Introduction: Engineering application of optimization, Statement and classification
of optimization problem, single variable and multivariable optimization with and
without constraints.
Units: II
Linear Programming: Formulation of Linear Programming problem, Graphical
Approach, General Linear Programming problem, Simple Method. Duality in Linear
Programming and Transportation Problems.
Units: III
Project Scheduling: Project Scheduling by PERT and CPM Network Analysis.
Sequencing Theory: General Sequencing problem n-jobs through 2 machines & 3
machines and 2-jobs through m machines.
Units: IV
LAPLACE TRANSFORM: Laplace transform with its simple properties. Inverse
Laplace transform, convolution theorem (without proof), solution of ordinary
differential equation with constant coefficient, solution of partial differential
equation having constant coefficient with special reference to diffusion, Heat
conduction and wave equation. Boundary value problems
Units: V
NUMERICAL ANALYSIS: Difference operators forward, backward, control, shift
and average operators and relation between them. Newton’s and Gauss forward and
backward interpolation formula for equal interval, Sterling & formula for control
difference. Lagrange’s Interpolation formula. Inverse Interpolation.
Numerical differentiation by Newton’s, Gauss and Sterling’s formula. Numerical
Integration by Simpson’s one third and there eight rule. Numerical Integration of
ordinary differential equation of first order by Picard’s method, Euler’s and modified
Euler’s method, Milure’s method and Runga Kutta fourth order method. Solution of
difference equation.