Как найти изображение по лапласу онлайн - Исправление недочетов и поиск решений вместе с Examum.ru

Преобразованием Лапласа некоторой функции

называется интегральное преобразование вида:

Функция
называется оригиналом, функция
— изображением. Причём

является функцией комлексной переменной, т.е.
.

В качестве примера, найдём изображение

функции оригинала
.

Для этого нам необходимо воспользоваться приведённой выше формулой и
вычислить интеграл:

То, что функция
является изображением функции
записывается как
или
.

Важным свойством
преобразования Лапласа
является то, что если
, то

Указанное свойство активно используется при
решении дифференциальных уравнений
поскольку позволяет сводить последние к алгебраическим.

Наш онлайн калькулятор, построенный на основе системы Wolfram Alpha позволяет найти преобразование Лапласа практически любой, даже очень сложной функции.

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Интегральное преобразование Лапласа онлайн, калькулятор изображения функций.

Теория функций комплексного переменного.

Основные функции

$x^{a}$ : x^a

модуль x: abs(x)

: Sqrt[x]
: x^(1/n)
$a^{x}$ : a^x
$log_{a}x$ : Log[a, x]
: Log[x]
: cos[x] или Cos[x]

: sin[x] или Sin[x]

: tan[x] или Tan[x]

: cot[x] или Cot[x]

: sec[x] или Sec[x]

: csc[x] или Csc[x]

: ArcCos[x]

: ArcSin[x]

: ArcTan[x]

: ArcCot[x]

: ArcSec[x]

: ArcCsc[x]

: cosh[x] или Cosh[x]

: sinh[x] или Sinh[x]

: tanh[x] или Tanh[x]

: coth[x] или Coth[x]

: sech[x] или Sech[x]

: csch[x] или Csch[е]

: ArcCosh[x]

: ArcSinh[x]

: ArcTanh[x]

: ArcCoth[x]

: ArcSech[x]

: ArcCsch[x]

[19.67] =19: integral part of (19.67) — выделяет целую часть числа (integerPart)

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Examples

laplace:e^{frac{t}{2}}
laplace:e^{-2t}sin^{2}(t)
laplace:8pi
laplace:g(t)=3sinh(2t)+3sin(2t)
inverse:laplace:frac{s}{s^{2}+4s+5}
inverse:laplace:frac{1}{x^{frac{3}{2}}}
inverse:laplace:frac{sqrt{pi}}{3x^{frac{3}{2}}}
inverse:laplace:frac{5}{4x^2+1}+frac{3}{x^3}-5frac{3}{2x}
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Description

Find the Laplace and inverse Laplace transforms of functions step-by-step

Frequently Asked Questions (FAQ)

How do you calculate the Laplace transform of a function?
The Laplace transform of a function f(t) is given by: L(f(t)) = F(s) = ∫(f(t)e^-st)dt, where F(s) is the Laplace transform of f(t), s is the complex frequency variable, and t is the independent variable.
What is mean by Laplace equation?
The Laplace equation is a second-order partial differential equation that describes the distribution of a scalar quantity in a two-dimensional or three-dimensional space. The Laplace equation is given by: ∇^2u(x,y,z) = 0, where u(x,y,z) is the scalar function and ∇^2 is the Laplace operator.
What kind of math is Laplace?
Laplace transforms are a type of mathematical operation that is used to transform a function from the time domain to the frequency domain. They are a specific example of a class of mathematical operations called integral transforms.
Why is it called Laplace?
The Laplace equation is named after the discoverer Pierre-Simon Laplace, a French mathematician and physicist who made significant contributions to the field of mathematics and physics in the 18th and 19th centuries.
What does the Laplace equation use for?
The Laplace equations are used to describe the steady-state conduction heat transfer without any heat sources or sinks
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laplace-calculator

How to Use the Laplace Transform Calculator?

The procedure to use the Laplace transform calculator is as follows:

Step 1: Enter the function, variable of function, transformation variable in the input field

Step 2: Click the button “Calculate” to get the integral transformation

Step 3: The result will be displayed in the new window

What is the Laplace Transform?

In Mathematics, the Laplace transform is an integral transformation, which transforms the real variable function “t” to the complex variable function. The main purpose of this transformation is to convert the ordinary differential equations into an algebraic equation that helps to solve the ordinary differential equations easily. Laplace transform has many applications in the field of Science and Engineering.

Standard Form

The standard form to represent the Laplace transform is as follows:

(begin{array}{l}F(s)=L(f(t))= int_{0}^{infty }e^{-st}f(t)dtend{array} )

Where

f(t) is defined for all real numbers t ≥ 0

“s” is the complex number frequency parameter

Frequently Asked Questions on Laplace Transform Calculator

What is the main purpose of the Laplace Transform?

The main purpose of the Laplace transform is to transform the Ordinary Differential Equations (ODEs) into algebraic equations. This conversion helps to solve the ODEs easily.

Mention the significance of the Laplace Transform

The Laplace transform gives useful techniques for determining certain types of differential equations when initial conditions are given, especially when the primary values are zero.

Write down the applications of the Laplace transform.

The applications of the Laplace transform are:

Circuit Analysis
Signal processing
Communication Systems

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