1.1.3 - Laplace Transform of the First Derivative
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Practice Questions
Test your understanding with targeted questions
What is the Laplace Transform of the function f(t) = t?
💡 Hint: Use the formula for the Laplace Transform.
Write down the formula for the Laplace Transform of the first derivative.
💡 Hint: Remember the connection between `F(s)` and `f(0)`.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Laplace Transform of the first derivative?
💡 Hint: Recall the derived formula from class.
Laplace Transform converts which type of equations into algebraic ones?
💡 Hint: Think about how we convert differential terms into algebraic ones.
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Challenge Problems
Push your limits with advanced challenges
Derive the Laplace Transform of f(t) = e^{at} and show how to apply it to a differential equation.
💡 Hint: Start from basic properties of the Laplace Transform.
Given y' + 2y = e^{3t} with y(0) = 1, use Laplace Transform to find y(t).
💡 Hint: Remember to apply the Laplace of the forcing term correctly.
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