3CS6A Advanced Engineering Mathematics
Unit I
Introduction: Engineering application of optimization, Statement and classification
of optimization problem, single variable and multivariable optimization with and
without constraints.
Unit II
Linear Programming: Formulation of Linear Programming problem, Graphical
Approach, General Linear Programming problem, Simplex Method. Duality in
Linear Programming and Transportation Problems.
Unit III
Elements of Number Theory: Divisibility and Euclid Algorithm, Primes and the
Sieve of Eratosthenes, testing for primes, Prime Number Theorem, Euler’s, Fermat’s
Little theorems, Congruences, Computing Inverse in Congruences, Legendre and
Jacobi Symbols, Chinese Remainder Theorem,
Algebraic Structures in Computing (Definitions, properties and Elementary
Operations Only): Groups, subgroup, order of group, cyclic group, ring, field,
division algorithm, polynomial over a field. Galois Field
Unit 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
Unit V
NUMERICAL ANALYSIS: Difference operators forward, backward, central, shift
and average operators and relation between them. Newton’s and Gauss forward and
backward interpolation formula for equal interval, Stirling’s formula for central
difference. Lagrange’s Interpolation formula and 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, Milne’s method and Runga-Kutta fourth order method. Solution of
difference equation.
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