18.5. Summary

Try these first

1. 1.

   Define an integral equation.

   Hint

   Focus on the definition part.

2. 2.

   What is a kernel in an integral equation?

   Hint

   Think about the components of the integral.

3. 3.

   What is a Volterra Integral Equation?

   • An equation incapable of being solved
   • An equation with limits dependent on the variable
   • A transformation method

   Hint

   Remember, it’s named after the mathematician Volterra.

4. 4.

   Laplace Transforms help in simplifying what type of equations?

   • True
   • False

   Hint

   Consider the main purpose of this transform.

5. 5.

   Derive the solution for the integral equation: f(t) = t^2 + ∫(t - τ)f(τ) dτ with a kernel representing linear growth.

   Hint

   Pay close attention to how the powers in the kernel affect your algebra.

6. 6.

   Explain the usage of Laplace Transforms in a practical engineering problem such as an electric circuit's response?

   Hint

   Think about the systematic approach to circuit analysis.