MA8251 ENGINEERING MATHEMATICS – 2 REGULATION 2017

UNIT I MATRICES

Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of
Eigenvalues and Eigenvectors – Cayley-Hamilton theorem – Diagonalization of matrices –
Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic
forms.

UNIT II VECTOR CALCULUS

Gradient and directional derivative – Divergence and curl – Vector identities – Irrotational and
Solenoidal vector fields – Line integral over a plane curve – Surface integral – Area of a curved
surface – Volume integral – Green’s, Gauss divergence and Stoke’s theorems – Verification and
application in evaluating line, surface and volume integrals.

UNIT III ANALYTIC FUNCTIONS

Analytic functions – Necessary and sufficient conditions for analyticity in Cartesian and polar
coordinates – Properties – Harmonic conjugates – Construction of analytic function – Conformal
mapping – Mapping by functions, – Bilinear transformation.

UNIT IV COMPLEX INTEGRATION

Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s and Laurent’s
series – Singularities – Residues – Residue theorem – Application of residue theorem for
evaluation of real integrals – Use of circular contour and semicircular contour.

UNIT V LAPLACE TRANSFORMS

Existence conditions – Transforms of elementary functions – Transform of unit step function and
unit impulse function – Basic properties – Shifting theorems -Transforms of derivatives and
integrals – Initial and final value theorems – Inverse transforms – Convolution theorem –
Transform of periodic functions – Application to solution of linear second order ordinary differential
equations with constant coefficients.

DOWNLOAD SYLLABUS CLICK HERE