Full Range Fourier Series - Problem 7 - Fourier Series - Engineering Mathematics 3

TL;DR

This video explains how to find the coefficients for an odd function in a Fourier series.

Transcript

hello friends in this video we'll be discussing one more example of Fourier series we are into full range series and interval minus PI to PI this is our 7th problem welcome back friends let's have a look on the given problem f of X is equal to X in the interval minus PI to PI one of the simplest problem let's start solving it first of all as soon a... Read More

Key Insights

• ❓ The given problem involves finding the coefficients for a function in a Fourier series over the interval -π to π.
• ☺️ By replacing x with -x and comparing it to the original function, it is determined that the given function is odd.
• ❓ The formula for finding the coefficients Bn involves integrating the product of the function and sin(nx) over the interval.

Questions & Answers

Q: How do you determine if a function is odd or even in a Fourier series?

To determine if a function is odd or even, you check if f(-x) is equal to -f(x). If it is, the function is odd; if not, it is even.

Q: What is the formula for finding the coefficients Bn in a Fourier series?

The formula for finding the coefficients Bn is 2/π * ∫(f(x) * sin(nx)) dx, where the integral is taken over the specified interval.

Q: How do you calculate the coefficients for an odd function in a Fourier series?

For an odd function, the coefficients Bn can be calculated using the formula Bn = (-2/π) * ∫(f(x) * sin(nx)) dx, where the limits are over the specified interval.

Q: What is the solution for the given problem f(x) = x?

The solution for f(x) = x is a Fourier series representation of f(x) as a summation of n = 1 to infinity of (-2(-1)^n/n) * sin(nx).

Summary & Key Takeaways

• The given problem involves finding the coefficients for the function f(x) = x over the interval -π to π.

• By checking if f(-x) = -f(x), it is determined that the function is odd.

• The formula for finding the coefficients Bn is used to calculate the value for this specific function.

• The final solution for f(x) is obtained as a summation of n = 1 to infinity of (-2(-1)^n/n) * sin(nx).