MAT 490 - Advanced Engineering Mathematics
||Laplace Transform, Existence of Laplace Transform, Inverse Laplace Transform, Laplace Transform of Derivatives and Integrals, Shifting on the s-axis, Shifting on the t-axis, Differentiation and Integration of Laplace Transform , Convolution, Inverse Laplace Transform of partial Fractions, Inverse Laplace Transform of periodic Functions, Fourier Series (FS) for Functions of period 2? or arbitrary period, Fourier Series for Even and odd Functions, Half?Range Fourier Expansion, Determination of Fourier Coefficients without Integration, Fourier Approximation and minimum square error, The Fast Fourier Transform, Complex Variable Functions, Limits and Continuity, Derivatives, Analyticity and Cauchy-Riemann Equations, Conformal Mapping, Relation between Analyticity and Conformality, Mobius and other Transformations, Complex Integrals, Cauchy?s Integral Formulae, Taylor?s Series, Singular Points, Laurent?s Series, Residues and Residue Theorem, Evaluation of Real Definite Integrals using Complex Integrals.
[Pre-requisite: MAT 250 ]
[Credit Hours: 3]