Website owner:  James Miller

Laplace Transform

Laplace transform. Dirichlet conditions. Sectionally continuous (or piecewise continuous) function. Function of exponential order. Piecewise regular function. Inverse Laplace transform. Properties of Laplace transforms. Initial and final-value theorems.

Special functions and their transforms. Gamma function. Bessel functions. Error function. Complementary Error function. Exponential integral. Sine and cosine integrals. Dirac delta function. Unit Step Function. Null function.

Methods of finding Laplace transforms and inverse transforms. Properties of inverse Laplace transforms. Convolution of two functions. Convolution theorem. Heaviside expansion formulas.

Applications of the Laplace transform in solving ordinary differential equations

Applications of the Laplace transform in solving integral equations. Laws for convolution. Abel's integral equation. The tautochrone problem. Integro-differential equations. Conversion of linear differential equations into integral equations.

The Complex Inversion Formula. Bromwich contour.

Laplace transform of partial derivatives. Applications of the Laplace transform in solving partial differential equations.