Matrix algebra, Systems of linear equations, Eigen values
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
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.
Analytic functions, Cauchy’s integral theorem, Taylor and
Probability and Statistics:
Definitions of probability and sampling theorems,
Conditional probability, Mean, median, mode and standard
deviation, Random variables, Poisson, Normal and Binomial
Numerical solutions of linear and non-linear algebraic
equations Integration by trapezoidal and Simpson’s rule,
single and multi-step methods for differential equations.
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.
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 Technology- properties of concrete, basics of mix
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.
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.
Origin of soils, soil classification, three - phase system,
fundamental definitions, relationship and
interrelationships, permeability and seepage, effective
stress principle, consolidation, compaction, shear strength.
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 and clays.
Deep foundations – pile types, dynamic and static formulae,
load capacity of piles in sands and clays, negative skin
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.
Hydrologic cycle, rainfall, evaporation, infiltration, stage
discharge relationships, unit hydrographs, flood estimation,
reservoir capacity, reservoir and channel routing. Well
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.
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
waste water, 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
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
Impacts of noise, permissible limits of noise pollution,
measurement of noise and control of noise pollution.
Geometric design of highways, testing and specifications of
paving materials, design of flexible and rigid pavements.
Traffic characteristics, theory of traffic flow,
intersection design, traffic signs and signal design,
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