The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by: : The parameter s is a complex number: : with real numbers σ and ω. A complex number is defined as a number comprising a real numberpart and an imaginary number part. An imaginary number is a number in the form bi where b is a real number and i is the square root of minus one. (Wiki search)
laplace of sin(at) = (a ) / (s^2 + a^2) thus, laplace of sin 23t, just fill in for a=23 (23) / (s^2 + 23^2) thats it...
The Laplace transform is a widely used integral transform in mathematics with many applications in physics and engineering. It is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms f(t) to a function F(s) with complex argument s, given by the integral F(s) = \int_0^\infty f(t) e^{-st}\,dt.
s
2/s
LaplaceTransform [1, t, s] = 1/s
What are the uses of laplace transforms in engineering fields, good luck :) laplace transforms are so boring i dont have a clue what they do.
Laplace Transforms are used to solve differential equations.
Fritz Oberhettinger has written: 'Tables of Laplace transforms' -- subject(s): Laplace transformation 'Tabellen zur Fourier Transformation' -- subject(s): Mathematics, Tables, Fourier transformations 'Tabellen zur Fourier Transformation' -- subject(s): Mathematics, Tables, Fourier transformations 'Tables of Bessel transforms' -- subject(s): Integral transforms, Bessel functions 'Anwendung der elliptischen Funktionen in Physik und Technik' -- subject(s): Elliptic functions
Some differential equations can become a simple algebra problem. Take the Laplace transforms, then just rearrange to isolate the transformed function, then look up the reverse transform to find the solution.
J. Radlow has written: 'On the double Laplace transforms of some Green's functions' -- subject(s): Accessible book
D. V. Widder was an American mathematician who is best known for his book "Advanced Calculus," which is a popular text on the subject. He also made significant contributions to the field of mathematical analysis.
Laplace is used to write algorithms for various programs. More info is available on wiki .
Laplace transforms are used in electronics to quickly build a mathematical circuit in the frequency domain (or 's' plane) that can then can be converted quickly into the time domain. The theory of how this works is still a puzzle to me, but the methods used are straightforward. Simply solve the integral of the function in question multiplied by the exponential function e-st with limits between 0 and infinity.
yes
Laplace transforms to reduce a differential equation to an algebra problem. Engineers often must solve difficult differential equations and this is one nice way of doing it.
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
Spiegel. has written: 'Trance & Treatment' 'Cost Containment & Drgs' 'Laplace Transforms' 'Complex Variables'