Laplace Transform ( 1 Credit)

Laplace Transforms, Inverse Transforms, Linearity, Shifting, Transforms of Derivatives and Integrals, Differential Equations, Unit Step Function, Second Shifting Theorem, Dirac’s Delta Function. Differentiation and Integration of Transforms. Convolution, Integral Equations, Partial Fractions, Differential Equations, Systems of Differential Equations.

Fourier Series and Fourier Transform

Complex Line Integral, Cauchy Integral Theorem, Cauchy Integral Formula, Derivatives of Analytic Functions. (Sections : 14.1-14.3)

Unit 3

Fourier series, Half range Expansions, Parseval’s Identity, Fourier Integrals, Fourier integral theorem. Sine and Cosine Integrals. Fourier Transforms, Sine and Cosine Transforms, Properties, Convolution theorem.