**Linear Algebra:** Matrix algebra; Systems of linear equations; Eigen values and Eigen vectors.

**Calculus:** Functions of single variable; Limit, continuity and differentiability; Mean value
theorems, local maxima and minima, Taylor and Maclaurin series; Evaluation of definite
and indefinite integrals, application of definite integral to obtain area and volume; Partial
derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities, Directional
derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

**Ordinary Differential Equation (ODE):** First order (linear and non-linear) equations; higher
order linear equations with constant coefficients; Euler-Cauchy equations; Laplace
transform and its application in solving linear ODEs; initial and boundary value problems.

**Partial Differential Equation (PDE):** Fourier series; separation of variables; solutions of onedimensional
diffusion equation; first and second order one-dimensional wave equation
and two-dimensional Laplace equation.

**Probability and Statistics:** Definitions of probability and sampling theorems; Conditional
probability; Discrete Random variables: Poisson and Binomial distributions; Continuous
random variables: normal and exponential distributions; Descriptive statistics - Mean,
median, mode and standard deviation; Hypothesis testing.

**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.

**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.

**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 analysisinsands & clays. Deep foundations–pile types, dynamic
& static formulae, load capacity of piles in sands & clays, negative skin friction.

**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.

**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.

**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.