Problem 3 Based on Inverse Laplace Transform of log & tan¯¹ Function - Engineering Mathematics 3 | Summary and Q&A

TL;DR

Learn how to find the inverse Laplace transform of a logarithmic function by using the differentiation of phi of s property.

Key Insights

• ❓ The inverse Laplace transform of a logarithmic function cannot be found using standard formulas.
• 👻 The differentiation of phi of s property allows finding the inverse Laplace transform by using the derivative of the function.
• ❓ Simplifying the logarithmic function using logarithmic properties before differentiation simplifies the calculation.
• ✅ Checking if the inverse Laplace transform of the derivative is possible is crucial in determining if the property can be applied.
• ✖️ The inverse Laplace transform of the derivative is then multiplied by negative 1 divided by t to obtain the final answer.
• 🎮 The video emphasizes the importance of understanding the properties and methods to solve inverse Laplace transform problems.

Transcript

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Questions & Answers

Q: What is the property used to find the inverse Laplace transform of a logarithmic function?

The property used is the differentiation of phi of s property, derived from the multiplication by t theorem.

Q: Why is it important to check if the inverse Laplace transform of the derivative is possible?

It is important to check because if the inverse Laplace transform of the derivative is not possible, the property cannot be applied and another method needs to be used.

Q: How is the derivative of the logarithmic function found?

The logarithmic function is simplified using logarithmic properties before finding its derivative, making it easier to calculate.

Q: What is the equation used to calculate the inverse Laplace transform of the derivative?

The equation is negative 1 divided by t multiplied by the inverse Laplace transform of the derivative, obtained by applying the differentiation of phi of s property.

Summary & Key Takeaways

• The video demonstrates how to find the inverse Laplace transform of a logarithmic function using the differentiation of phi of s property.

• It explains the property derived from the multiplication by t theorem and the process of finding the derivative and inverse Laplace transform.

• The video emphasizes the importance of checking if the inverse Laplace transform of the derivative is possible before applying the property.