ENGINEERING MATHEMATICS
Linear Algebra
Algebra of matrices, system of linear equations, eigenvalues and eigenvectors.
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Calculus
Taylor Series, Fourier Series, partial derivatives, total derivatives, definite and improper
integrals, multiple integrals.
Vector Calculus
Gradient, divergence and curl, line and surface integrals, Green, Gauss and Stokes’ theorems.
Differential Equations
Linear ODE’s, first order non-linear ODE’s, initial and boundary value problems, Laplace transform,
PDE’s-Laplace, wave and diffusion equations.
Numerical Methods
Solution of system of linear equations, interpolation, numerical integration, Newton-Raphson method,
Runge-Kutta method.
Probability and Statistics
Gaussian, Weibul distribution and their properties, method of least squares, regression analysis,
analysis of variance.
APPLIED MECHANICS AND DESIGN
Engineering Mechanics
Equivalent force systems, free-body concepts, equations of equilibrium, trusses and frames, virtual work
and minimum potential energy. Kinematics and dynamics of particles and rigid bodies, impulse and momentum
(linear and angular), energy methods, central force motion.
Strength of Materials
Stress and strain, stress-strain relationship and elastic constants, Mohr’s circle for plane stress
and plane strain, shear force and bending moment diagrams, bending and shear stresses, deflection of beams
torsion of circular shafts, thin and thick cylinders, 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, planar cams and followers, gear tooth profiles, kinematics and design of gears, governors and flywheels,
balancing of reciprocating and rotating masses.
Vibrations
Free and forced vibration of single degree freedom systems, effect of damping, vibration isolation,
resonance, critical speed of rotors.
Design of Machine Elements
Design for static and dynamic loading, failure theories, fatigue strength -- design of bolted, riveted
and welded joints -- design of shafts and keys -- design of spur gears, rolling and sliding contact bearings
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