MA8251 ENGINEERING MATHEMATICS II Important Topics

Regulation 2017

UNIT I MATRICES

Eigenvalues and Eigenvectors of a real matrix
Cayley-Hamilton theorem
Reduction of a quadratic form to canonical form by orthogonal transformation

UNIT II VECTOR CALCULUS
Divergence and curl
Green‘s, Gauss divergence and Stoke‘s theorems

UNIT III ANALYTIC FUNCTIONS
Analytic functions
Harmonic conjugates
Conformal mapping
Bilinear transformation.
UNIT IV COMPLEX INTEGRATION
Cauchy‘s integral theorem
Cauchy‘s integral formula
Taylor‘s and Laurent‘s
Residue theorem

UNIT V LAPLACE TRANSFORMS

Transforms of elementary functions
Shifting theorems
Initial and final value theorems
Convolution theorem