ENGINEERING MATHEMATICS
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, 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.
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.
Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames;
Virtual work; kinematics and dynamics of particles and of rigid
Bodies in plane motion, including impulse and momentum
(Linear and angular) and energy formulations; impact.
Strength of Materials: Stress and strain, stress-strain relationship and elastic
Constants, 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; strain energy methods;
Thermal stresses.
Theory of Machines: Displacement, velocity and acceleration analysis of plane
Mechanisms; dynamic analysis of slider-crank mechanism;
Gear trains; flywheels.
Vibrations: Free and forced vibration of single degree of freedom systems;
Effect of damping; vibration isolation; resonance, critical
Speeds of shafts.
Design: 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, spur gears, rolling and sliding contact bearings, brakes
and clutches.
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; control-
Volume analysis of mass, momentum and energy; fluid
Acceleration;
differential equations of continuity and momentum; Bernoulli’s
equation; viscous flow of incompressible fluids; boundary layer;
Elementary turbulent flow; flow through pipes, head losses in
pipes, bends etc.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction,
resistance concept, electrical analogy, unsteady heat
conduction, fit, dimensionless parameters in free and forced
convective heat transfer, various correlations for heat transfer
in flow over flat plates and through pipes; thermal boundary
layer; effect of turbulence; radiative heat transfer, black and
grey surfaces, shape factors, network analysis; heat
exchanger performance, LMTD and NTU methods.
Thermodynamics: Zeroth, First and Second laws of thermodynamics;
Thermodynamic system and processes; Carnot
cycle. Irreversibility and availability; behavior of ideal and real
gases, properties of pure substances, calculation of work and
heat in ideal processes; analysis of thermodynamic cycles
related to energy conversion.
Applications: Power Engineering: Steam Tables, Rankine, Brayton cycles with
Regeneration and reheat.I.C. Engines: air-standard Otto, Diesel
cycles. Refrigeration and air-conditioning: Vapor refrigeration cycle,
heat pumps, gas refrigeration, Reverse Brayton cycle; moist
air: psychometric chart, basic psychometric
Processes. Turbomachinery: Pelton-wheel, Francis and Kaplan
Turbines — impulse and reaction principles, velocity diagrams.
Engineering Materials: Structure and properties of engineering materials, heat
Treatment, stress-strain diagrams for engineering
Materials.
Metal Casting: Design of patterns, moulds and cores; solidification and
Cooling; riser and gating design, design considerations.
Forming: 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.
Joining: Physics of welding, brazing and soldering; adhesive
Bonding; design considerations in welding.
Machining and Machine Tool Operations: Mechanics of machining, 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, principles of
design of jigs and fixtures
Metrology and Inspection: 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.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration
Tools.
Production Planning and Control: Forecasting models, aggregate production planning,
Scheduling, materials requirement planning.
Inventory Control: 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.
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.
APPLIED MECHANICS AND DESIGN
Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames;
Virtual work; kinematics and dynamics of particles and of rigid
Bodies in plane motion, including impulse and momentum
(Linear and angular) and energy formulations; impact.
Strength of Materials: Stress and strain, stress-strain relationship and elastic
Constants, 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; strain energy methods;
Thermal stresses.
Theory of Machines: Displacement, velocity and acceleration analysis of plane
Mechanisms; dynamic analysis of slider-crank mechanism;
Gear trains; flywheels.
Vibrations: Free and forced vibration of single degree of freedom systems;
Effect of damping; vibration isolation; resonance, critical
Speeds of shafts.
Design: 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, spur gears, rolling and sliding contact bearings, brakes
and clutches.
FLUID MECHANICS AND THERMAL SCIENCES
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; control-
Volume analysis of mass, momentum and energy; fluid
Acceleration;
differential equations of continuity and momentum; Bernoulli’s
equation; viscous flow of incompressible fluids; boundary layer;
Elementary turbulent flow; flow through pipes, head losses in
pipes, bends etc.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction,
resistance concept, electrical analogy, unsteady heat
conduction, fit, dimensionless parameters in free and forced
convective heat transfer, various correlations for heat transfer
in flow over flat plates and through pipes; thermal boundary
layer; effect of turbulence; radiative heat transfer, black and
grey surfaces, shape factors, network analysis; heat
exchanger performance, LMTD and NTU methods.
Thermodynamics: Zeroth, First and Second laws of thermodynamics;
Thermodynamic system and processes; Carnot
cycle. Irreversibility and availability; behavior of ideal and real
gases, properties of pure substances, calculation of work and
heat in ideal processes; analysis of thermodynamic cycles
related to energy conversion.
Applications: Power Engineering: Steam Tables, Rankine, Brayton cycles with
Regeneration and reheat.I.C. Engines: air-standard Otto, Diesel
cycles. Refrigeration and air-conditioning: Vapor refrigeration cycle,
heat pumps, gas refrigeration, Reverse Brayton cycle; moist
air: psychometric chart, basic psychometric
Processes. Turbomachinery: Pelton-wheel, Francis and Kaplan
Turbines — impulse and reaction principles, velocity diagrams.
MANUFACTURING AND INDUSTRIAL ENGINEERING
Engineering Materials: Structure and properties of engineering materials, heat
Treatment, stress-strain diagrams for engineering
Materials.
Metal Casting: Design of patterns, moulds and cores; solidification and
Cooling; riser and gating design, design considerations.
Forming: 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.
Joining: Physics of welding, brazing and soldering; adhesive
Bonding; design considerations in welding.
Machining and Machine Tool Operations: Mechanics of machining, 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, principles of
design of jigs and fixtures
Metrology and Inspection: 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.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration
Tools.
Production Planning and Control: Forecasting models, aggregate production planning,
Scheduling, materials requirement planning.
Inventory Control: 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.
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