Definition of Laplace Transform: The Definition of Laplace Transform is used to solve differential equations and corresponding initial and final value problems. Laplace transforms are widely used in engineering, particularly when the driving function has discontinuities and appears for a short … (Read More)

Laplace Properties: Laplace transforms have the following Laplace Properties. (a) Superposition Property: The first Laplace Properties is Superposition Property. The Laplace transform of the sum of the two or more functions is equal to the sum of transforms of the individual function, i.e. if Consider … (Read More)

Laplace Theorem: The Laplace theorem is given by Differentiation Theorem Integration Theorem Differentiation of Transforms Integration of transforms First Shifting Theorem Second Shifting Theorem Initial Value Theorem Final Value Theorem (a) Differentiation Theorem: If a function f(t) is piecewise continuous, then the Laplace transform of its derivative d/dt is given … (Read More)

Inverse Transformation: We already discussed Laplace transforms of a functions f(t). If the function in frequency domain F(s) is given, the Inverse Transformation can be determined by taking the partial fraction expansion which will be recognizable as the transform of known … (Read More)

Laplace Transform Partial Fraction: Most transform methods depend on the partial fraction of a given transform function. Given any solution of the form N(s) = P(s)/Q(s), the inverse Laplace transform can be determined by expanding it into partial fractions. The Laplace … (Read More)

Application of Laplace Transform: Application of Laplace Transform methods are used to find out transient currents in circuits containing energy storage elements. To find these currents, first the differential equations are formed by applying Kirchhoff’s laws to the circuit, then these … (Read More)