Practice Summary - 1.3 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
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Summary

1.3 - Summary

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Laplace Transform of the first derivative?

💡 Hint: Remember the general transformation rule.

Question 2 Easy

What transformation does L{f(t)} yield?

💡 Hint: Think about the integral of the function.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is L{f'(t)}?

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

💡 Hint: Think about the basic formula for the Laplace transformation.

Question 2

True or False: The Laplace Transform can only be applied to first derivatives.

True
False

💡 Hint: Review the formulas for different orders of derivatives.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Derive the Laplace Transform of f'(t) using integration by parts from first principles.

💡 Hint: Pay close attention to the boundary terms as t approaches infinity.

Challenge 2 Hard

Prove that L{f' + g' (t)} = L{f(t)} + L{g(t)} for two functions and their derivatives.

💡 Hint: Consider how the Laplace Transform can be distributed across addition.

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