An admirer of Euler called Joseph Lagrange made some modifications to Euler’s work and did further work. Euler however did not pursue it very far and left it. This is when another great mathematician called Leonhard Euler was researching on other types of integrals. The complete history of the Laplace Transforms can be tracked a little more to the past, more specifically 1744. Other famous scientists such as Niels Abel, Mathias Lerch, and Thomas Bromwich used it in the 19th century. This transform was made popular by Oliver Heaviside, an English Electrical Engineer. ![]() He used a similar transform on his additions to the probability theory. This transform is named after the mathematician and renowned astronomer Pierre Simon Laplace who lived in France. The transform method finds its application in those problems which can’t be solved directly. Transformation in mathematics deals with the conversion of one function to another function that may not be in the same domain. If you do have an equation without the known constants, then this method is useless and you will have to find another method. That is, you can only use this method to solve differential equations WITH known constants. Laplace transforms can only be used to solve complex differential equations and like all great methods, it does have a disadvantage, which may not seem so big. ![]() ![]() Where the Laplace Operator, s = σ + jω will be real or complex j = √(-1) Disadvantages of the Laplace Transformation Method Then the Laplace transform of f(t), F(s) can be defined as To understand the Laplace transform formula: First Let f(t) be the function of t, time for all t ≥ 0
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