10.1.2. Inverse Fourier Cosine Transform

Try these first

1. 1.

   Define the Inverse Fourier Cosine Transform.

   Hint

   Recall the mathematical expression for the inverse transform.

2. 2.

   What condition must f(x) satisfy for the Inverse Fourier Cosine Transform?

   Hint

   Think about continuity and how integrals behave.

3. 3.

   What does the Inverse Fourier Cosine Transform do?

   • Recovers original functions
   • Finds maxima
   • Calculates integrals

   Hint

   Think about the purpose of the transform.

4. 4.

   True or False: The function must be continuous for the Inverse Fourier Cosine Transform to apply.

   • True
   • False

   Hint

   Consider the conditions needed for Fourier transforms.

5. 5.

   Solve the deflection equation of a cantilever beam under a distributed load using the Inverse Fourier Cosine Transform.

   Hint

   Start with finding the Fourier Cosine Transform of the load.

6. 6.

   Show how to apply the Inverse Fourier Cosine Transform to recover the temperature profile in a semi-infinite rod after a sudden temperature change at one end.

   Hint

   Think about how the boundary conditions influence the solution.