Solution of Differential Equations using Exponential of a Matrix

Abstract

Our main purpose in this project is to help reader find a clear and glaring relationship between linear algebra and differential equations, such that the applications of the former may solve the system of the latter using exponential of a matrix. Applications to linear differential equations on account of eigen values and eigenvectors, diagonalization of n-square matrix using computation of an exponential of a matrix using results and ideas from elementary studies form the core study of our project. Keywords : matrix,fundamental matrix, ordinary differential equations, systems of ordinary differential equations, eigenvalues and eigenvectors of a matrix, diagonalisation of a matrix, nilpotent matrix, exponential of a matrix