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Definition, Laplace transforms of elementary functions. Properties of Laplace transform, Laplace transform of derivatives, integrals. Multiplication by tn and division by t properties. Periodic functions and their Laplace transforms. Inverse Laplace transforms and their properties. Convolution theorem, Inverse Laplace transforms by integral and partial fraction methods. Heavisides expansion formula. Solution of ordinary differential equations by Laplace transform. Applications of Laplace transformation on various fields of engineering.

Introduction. The solution of p0(x) y” + p1(x) y’+ p2(x) y =0, when p0(0)≠0. Validity of series solution. Ordinary point, singular point. Forbenius method, indicial equation. Bessel’s differential equation, its solution of first kind and its recurrence formulae. Legendre differential equation and its solution. Rodrigues formula.

Definition, Fourier transform of simple function, magnitude and phase spectra, Fourier transform theorems, inverse Fourier transform, solution of differential equations using Fourier transform.

Introduction, Sets, relations, equivalence relations, functions, algorithms, complexity of algorithms, mathematical induction, Basic principles, Permutations and combinations, generalized permutations and combinations, binomial coefficients and combinatorial identities, recurrence relations, solving recurrence relations, an application to the analysis of algorithm, Graph Theory, Examples, representation of graphs, paths and circuits, a shortest- path algorithm, isomorphism of graphs, planar graphs, Trees, Properties of trees, spanning trees, minimal spanning trees, tree traversal, sorting, game trees