Engineering Mathematics
Linear Algebra:
Matrix algebra, Systems of linear equations, Eigen values 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, Solutions of one dimensional heat and wave equations
and Laplace equation.
Complex variables:
Analytic functions, Cauchy's integral theorem, Taylor and Laurent series.
Probability and Statistics:
Definitions of probability and sampling theorems, Conditional probability, Mean, median,
mode and standard deviation, Random variables, Poisson, Normal and Binomial
distributions.
Numerical Methods:
Numerical solutions of linear and non-linear algebraic equations Integration by
trapezoidal and Simpson's rule, single and multi-step methods for differential equations.
Structural Engineering
Mechanics:
Bending moment and shear force in statically determinate beams. Simple stress and
strain relationship: Stress and strain in two dimensions, principal stresses, stress
transformation, Mohr's circle. Simple bending theory, flexural and shear stresses,
unsymmetrical bending, shear centre. Thin walled pressure vessels, uniform torsion,
buckling of column, combined and direct bending stresses.
Structural Analysis:
Analysis of statically determinate trusses, arches, beams, cables and frames,
displacements in statically determinate structures and analysis of statically
indeterminate structures by force/ energy methods, 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:
Concrete Technology- properties of concrete, basics of mix design. Concrete design-
basic working stress and limit state design concepts, analysis of ultimate load capacity
and design of members subjected to flexure, shear, compression and torsion by limit
state methods. 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.
Geotechnical Engineering
Soil Mechanics:
Origin of soils, soil classification, three-phase system, fundamental definitions,
relationship and interrelationships, permeability & seepage, effective stress principle,
consolidation, compaction, shear strength.
Foundation Engineering:
Sub-surface investigations- scope, drilling bore holes, sampling, penetration 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 & clays. Deep foundations pile types, dynamic
& static formulae, load capacity of piles in sands & clays, negative skin friction.
Water Resources Engineering
Fluid Mechanics and Hydraulics:
Properties of fluids, principle of conservation of mass, momentum, energy and
corresponding equations, potential flow, applications of momentum and Bernoulli's
equation, laminar and turbulent flow, 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
measurements in channels, tanks and pipes. Dimensional analysis and hydraulic
modeling. Kinematics of flow, velocity triangles and specific speed of pumps and
turbines.
Hydrology:
Hydrologic cycle, rainfall, evaporation, infiltration, stage discharge relationships, unit
hydrographs, flood estimation, reservoir capacity, 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 spillways. Design of
weirs on permeable foundation. Types of irrigation system, irrigation methods. Water
logging and drainage, sodic soils.
Environmental Engineering
Water requirements:
Quality standards, basic unit processes and operations for water treatment. Drinking
water standards, water requirements, basic unit operations and unit processes for
surface water treatment, distribution of water. Sewage and sewerage treatment,
quantity and characteristics of wastewater. Primary, secondary and tertiary treatment of
wastewater, sludge disposal, effluent discharge standards. Domestic wastewater
treatment, quantity of characteristics of domestic wastewater, primary and secondary
treatment Unit operations and unit processes of domestic wastewater, sludge disposal.
Air Pollution:
Types of pollutants, their sources and impacts, air pollution meteorology, air pollution
control, air quality standards and limits.
Municipal Solid Wastes:
Characteristics, generation, collection and transportation of solid wastes, engineered
systems for solid waste management (reuse/ recycle, energy recovery, treatment and
disposal).
Noise Pollution:
Impacts of noise, permissible limits of noise pollution, measurement of noise and control
of noise pollution.
Transportation Engineering
Highway Planning:
Geometric design of highways, testing and specifications of paving materials, design of
flexible and rigid pavements.
Traffic Engineering:
Traffic characteristics, theory of traffic flow, intersection design, traffic signs and signal
design, highway capacity.
Surveying
Importance of surveying, principles and classifications, mapping concepts, coordinate
system, map projections, measurements of distance and directions, leveling, theodolite
traversing, plane table surveying, errors and adjustments, curves.
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