Practice Laplace Transform: Basic Definition - 7.3 | 7. Multiplication by tn (Power of t) | 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: Basic Definition

7.3 - Laplace Transform: Basic Definition

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?

💡 Hint: Look for the integral definition of the Laplace Transform.

Question 2 Easy

What does differentiating a function mean?

💡 Hint: Think about how slopes of curves are determined.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the general formula for the Laplace Transform?

L{f(t)} = ∫[0,∞] e^(-st) f(t) dt
L{f(t)} = ∫[0,∞] e^(st) f(t) dt
L{f(t)} = ∫[0,∞] f(t)e^(st) dt

💡 Hint: Think about the integral form involving an exponential decay.

Question 2

True or False: The Multiplication by tn Property results in differentiation in the s-domain.

True
False

💡 Hint: Recall how differentiation affects functions in calculus.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove the multiplication by t^n property for n=2 by calculation, starting from L{f(t)}.

💡 Hint: Pay attention to the orders of differentiation and exponential decay in your integral expressions.

Challenge 2 Hard

Using the properties of Laplace Transforms, solve for L{e^{2t}sin(3t)}. Express in terms of s.

💡 Hint: Identify the base transformation of e^{2t} and use it effectively!

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.