Laplace Calculator

The Laplace Transform Calculator helps users compute the Laplace transform, region of convergence, and original function of given mathematical expressions based on function type and corresponding parameters.

Use Our Laplace Calculator

Using the Laplace Transform Calculator

Introduction

This guide helps you use the Laplace Transform Calculator to find the Laplace transform of various mathematical functions. The calculator supports four function types: exponential, sine, cosine, and polynomial functions. It also provides information on the region of convergence and the original function.

Step 1: Selecting the Function Type

1.1: Start by selecting the type of function you wish to analyze. Options include:

  • Exponential (eat)
  • Sine (sin(at))
  • Cosine (cos(at))
  • Polynomial (tn)

This selection is crucial as it dictates the form and parameters needed for the Laplace transform.

Step 2: Entering Function Parameters

2.1 Coefficient (a):
Enter the coefficient value associated with the function. This value must be between -100 and 100 and can be entered with a step of 0.1.

2.2 Power (n):
If you selected “Polynomial” in the previous step, enter the power (n) for t. This value should be between 0 and 10, with a step value of 1. For other function types, this field is not required.

Step 3: Selecting the Complex Variable

3.1: Choose the form of the complex variable ‘s’ in the Laplace transform. You have two options:

  • Real Part Only
  • Complex Form

Ensure you select the appropriate option based on your analysis needs.

Step 4: Calculating the Results

After entering all the necessary inputs, the calculator will automatically provide the following results:

4.1 Laplace Transform F(s):
The calculator will display the Laplace transform of the selected function as a mathematical expression. It will be formatted as a number with two decimal places.

4.2 Region of Convergence:
It will show a textual description of the region where the Laplace transform converges. Normally, it provides a condition involving the real part of ‘s’.

4.3 Original Function f(t):
The original mathematical representation of the function will also be displayed, showing the initial function relationship with respect to ‘t’.

Conclusion

By following these steps and utilizing each section of the calculator as described, you can effectively calculate and analyze the Laplace transforms of various functions with ease.