9.13. Comparison: Fourier Series vs Fourier Integral

Try these first

1. 1.

   What type of functions does Fourier Series apply to?

   Hint

   Consider the intervals they are defined over.

2. 2.

   Name the coefficients used in Fourier Series.

   Hint

   Think about the functions involved in the summation.

3. 3.

   What does the Fourier Series primarily apply to?

   • Periodic Functions
   • Non-Periodic Functions
   • Both

   Hint

   Think about the definition of periodicity.

4. 4.

   True or False: Fourier Integrals can represent periodic functions.

   • True
   • False

   Hint

   Consider the nature of the functions represented by each tool.

5. 5.

   Consider a function f(x) defined on a finite interval. Derive the Fourier Series representation of that function.

   Hint

   Don’t forget to apply the correct integration limits!

6. 6.

   Evaluate the use of Fourier Integrals in analyzing stress waves in soil mechanics for earthquake engineering.

   Hint

   Relate the mathematical approach to physical stress phenomena during quakes.