Practice Applications in Engineering - 18.4 | 18. Application to Integral Equations | Mathematics - iii (Differential Calculus) - Vol 1
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is an integral equation?

💡 Hint: Think about where the unknown function is located in the equation.

Question 2

Easy

What is a Volterra Integral Equation?

💡 Hint: Consider when limits in integrals depend on the 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 does an integral equation contain?

  • Only constants
  • An unknown function under an integral sign
  • A polynomial expression

💡 Hint: Recall what differentiates each type of equation.

Question 2

True or False: The Laplace Transform can convert differential equations into algebraic equations.

  • True
  • False

💡 Hint: Think about the purpose of the Laplace Transform.

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Challenge Problems

Push your limits with challenges.

Question 1

Solve the following Volterra equation and discuss its engineering significance: f(t) = t² + ∫_0^t (t - τ)²f(τ)dτ.

💡 Hint: Revisit the steps for applying the transform carefully.

Question 2

Analyze the effect of varying kernels on the solution of an integral equation and provide an example.

💡 Hint: Explore how changing K in the integral impacts f(t).

Challenge and get performance evaluation