Fourier Analysis

Fourier series and Fourier co-efficient, Dirichlet’s condition and Fourier expansion, Convergence of Fourier series, Exponential form of Fourier series, Change of interval, Half range series, Parseval’s identity, Fourier integrals.

Fourier Transforms

General transforms, Fourier sine and cosine transforms and their use in boundary value problems.

Z-transform

Discrete transform and definition of Z-transform, Properties, Stability, Causality, Region of convergence, Inverse Z-transform.

Linear Algebra

Matrix Operations: Field and matrices over a field, Product of matrices by partitioning, Symmetric, Diagonal and other special types of matrices with their properties, Elementary transformations and equivalent matrices, Rank, Inverse of a square matrix by elementary row operation.

Systems of Linear Equations

Solutions of systems of homogeneous linear equations, Existence of nontrivial solutions of set of homogeneous linear equations, Consistency of system of linear equations, Solution of non-homogenous equations using matrix.

Vector Spaces

General vector spaces, Column, row and null Spaces, Basis and Dimension.

Eigen Systems

Eigen values and Eigen vectors, Estimation of the size of Eigen values.

Inner-Product Vector Spaces

Inner-Product Spaces, Orthogonality.
Fourier Analysis and Linear Algebra