1.1.7 - Laplace Transform of the n-th Derivative
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Practice Questions
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What is the formula for the Laplace Transform of the first derivative?
💡 Hint: Remember the structure involves s and the initial function value.
True or False: The Laplace Transform can only be applied to continuous functions.
💡 Hint: Consider the nature of functions required for transformation.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does L{f′(t)} equal?
💡 Hint: Think about how derivatives reduce to algebra.
True or False: The Laplace Transform can be used for integral equations.
💡 Hint: Recall the scope of the transform discussed.
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Challenge Problems
Push your limits with advanced challenges
Find the Laplace Transform of f(t) = e^3t cos(4t), using the property L{e^{at} f(t)} = F(s-a).
💡 Hint: Identify a and b from the exponential and cosine components.
Solve the differential equation y'' + 4y = 0 with y(0)=1 and y'(0)=0 using the Laplace Transform.
💡 Hint: Transform each term carefully while applying initial conditions.
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