Subject : Applied Mathematics IV
Module :
1) Matrices :
1.1 Brief revision of vectors over a real field, inner pr oduct, norm,
Linear independence and orthogonality of vectors.
1.2 Characteristic polynomial, character istic equation,
characteristic roots and characteristic vectors of a square
matrix, properties of character istic roots and vectors of different
types of matrices such as orthogonal matrix, Hermitian matrix,
Skew-Hermitian matr ix, Diagonable matr ix , Cayley
Hamilton’s theorem ( without proof) Functions of a square
matrix, Minimal polynomial and Derogator y matrix.
2) Complex variables :
2.1 Functions of complex variables, Analytic function, necessary
f(z)and sufficient conditions forto be analytic (without proof)
2.2 Milne- Thomson method to determine analytic function()
when it’s real or imaginary or its combination is given.
Harmonic function, orthogonal trajectories.
2.3 Mapping: Conformal mapping, linear, bilinear mapping, cross
ratio, fixed points and standard transformations such as Rotation
and magnification, invertion and reflection, translation.
2.4 line integral of a function of a complex variable, Cauchy’s
theorem for analytic function, Cauchy’s Goursat theorem(without proof),
properties of line integral, Cauchy’s integral formula and deductions.
2.5 Singular ities and poles:
Idea of Taylor ’s and Laurent’s ser ies development (without proof)for Residue
2.6 Residue’s theorem, application to evaluate real integrals of type
3) FMathematical programming :
3.1 Linear optimization problem, standard and canonical form of
LPP, basic and feasible solutions, primal simplex method (more
than two variables).
3.2 Artificial variables, Big-M method (method of penalty)
3.3 Dual problem, duality principle Dual simplex method,
degeneracy andalternative optima, unbounded solution.
3.4 Nonlinear Programming, unconstrained optimization, problem
with equality constraints Lagranges Multiplier Method, Problem
with inequality constraints Kuhn-Tucker conditions.
Notes (Reference Book) :
1) Higher Engineering Mathematics 6th Edition By John Bird
http://rapidlibrary.com/files/teraleech-com-185617767x-rar_ulfmvqcm9mifton.html
