Functions of Several Variables Anna University

Can you provide me the syllabus of Functions of Several Variables under Applied Mathematics subject under B.E. Electronics and Communication Engineering (Part Time) course offered by Anna University?

[Shaleen]

The syllabus of Functions of Several Variables under Applied Mathematics subject under B.E. Electronics and Communication Engineering (Part Time) course offered by Anna University is as follows:

Applied Mathematics

Functions of Several Variables
Partial derivatives – Homogeneous functions and Euler’s theorem – Total derivative – Differentiation of implicit functions – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of two variables - Maxima and minima of functions of two variables.

Matrices
Characteristic equation – Eigenvalues and Eigenvectors of a real matrix – Properties of eigenvalues and eigenvectors – Cayley-Hamilton Theorem – Diagonalization of matrices - Reduction of a quadratic form to canonical form by orthogonal transformation.
Analytic Function
Analytic functions – Necessary and sufficient conditions for analyticity – Properties – Harmonic conjugates – Construction of analytic function – Conformal Mapping – Mapping by functions w = a + z , az, 1/z, - Bilinear transformation.

Complex Integration
Line Integral – Cauchy’s theorem and 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 with no pole on real axis.

Laplace Transforms
Existence conditions – Transforms of elementary functions – Basic properties – Transforms of derivatives and integrals –Inverse transforms – Convolution theorem – Transform of periodic functions - Application to solution of linear ordinary differential equations with constant coefficients.