15.1. Basics of Fourier Series

Try these first

1. 1.

   What is a Fourier series?

   Hint

   Think about periodic functions and their representation.

2. 2.

   What conditions must a function satisfy to be expressed as a Fourier series?

   Hint

   Recall the term 'Dirichlet conditions'.

3. 3.

   What is a Fourier Series?

   • A sum of squares
   • A sum of exponential functions
   • A sum of sine and cosine functions

   Hint

   Focus on the trigonometric aspect of the series.

4. 4.

   Fourier Series can only be applied to non-periodic functions. True or False?

   • True
   • False

   Hint

   Think about the conditions that define a Fourier series.

5. 5.

   Find the Fourier series representation for the function f(x) = x on the interval [-π, π].

   Hint

   Take care with the integration limits and ensure to include symmetry considerations.

6. 6.

   Given a periodic function with known values, derive its Fourier coefficients and reconstruct the first three terms of its series.

   Hint

   Make sure to draw from past homework example problems for guidance.