MASTER OF SCIENCE(ENVIRONMENTAL SCIENCE)The University of Kashmir
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Unit I: Fourier Transform
Dirichlet's Condition , Determination of Fourier Coefficients, Fourier Series for arbitrary period, Half-wave expansion, Fourier Integral Theorem, Fourier Sine and Cosine integrals, Fourier Transforms, Properties of Fourier Transforms, Fourier Transform and Dirac delta function, Image processing by Fourier Transform, Improvement of Signal to noise ratio by Fourier Transformation.
Unit II: Laplace Transformation
Integral transforms, Laplace transforms, Simple properties of Laplace transforms, First and second shifting theorem, Deviates of Laplace Transform, Laplace transforms of integrals, Integration of laplace Transform, Inverse of Laplace transform by partial fractions , Laplace transform of solving second order differential equation, Simple applications of Laplace transform in Electronics.
Unit III: Function of complex Variable
Analyticity of Complex variables, Cauchy Riemenn Conditions, Cauchy integral Theorem, Laurent's Series, Singularities, Poles, Residue, Residue Theorem Contour integration for Trigonometric functions( 0 to 2 π) , Contour Integration for functions (-∞ to + ∞ )
Unit IV: Special Function
Power Series solution to differential equations, Power Series solution to Bessel Legendre and Hermit's differential equations, Bessel function, Legndre Polynomial, Hermite Polynomial, Recurrence relations for Legendre, Bessel and Hermite Polynomials.