Practice Laplace Transforms & Applications - 1 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
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Laplace Transforms & Applications

1 - Laplace Transforms & Applications

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Laplace Transform of a constant function, L{1}?

💡 Hint: Consider how the Laplace Transform deals with constants.

Question 2 Easy

Write down the formula for L{f′(t)}.

💡 Hint: Think about the first derivative in the Laplace domain.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the Laplace Transform of the first derivative?

L{f′(t)} = sF(s) - f(0)
L{f′(t)} = sF(s) + f(0)
L{f′(t)} = F(s) - sf(0)

💡 Hint: Focus on the relationship between derivatives and algebraic transformations.

Question 2

True or False: The Laplace Transform can only be applied to linear differential equations.

True
False

💡 Hint: Remember the nature of types of differential equations.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using Laplace Transforms, derive the solution for the system y'' + 4y' + 4y = 0, y(0) = 1, y'(0) = 0.

💡 Hint: Apply the transformations step by step for clarity.

Challenge 2 Hard

Demonstrate the use of Laplace Transforms in finding L{e^at sin(bt)}.

💡 Hint: Plug into the transformation formulas wisely.

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