Laplace Transform Calculator
Results
What is Laplace Transform
The Laplace transform is a powerful mathematical tool that converts a function of time (t) into a function of complex frequency (s). It’s defined as:
F(s) = L{f(t)} = ∫[0 to ∞] f(t)e^(-st)dt
This transformation is particularly useful in solving differential equations, analyzing control systems, and processing signals. It converts complex time-domain operations into simpler algebraic operations in the frequency domain.
How to Use the Laplace Transform Calculator
Step 1: Enter Your Function
Input your time-domain function f(t) in the designated field. Use standard mathematical notation (e.g., sin(t), e^t, t^2).
Step 2: Review Input Format
Ensure your function follows the correct syntax. For example, write exponentials as ‘e^t’ and trigonometric functions as ‘sin(t)’ or ‘cos(t)’.
Step 3: Calculate Transform
Click the calculate button to perform the transformation. The calculator will process your input and generate the result.
Step 4: Interpret Results
Examine the displayed result F(s) and the provided explanation. The result shows the transformed function in terms of the complex variable s.
Step 5: Analyze Explanation
Review the step-by-step explanation provided below the result to understand how the transform was calculated and its mathematical significance.