Examples: How To Apply The Properties and Theorems
The Laplace transform is used frequently in engineering and physics; the output of a linear time invariant system can be calculated by convolving its unit impulse response with the input signal. Performing this calculation in Laplace space turns the convolution into a multiplication; the latter being easier to solve because of its algebraic form. For more information, see control theory.
The Laplace transform can also be used to solve differential equations and is used extensively in electrical engineering. The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra. The original differential equation can then be solved by applying the inverse Laplace transform. The English electrical engineer Oliver Heaviside first proposed a similar scheme, although without using the Laplace transform; and the resulting operational calculus is credited as the Heaviside calculus.
Read more about this topic: Laplace Transform
Famous quotes containing the words apply and/or properties:
“When a bachelor of philosophy from the Antilles refuses to apply for certification as a teacher on the grounds of his color I say that philosophy has never saved anyone. When someone else strives and strains to prove to me that black men are as intelligent as white men I say that intelligence has never saved anyone: and that is true, for, if philosophy and intelligence are invoked to proclaim the equality of men, they have also been employed to justify the extermination of men.”
—Frantz Fanon (1925–1961)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)