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 designbasic
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 slopesinfinite
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.
Source: http://gate.iitd.ac.in
Edited by: http://ipuedu.blogspot.com
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