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Laplace Transforms

Many Engineering applications which are not solvable using ordinary differential equations can be solved by Laplace transforms provided the Laplace transforms exist. The Laplace transforms seek the exponential order to exist. Many real life Engineering applications can be brought into the purview of exponential order and also it insists the derivative to exist and piecewise continuity must be present. The foremost advantage of Laplace transforms is it converts difficult differential and integral equations to simple algebraic equations which is easily solvable rather than the original differential/integral equations. It can be used in electrical circuit theory to know the original current passing through a circuit for a given electromotive force, inductance, resistance and capacitance. It is used in vibration theory because it resolves function into moments. It is used to find the bending moment of any RC column in Civil Engineering applications. In circuit theory it is more used. In harmonic oscillators, optical devices also Laplace transforms are used. In spring vibrations relating to Mechanical Engineering problems it is much used. In chemical reactions involving differential equations, Laplace transforms are used. Because of the nature of converting from time domain to frequency domain it is used in Biological (genetical) and stochastic applications. It is widely used in Engineering since many Engineering problems involve the complex differential and the integral equations. ...

Download paper In the paper “Laplace Transforms” the author analyzes Laplace transforms as an integral transforms used to transform a real valued variable t (t≥0) into a complex valued phenomenon s. Laplace transforms are used to solve many complicated differential equations which otherwise are difficult to solve.

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