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 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; simple bending 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; 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.
GEOTECHNICAL ENGINEERING
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.
ENVIRONMENTAL ENGINEERING
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.
TRANSPORTATION ENGINEERING
Highway planning; geometric design of
highways; testing and specifications of
paving materials; design of flexible and
rigid pavements.
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