Laplace Transforms And Fourier Analysis

Laplace transforms: definition, properties, transforms of derivatives and integrals, shifting theorems, unit step function, Dirac delta function, inverse Laplace transforms, convolution theorem, solution of ordinary differential equations; Fourier analysis: Fourier series, functions of arbitrary period, half-range expansions, Sturm-Liouville problems, introduction to Fourier transforms and engineering applications.