Practice Example Problems - 1.2.1.1 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
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Example Problems

1.2.1.1 - Example Problems

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Find L{t^2}.

💡 Hint: Use the formula L{t^n}.

Question 2 Easy

What is L{1}?

💡 Hint: Use the basic transformation for constant function.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for L{f'(t)}?

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

💡 Hint: Think about how initial values affect the transform.

Question 2

True or False: The Laplace Transform can simplify the process of solving differential equations.

True
False

💡 Hint: Review how Laplace transforms are used in various applications.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Find the Laplace Transform of y''' + 4y'' + 3y' = 0 with y(0) = 1, y'(0) = 0, y''(0) = 2.

💡 Hint: Don't forget to express the initial conditions with their correct derivatives.

Challenge 2 Hard

Prove L{f(n)(t)} formula from the base principles of Laplace transformations.

💡 Hint: Systematically apply the transformations step by step, checking the contribution of each term carefully.

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