# Easy Laplace Transform Calculator

By | October 15, 2017

# What is Laplace Transform Calculator?

For mathematical integral transform,  Laplace Transform Calculator is used to solve linear variant equations. Pierre-Simon Laplace is discoverer of Laplace transform.

The Laplace Transforms have several main programs inside the math, technology, production and chance principle. It remedy functions into with Fourier transform. it’s far a laplace solver or laplace rechner. It also used for resolving the differential and important equations.

# What is Laplace Transform?

The laplace trasnformation is a completely beneficial tool in fixing differential equations bobbing up out of many physical conditionsdue to its simplicity and usefulness it’s miles extensively used in engineering maths. Laplace transforms reduce the problem of solving differential equation to an algebraic problem. The switching from operations of calculus to algebraic operations is referred to as Operational calculus, a completely essential vicinity
of carried out mathematics, and the laplace transform technique is practically the maximum crucial method for this motive.

# How to use Laplace Transform Calculator?

Below is the calculator to calculate Laplace Transform :

1. Input the text of which you want to transform in first field name “Laplace Transform of” e.g cos,sin etc.
2. Enter the variable of function in second field.
3. Enter Transform variable in third field
4. Click on calculate button to calculate filled data.

Also check out Inverse Laplace Transform Calculator.

# Manual Transformation of  Function

Manual laplace transformation is depends on formulas.

### Formulas for transform :

L[tn] = $$\frac{n!}{s^{n + 1}}$$

L[eat] = $$\frac{1}{s – 1}$$
L[Sin at] = $$\frac{a}{s^2 + a^2}$$
L[Cos at] = $$\frac{s}{s^2 + a^2}$$
L[Sinh at] =$$\frac{a}{s^2 – a^2}$$
L[Cosh at] =$$\frac{s}{s^2 – a^2}$$
L[t sin at] = $$\frac{2as}{(s^2 + a^2)^{2}}$$
L[t cos at] =$$\frac{s^{2} – a^{2}}{(s^2 + a^2)^{2}}$$
L[eat tn] =$$\frac{n!}{(s – a)^{n+1}}$$
L[t e-t] = $$\frac{1}{(s + 1)^{2}}$$

Step 1 : Observe the function which you want to solve.

Step 2 : Now check out the above given formulas and solve given function according to formula.

### Example of  Manual Laplace Transform :

Laplace Transform of Cos 5t  is :

As per given formulas above L[Cos at] =  $$\frac{s}{s^2 + a^2}$$

then L[Cos at] = $$\frac{s}{s^2 + 5^2}$$ = $$\frac{s}{s^2 + 25}$$

Answer is :  L[Cos at] = $$\frac{s}{s^2 + 25}$$