**Civil Engineering**

**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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