**PIERRE SIMON LAPLACE**

**The Laplace transform is a simple way of converting functions in one domain to functions of another domain**.

**Here's an example**

**:**

Suppose we have a function of time, such as cos(w*t). With the Laplace transform, we can convert this to a function of frequency, which is

**cos(w*t) ----L{}-----> w / (s^2 + w^2)**

**This is useful for a very simple reason**: it makes solving differential equations much easier.

- The development of the logarithm was considered the most important development in studying astronomy. In much the same way, the
**Laplace transform makes it much easier to solve differential equations.**

- Since the Laplace transform of a derivative becomes a multiple of the domain variable, the Laplace transform turns a complicated n-th order differential equation to a corresponding nth degree polynomial. Since polynomials are much easier to solve, we would rather deal with them. This occurs all the time.

- In brief, the
**Laplace transform is really just a shortcut for complex calculations**. It may seem troublesome, but it bypasses some of the most difficult mathematics.

- Laplace transform is a technique mainly utilized in engineering purposes for system modeling in which a large differential equation must be solved.

- The Laplace transform can also be used to solve differential equations and is used extensively in electrical engineering.

- Laplace Transform is used in electrical circuits for the analysis of linear time-invariant systems

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