Inverse Laplace trnasform

In summary, the conversation is about finding inverse transforms in Laplace transforms, specifically dealing with partial fractions in a complex equation. The person has attempted to solve a problem and has a question about their answer. They want to know if their answer is equivalent to the one in the book and if the book's answer can be converted into exponential functions for easier comparison. They are provided with a helpful resource for working with complex numbers.
  • #1
mxpxer7
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I'm doing lapace transforms and I'm to the stage where I am finding inverse transforms. A problem I am stuck on involves doing partial fractions of a complex equation. I have attempted to do it, and now I have a question about my answer.

My answer is

-2i+1exp((1-i)*t) + -2i+1exp((1+i)*t)

Books answer

2exp(t)cos(t)+3exp(t)sin(t)

Is my answer equivalent?
 
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  • #2


Can you convert the book's answer into exp functions (no trig)? Then they should be easy to compare.
 

1. What is an Inverse Laplace Transform?

An Inverse Laplace Transform is a mathematical operation that takes a Laplace domain function and transforms it back into its original time domain function. It is used to solve differential equations, control systems, and other engineering problems.

2. How is an Inverse Laplace Transform calculated?

The Inverse Laplace Transform is calculated using integration techniques, specifically the Bromwich integral. This involves finding the residues of the Laplace domain function and using them to calculate the inverse transform.

3. What are the applications of Inverse Laplace Transform?

The Inverse Laplace Transform is widely used in engineering, physics, and mathematics for solving differential equations and analyzing complex systems. It is also used in signal processing and control theory to model and analyze dynamic systems.

4. Can I use a table to find the Inverse Laplace Transform?

Yes, there are tables available that list common Laplace transforms and their corresponding inverse transforms. However, for more complex functions, it may be necessary to use integration techniques to calculate the inverse transform.

5. Is the Inverse Laplace Transform unique?

No, the Inverse Laplace Transform is not always unique. Some functions may have multiple inverse transforms, and others may not have an inverse transform at all. It is important to consider the region of convergence when calculating the inverse transform to ensure uniqueness.

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