This comprehensive and assimilable text introduces to the students the Mathematical concepts such as Matrices, Vector Calculus, Analytic Functions, Complex Integration and Laplace Transforms. The simple and systematic presentation will enable the students to grasp the concepts easily.

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.

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.

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 w = z+c, cz, 1/z, z2- Bilinear transformation.

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.

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 cons ......

Pages: 162

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