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 a Volterra Integral Equation.
π‘ Hint: Look for the structure of the integral involving an unknown function.
Question 2
Easy
What does the kernel represent in an integral equation?
π‘ Hint: Consider it as a weight assigned to different inputs.
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 type of equation is \( f(t) = g(t) + \int_0^t K(t-\tau) f(\tau) d\tau \)?
- Differential Equation
- Integral Equation
- Algebraic Equation
π‘ Hint: Look for the presence of an integral with an unknown.
Question 2
True or False: The Convolution Theorem allows the Laplace Transform of a convolution to be expressed as a product.
- True
- False
π‘ Hint: Think about how operations change during transformation.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if \( f(t) = \int_0^t f(\tau) d\tau \), the solution can be expressed as \( f(t) = te^t \) using Laplace Transforms.
π‘ Hint: Focus on how integral arguments are expressed in the transformed domain.
Question 2
Given \( K(t - \tau) = sin(t - \tau) \), derive the explicit formula for \( f(t) \) if \( g(t) = t^2 \).
π‘ Hint: You will need to remember properties of sine when finding inverse transforms.
Challenge and get performance evaluation