Understanding the Role of n in the Denominator of Fourier Series

In summary, a Fourier series is a mathematical representation of a periodic function using a sum of sine and cosine functions. It is called a "series" because it involves adding multiple terms together. Fourier series have numerous applications in science, including their use in analyzing periodic phenomena and solving differential equations. They are calculated by finding the coefficients of the sine and cosine functions that best fit the given function, and they can only approximate periodic functions. However, the concept can be extended to non-periodic functions using Fourier transforms.
  • #1
robertjford80
388
0

Homework Statement



Screenshot2012-06-15at30300AM.png





The Attempt at a Solution



I don't see why the n is in the denominator
 
Physics news on Phys.org
  • #2
reverse chain rule. What's the derivative of [itex]\frac{\sin(nx)}{n}?[/itex]

If that doesn't make sense, then...

you could use u-substitution to avoid going backwards.

If you don't know u-substitution, that can be part of the problem.
 
  • #3
thanks, got it
 

1. What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function using a sum of sine and cosine functions. It allows us to approximate a complicated function with a simpler one and is used in many areas of science and engineering.

2. Why is it called a "series"?

A series is a sum of terms. In a Fourier series, we are summing different sine and cosine functions to approximate a given function. This sum is called a series because it involves adding multiple terms together.

3. What is the importance of Fourier series in science?

Fourier series have a wide range of applications in science. They are used to analyze and describe periodic phenomena in fields such as physics, engineering, signal processing, and more. They also play a significant role in solving differential equations, which are fundamental in many scientific disciplines.

4. How is a Fourier series calculated?

A Fourier series is calculated by finding the coefficients of the sine and cosine functions that best fit the given function. These coefficients can be determined using integral calculus or by using a Fourier series calculator. Once the coefficients are found, they can be used to construct the series.

5. Can a Fourier series approximate any function?

No, a Fourier series can only approximate periodic functions. If a function is not periodic, it cannot be accurately represented by a Fourier series. However, by using a technique called Fourier transforms, we can extend the concept of Fourier series to non-periodic functions.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
165
  • Calculus and Beyond Homework Help
Replies
2
Views
323
  • Calculus and Beyond Homework Help
Replies
6
Views
274
  • Calculus and Beyond Homework Help
Replies
1
Views
97
  • Calculus and Beyond Homework Help
Replies
3
Views
267
  • Calculus and Beyond Homework Help
Replies
16
Views
475
  • Calculus and Beyond Homework Help
Replies
1
Views
134
  • Calculus and Beyond Homework Help
Replies
1
Views
253
  • Calculus and Beyond Homework Help
Replies
1
Views
492
  • Calculus and Beyond Homework Help
Replies
20
Views
1K
Back
Top