triangles and specific speed of pumps and turbines.
Hydrology: Hydrologic cycle; rainfall; evaporation infiltration, unit hydrographs, flood estimation, reservoir design, reservoir and channel routing, well hydraulics.
Irrigation: Duty, delta, estimation of evapo-transpiration; crop water requirements; design of lined and unlined canals; waterways; head works, gravity dams and Ogee spillways. Designs of weirs on permeable '' foundation, irrigation methods.
Water requirements; quality and standards, basic unit processes and operations for water treatment, distribution of water. Sewage and sewerage treatment: quantity and characteristic of waste water sewerage; primary and secondary treatment of waste water; sludge disposal; effluent discharge standards.
Highway planning; geometric design of highways; testing and specifications of paving materials; design of flexible and rigid pavements.