Laplace transform of the first derivative, L{f't}

TL;DR

The video explains how to derive the Laplace transform of a derivative formula and demonstrates its usefulness in solving differential equations.

Transcript

the goal for this video is to figure out what seller plus transform of f Prime of T and here let's assume that F Prime T and its original function f of T they are both of exponential order so that will make sure that we will be able to get along plus transform of these functions so this is something that we're trying to do and we hope to reduce thi... Read More

Key Insights

• 🥳 The Laplace transform of a derivative can be found by using the definition of Laplace transform and integration by parts.
• 😑 The Laplace transform of a derivative formula allows for the reduction of Laplace transforms to simpler expressions.
• ❓ The Laplace transform of a derivative formula is useful in solving differential equations.
• ➖ The Laplace transform of a derivative can be represented as the Laplace transform of the original function minus the value of the original function at t=0.
• 🪈 The Laplace transform of a derivative formula assumes that the original function and its derivative are of exponential order.
• ❓ The Laplace transform of a derivative formula involves the integral of the product of two functions.
• 🥳 Integration by parts is used to simplify the integral in the Laplace transform of a derivative formula.

Questions & Answers

Q: What is the goal of the video?

The goal of the video is to find the Laplace transform of F'(t) using the definition of Laplace transform.

Q: How is the Laplace transform of F'(t) defined?

The Laplace transform of F'(t) is defined as the integral of e^(-st) times F'(t) with respect to t.

Q: What is the method used to derive the Laplace transform of F'(t)?

The video explains that integration by parts is used to derive the Laplace transform of F'(t).

Q: What is the final formula obtained for the Laplace transform of F'(t)?

The Laplace transform of F'(t) can be written as Laplace transform of F(t) minus F(0).

Summary & Key Takeaways

• The goal of the video is to find the Laplace transform of F'(t) by using the definition of Laplace transform.

• The Laplace transform of F'(t) is defined as the integral of e^(-st) times F'(t) with respect to t.

• By using integration by parts, the Laplace transform of F'(t) can be reduced to the Laplace transform of F(t) minus F(0).