Course Objectives:

The subject aims to provide the student with

Mathematics fundamental necessary to formulate, solve and analyze engineering problems.
An understanding of Fourier Series and Laplace Transform to solve real world problems.
An understanding of Linear Algebra through matrices.
An understanding of Complex integration.

Course Outline:

Types of matrices, Determinant, adjoint, inverse of matrix, elementary transformation, Elementary matrices, Rank of matrix, Reduction to normal form, canonical form. Rank using elementary transformation, Linear independence end dependence. System of the form AX=0 and AX=B, their solutions. Eigen values, Eigen vectors with properties. Cayley Hamilton theorem with Applications. Minimal polynomial, Diagonalisation.
Laplace Transforms: Definition. Existence conditions, Properties, Laplace transform of periodic functions, Laplace transform of Dirac-Delta function, Inverse Laplace Transform, Convolution theorem, Application of Laplace transforms in solving linear differential equations with initial conditions and system of linear simultaneous differential equations
Fourier Series, Fourier series of Periodic functions, Trigonometric Series, Euler‘s formulas, Dirichlets condition, Even and Odd functions, Half range series, Parseval‘s Identity. Wave equation derivation and solution using separation of variable method. Derivation and solution of one dimensional heat equation using separation of variable method.
Complex Integration, Cauchy‘s Integral theorem and its application. Integral formula for simply and multiply connected domains and its applications. Taylors and Laurents’ series and their application. Singular points. Liouvilles theorem with applications. Residue theorem and applications. Contour Integration. Boundary value problems.

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