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.
Engineering is an applied science that is heavily involved with mathematics. Every discipline of engineering (chemical, mechanical, structural, electrical, computer, etc.) uses a vast amount of mathematics ranging from algebra to Laplace Transforms to define, explain and understand the problems that arise with its area of expertise. Many other fields of pure science use mathematics beyond engineering but the aim of engineering is to apply mathematics to real world problems.
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.
We are using integrated circuits inside the CPU. Laplace Transformations helps to find out the current and some criteria for the analysing the circuits... So, in computer field Laplace tranformations plays vital role...
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.
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.
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.
Several types. To name a few:differential and integral caculus (Fourrier and Laplace transforms)algebrageometrystatistica dn probabilitymatriciesstatistics
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.
Engineering is an applied science that is heavily involved with mathematics. Every discipline of engineering (chemical, mechanical, structural, electrical, computer, etc.) uses a vast amount of mathematics ranging from algebra to Laplace Transforms to define, explain and understand the problems that arise with its area of expertise. Many other fields of pure science use mathematics beyond engineering but the aim of engineering is to apply mathematics to real world problems.
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.
The Laplace equation is used commonly in two situations. It is used to find fluid flow and in calculating electrostatics.
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We are using integrated circuits inside the CPU. Laplace Transformations helps to find out the current and some criteria for the analysing the circuits... So, in computer field Laplace tranformations plays vital role...
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.