Practice Step 3: Apply the inverse Laplace Transform to find 𝑓(𝑑) - 18.2.3 | 18. Application to Integral Equations | Mathematics - iii (Differential Calculus) - Vol 1
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Knowledge

18.2.3 - Step 3: Apply the inverse Laplace Transform to find 𝑓(𝑑)

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the purpose of the inverse Laplace Transform?

πŸ’‘ Hint: Think about what we want to achieve with the function after using Laplace Transform.

Question 2

Easy

Define a Volterra Integral Equation.

πŸ’‘ Hint: Consider the form of integral equations we discussed.

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 does the inverse Laplace Transform retrieve?

  • Algebraic equation
  • Time-domain function
  • Integral equation

πŸ’‘ Hint: Consider what you ultimately want to find in function analysis.

Question 2

True or False: The Laplace Transform can simplify integral equations to algebraic equations.

  • True
  • False

πŸ’‘ Hint: Recall how we use Laplace in engineering applications.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given 𝐹(𝑠) = 1 / (sΒ² + 9), find the inverse Laplace Transform and express 𝑓(𝑑).

πŸ’‘ Hint: Look for trigonometric forms in your inverse Laplace Transform tables.

Question 2

Consider the equation 𝑓(𝑑) = 1 + ∫ (t - Ο„)f(Ο„)dΟ„. Solve for 𝑓(𝑑) by following the steps of Laplace and inverse.

πŸ’‘ Hint: Follow the structured steps of the Laplace Transform to derive the equation and solve.

Challenge and get performance evaluation