Practice Applications - 1.2 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
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Applications

1.2 - Applications

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is L{f'(t)}?

💡 Hint: Recall the formula and how it converts derivatives.

Question 2 Easy

Define what an Initial Value Problem is.

💡 Hint: Focus on the 'initial' part.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

L{f'(t)} = sF(s) - f(0)
L{f'(t)} = s²F(s) - sf(0) - f'(0)
L{f(t)} = F(s)

💡 Hint: Look for the formula related to the first derivative.

Question 2

True or False: The Laplace Transform converts time-domain functions into frequency-domain functions.

True
False

💡 Hint: Think about the purpose of the Laplace Transform.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Demonstrate how you would transform the equation y' + y = e^(-t) into an algebraic equation using Laplace Transform.

💡 Hint: Remember to include y(0) when applying the transform to y'.

Challenge 2 Hard

Given initial conditions y(0) = 3 and y'(0) = 0, find the solution of the differential equation y'' + 4y = 0.

💡 Hint: Focus on the solution process for Y(s) first.

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