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# Laplace Transform

Select from the following:
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.

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