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# Fourier Series Application and Analysis

Created by
@WellInformedRuby

### What is a Fourier series?

• An expansion of a non-periodic function into a sum of trigonometric functions (correct)
• A sum of polynomials
• A series of exponential functions
• A series of rational functions
• ### Why are trigonometric functions used in Fourier series?

• Because they are well understood (correct)
• Because they are easy to differentiate
• Because they are always convergent
• Because they have simple integration rules
• ### Can Fourier series be used to approximate all functions?

• No, only for smooth functions
• Yes, for all periodic functions
• Yes, for all types of functions
• No, because most functions have infinitely many terms in their Fourier series (correct)
• ### What determines the coefficients of the Fourier series?

<p>Integrals of the function multiplied by trigonometric functions</p> Signup and view all the answers

### What do Fourier series convergence studies focus on?

<p>The behavior of the partial sums</p> Signup and view all the answers

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