SEMESTER III
MA211
LINEAR ALGEBRA, NUMERICAL ANALYSIS AND
TRANSFORMS
(3 ‐ 0 ‐ 0) 3 credits
Linear Algebra: matrices; solution space of system of equations Ax = b, eigenvalues and
eigenvectors, Cayley‐Hamilton theorem – Definition of Group, ring field – Vector spaces over
real field, subspaces, linear dependence, independence, basis, dimension – inner product –
Gram‐Schmidt orthogonalization process – linear transformation; null space and nullity, range
and rank of a linear transformation.
Numerical Methods: solution of algebraic and transcendental equations – solution of system of
linear equations – numerical integration – interpolation – solution of ordinary differential
equations.
Transforms: Fourier series expansion of periodic functions with period two – Fourier series of
even and odd functions – half‐range series – Fourier series of functions with arbitrary period –
conditions
of
convergence
of
Fourier
series.
Fourier integral – the Fourier transform pair – algebraic properties of Fourier transform –
convolution, modulation, and translation – transforms of derivatives and derivatives of
transform – inversion theory.
Laplace transforms of elementary functions – inverse Laplace transforms – linearity property –
first and second shifting theorem – Laplace transforms of d