|
Course
Code :: MA1202 |
(L-T-P) :: 2+2+0 |
Credits
:: 4 |
Detailed
Syllabus:
UNIT - I
Linear Algebra: Rank and inverse of a
matrix. Eigenvalues and
eigenvectors, Hermitian and skew Hermitian matrices. Numerical
solution of
system linear equations - Gauss, Gauss-Jordan elimination and
Gauss-Seidel
iteration methods. Vector spaces - linear dependance of vectors,
basis, linear
transformations.
UNIT-II
Vector Calculus: Scalar and
vector fields, level
surfaces, directional derivative, Gradient, Curl, Divergence,
Laplacian, line
and surface integrals, theorems of Green, Gauss and Stokes,
orthogonal
curvilinear coordinates.
UNIT-III
Numerical Analysis: Finite differences, Newton's
forward and backward
interpolation formulae, central difference interpolation
formulae. Trapezoidal
and Simpson's 1/3rd rule for numerical integration. Solution of
polynomial and
transcendental equations - bisection, Newton-Raphson and
regula-falsi methods.
UNIT-IV
Complex analysis: Limit,
Continuity,
Differentiability and Analyticity of functions, Cauchy-Riemann
equations, Line
integrals in complex plane, Cauchy's integral theorem,
Independence of paths,
Existence of indefinite integral, Cauchy's integral formula,
Derivatives of
analytic functions, Taylor's series, Laurent's series, Zeros and
singularities,
Residue theorem, Evaluation of real integrals.