AM -IV

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