Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the Laplace Transform of the function \( f(t) = t \)?
💡 Hint: Use integration by parts to derive.
Question 2
Easy
Calculate \( L\{f'''(t)\} \) for \( f(t) = e^{3t} \).
💡 Hint: Remember to apply the formula for the third derivative using initial values.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for the Laplace Transform of the first derivative?
- A) L{f'(t)} = sF(s) + f(0)
- B) L{f'(t)} = sF(s) - f(0)
- C) L{f'(t)} = F(s) - f(0)
💡 Hint: Remember the negative sign for the initial value.
Question 2
True or False: The Laplace Transform can convert time-domain functions into frequency-domain functions.
- True
- False
💡 Hint: Consider what the purpose of the Laplace Transform is.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the initial value problem defined by the second-order linear homogeneous ODE \( y'' - 3y' + 2y = 0 \) with initial conditions \( y(0) = 1 \) and \( y'(0) = 0 \), find the general solution using the Laplace Transform.
💡 Hint: Keep track of the initial values and re-arrange the equation.
Question 2
If \( f(t) = t^3 e^{-2t} \), derive L\{f^{(4)}(t)\} without computing the individual derivatives.
💡 Hint: Understand how to apply properties and series to achieve this without explicit derivative calculation.
Challenge and get performance evaluation