Fourier Trigonometric Series for Symmetric Function: Homework Check

In summary, a Fourier series is a mathematical representation of a periodic function as an infinite sum of sinusoidal functions. Its accuracy can be checked by comparing it with the original function, and it is used to decompose complex functions and make them easier to analyze. The key components of a Fourier series are the amplitude, frequency, and phase of each sinusoidal function, which determine the shape and behavior of the overall function. This mathematical tool is widely used in various real-world applications, including audio and image compression, data analysis, and modeling complex systems in fields like physics, chemistry, and economics.
  • #1
roldy
237
2

Homework Statement


Determine the first three terms in the Fourier trigonometric series for the function shown below.


Homework Equations


Look at attached jpeg. This tex tool is terrible. After making correction to the code, the preview still shows previous preview posts.


The Attempt at a Solution



See attached jpeg for solution and the other attachment for the function. Did I define the function correctly? I didn't solve for bn because this function is symmetric about the y-axis.

First three terms mean a0, a1, and a2 right?
Or is it n=1, 2, 3
 

Attachments

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    Fourier Series copy.jpg
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  • #2
Would anyone check this for me please?
 

1. What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as an infinite sum of sinusoidal functions. It is used to analyze and approximate a wide range of continuous functions.

2. How do you check the accuracy of a Fourier series?

The accuracy of a Fourier series can be checked by comparing the original function with the approximation obtained by the series. The closer the two are, the more accurate the series is.

3. What is the purpose of using a Fourier series?

A Fourier series is used to decompose a complex function into simpler sinusoidal functions, making it easier to analyze and understand. It is also used in signal processing, image analysis, and other areas of science and engineering.

4. What are the key components of a Fourier series?

The key components of a Fourier series are the amplitude, frequency, and phase of each sinusoidal function. These components determine the shape and behavior of the overall function.

5. How is a Fourier series used in real-world applications?

A Fourier series is used in various real-world applications, such as audio and image compression, data analysis, and solving differential equations. It is also used in fields like physics, chemistry, and economics to model and understand complex systems.

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