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 skillsβperfect 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.
π‘ Hint: What happens before and after time c?
Question 2
Easy
State the main statement of the Second Shifting Theorem.
π‘ Hint: Think about what happens with the function when itβs delayed.
Practice 3 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 does the Second Shifting Theorem help in modeling?
- Functions without delays
- Delayed activation of functions
- Nonlinear equations
π‘ Hint: Focus on the 'shifting' aspect of the theorem.
Question 2
True or False: The Heaviside step function must be included for the Second Shifting Theorem to apply.
- True
- False
π‘ Hint: Recall what the Heaviside function actually does in modeling.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove the Second Shifting Theorem by calculating the Laplace transform of f(t) = e^(at)u(t-b).
π‘ Hint: Introduce a substitution of u(t-b) correctly before integrating.
Question 2
Determine the Laplace transform for f(t) = sin(Ο(t-5))u(t-5).
π‘ Hint: Standardize to sin(Οt) first before incorporating the delay.
Challenge and get performance evaluation