Matrix algebra
Systems of linear equations
Eigen values and Eigen vectors
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.
separation of variables
solutions of onedimensional diffusion equation
first and second order one – dimensional wave equation and two-dimensional Laplace equation.
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.
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
Accuracy and precision
error analysis
Numerical solutions of linear and non – linear algebraic equations
Least square approximation
Newton's and Lagrange polynomials
numerical differentiation
Integration by trapezoidal and Simpson's rule
single and multi – step methods for first order differential equations
Free – body diagrams and equilibrium
trusses and frames
virtual work
kinematics and dynamics of particles and of rigid bodies in plane motion
impulse and momentum ( linear and angular ) and energy formulations, collisions.
Stress and strain, elastic constants
Poisson's rati
Mohr's circle for plane stress and plane strain
thin cylinders
shear force and bending moment diagrams
bending and shear stresses
deflection of beams
torsion of circular shafts
Euler's theory of columns
energy methods
thermal stresses
strain gauges and rosettes
testing of materials with universal testing machine
testing of hardness and impact strength.
Displacement
velocity and acceleration analysis of plane mechanisms;
dynamic analysis of linkages
cams
gears and gear trains
flywheels and governors
balancing of reciprocating and rotating masses
gyroscope.
Free and forced vibration of single degree of freedom systems
effect of damping
vibration isolation
resonance
critical speeds of shafts.
Design for static and dynamic loading failure theories
fatigue strength and the S-N diagram
principles of the design of machine elements such as bolted, riveted and welded joints
shafts
gears
rolling and sliding contact bearings
brakes and clutches, springs.
Fluid properties
fluid statics
manometry
buoyancy
forces on submerged bodies
stability of floating bodies
control-volume analysis of mass
momentum and energy
fluid acceleration
differential equations of continuity and momentum
Bernoulli's equation
Dimensional analysis
viscous flow of incompressible fluids
Boundary layer
Elementary turbulent flow
flow through pipes
Head losses in pipes, bends and fittings.
Modes of heat transfer
one dimensional heat conduction
resistance concept and electrical analogy
heat transfer through fins
unsteady heat conduction
lumped parameter system
Heisler's charts
thermal boundary layer
dimensionless parameters in free and forced convective heat transfer
heat transfer correlations for flow over flat plates and through pipes
effect of turbulence
heat exchanger performance
LMTD and NTU methods
radiative heat transfer
StefanBoltzmann law
Wien's displacement law
black and grey surfaces
view factors
radiation network analysis.
Thermodynamic systems and processes
properties of pure substances
Behaviour of ideal and real gases
zeroth and first laws of thermodynamics
Calculation of work and heat in various processes
Second law of thermodynamics
Thermodynamic property charts and tables
Availability and irreversibility
Thermodynamic relations.
Power Engineering
Air and gas compressors
vapour and gas power cycles
concepts of regeneration and reheat. I.C. Engines
Air – standard Otto
Diesel and dual cycles.
Refrigeration and air – conditioning
Vapour and gas refrigeration and heat pump cycles
Properties of moist air
Psychrometric chart
Basic psychrometric processes
Turbomachinery
Impulse and reaction principles
velocity diagrams
Pelton – wheel
Francis and Kaplan turbines.
Structure and properties of engineering materials
phase diagrams
heat treatment
stress-strain diagrams for engineering materials.
Mechanics of machining
Basic machine tools
single and multi – point cutting tools
tool geometry and materials
tool life and wear
economics of machining
principles of non – traditional machining processes
principles of work holding
design of jigs and fixtures.
Different types of castings design of patterns
moulds and cores
solidification and cooling
riser and gating design.
Plastic deformation and yield criteria
fundamentals of hot and cold working processes
Load estimation for bulk ( forging, rolling, extrusion, drawing ) and sheet ( shearing, deep drawing, bending )
Metal forming processes
principles of powder metallurgy.
Principles of welding, brazing, soldering and adhesive bonding
Limits, fits and tolerances
linear and angular measurements
comparators
gauge design
interferometry form and finish measurement
alignment and testing methods
tolerance analysis in manufacturing and assembly.
Basic concepts of CAD / CAM and their integration tools.
Forecasting models
aggregate production planning
scheduling
materials requirement planning
Deterministic and probabilistic models; safety stock inventory control systems.
Operations Research
Linear programming
simplex and duplex method
Transportation
Assignment
network flow models
simple queuing models
PERT and CPM.