Practice Laplace Transform of the n-th Derivative - 1.1.7 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Laplace Transform of the n-th Derivative

1.1.7 - Laplace Transform of the n-th Derivative

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

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

💡 Hint: Remember the structure involves s and the initial function value.

Question 2 Easy

True or False: The Laplace Transform can only be applied to continuous functions.

💡 Hint: Consider the nature of functions required for transformation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does L{f′(t)} equal?

sF(s) - f(0)
sF(s) + f(0)
F(s) - s

💡 Hint: Think about how derivatives reduce to algebra.

Question 2

True or False: The Laplace Transform can be used for integral equations.

True
False

💡 Hint: Recall the scope of the transform discussed.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.