MATH247

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Linear Algebra, Laplace Transformation and Fourier Analysis

4 Credit Hour Course

Intended For Level 2 Term 2 Students

Prerequisite:

Linear Algebra: Introduction to systems of linear equations; Gaussian elimination; Inverse of a matrix; Eigen values and eigen vectors; Cayley-Hamilton theorem; Euclidean n-space; Linear transformations from IRn to IRm; Properties of linear transformations from IRn to IRm; Real vector spaces and subspaces; Basis and Dimension, Change of basis, Rank and Nullity; Inner product spaces; Diagonalization; Linear transformations: Kernel and Range. (1.5 credit) Laplace Transform & Fourier Analysis: Laplace transforms of some elementary functions including unit step functions, Periodic functions etc.; Inverse Laplace transforms; Solutions of differential equations by Laplace transforms. (1 credit) Fourier Series: Fourier Integrals; Fourier transforms and their uses in solving boundary value problems of wave equations. (1.5 credit)