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
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the Heaviside step function.
💡 Hint: Consider how the function behaves over different time intervals.
Question 2
Easy
What does the Second Shifting Theorem state?
💡 Hint: Recall the notation and the meaning of each variable.
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 equation for the Second Shifting Theorem?
- ℒ{f(t-a)u_a(t)} = e^{-as}F(s)
- ℒ{f(t+a)u_a(t)} = e^{as}F(s)
- ℒ{f(t)u_a(t)} = F(s)
💡 Hint: Focus on the role of the negative exponent.
Question 2
True or False: The Heaviside function is zero for all time.
- True
- False
💡 Hint: Consider when it activates.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
What is the Laplace transform of (t-3)^3u_3(t)? Provide a detailed solution.
💡 Hint: Remember to find the initial Laplace transform of t^3.
Question 2
Consider a system where the response to an input signal starts after a delay of 5 seconds. How would you mathematically represent the output in terms of the Second Shifting Theorem?
💡 Hint: Think about how time delays linearly translate in the Laplace domain.
Challenge and get performance evaluation