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FD7 :
MATHEMATICS - II
1.
MATRICES
Definition,
Elements of matrix , Types of matrices ,Algebra of matrices ,
Properties of matrix multiplication, Method of finding the product
of two matrices, Transpose of matrix , Symmetric and Skew-symmetric
matrix , Theorem, Adjoint of a matrix, Inverse of matrix, Theorem ,
Adjoint of a matrix, Inverse of matrix, Elementary Transformation
of a matrix, Rank of matrix , Solution of simultaneous linear
Equation, consistency of equation, characteristics roots or Eigen
values, Caley- Hamilton Theorem, Question Bank, Examination papers.
2. FINITE
DIFFERENCE & DIFFERENCE EQUATION & NUMERICAL METHODS
Finite
Difference: Operators, Difference table, Newton’s formula ,
Lagrange’s interpolation formula, Difference Equation: Introduction
, Solution of a difference equation, Question Bank: Difference
Equation, Numerical methods: Newton Raphson method , Method of false
position, Iteration method.
3.
DIFFERENTIAL EQUATIONS
Definition,
Order and degree of differential equation, Formulation of
Differential Equation, Solution of a differential equation,
Differential Equation of first order and first degree , variable
seperable, Homogeneous Differential Equations , Equation Reducible
to homogeneous form, Linear differential equation,. Equation
Reducible to the linear form, Exact differential equation, Equation
of first order and higher degree, Complete Solution = C.F. + P.I.,
Method of finding the complementary function, Rules to find
particular integrals. Application of Differential Integrals:
Physical applications of linear equations.
4.
FUNCTIONS OF COMPLEX VARIABLE
Introduction, Complex variable, Functions of complex variable,
Limit of a complex variable, Continuity, Differentiability,
Analytic function, The necessary condition for f(z) to be analytic,
Sufficient condition for f(z) to be analytic, C-R equation in polar
form, Harmonic functions, Method to find the conjugate function,
Milne Thomson method, Mapping of transformation, Bilinear
transformation, Schwarz-Christoffel transformation.
Complex
Integration: Cauchy’s integral theorem, Cauchy’s integral formula,
Cauchy’s integral formula for the derivative of an analytic
function, Taylor’s theorem, Laurent series, Singularity if a
function, Residues, Cauchy’s Residue theorem.
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