Fourier Series - Am I Crazy or is My Teacher Tricking Me?

In summary, the first three terms of the Fourier series for f(θ) = tan(θ) from θ = -π/2 to π/2 are a0 + a1cos(θ) + b1sin(θ), with a0 and a1 both equal to 0 and b1 to be determined. The function being odd, cosine terms are not present, and it being undefined at the interval points may affect the final result. This thread appears to be a duplicate of a previous one.
  • #1
mundane
56
0
I am SO annoyed with this problem. Ready to jump out a window.

Homework Statement



Find the first three terms of the Fourier series that approximates f(θ) = tan(θ) from θ = -π/2 to π/2.

The Attempt at a Solution



So, I know that for an equation on [[itex]\frac{-b}{2}[/itex], [itex]\frac{b}{2}[/itex]], to define the Fourier series for that equation we use f(x)={a0+a1cosx+a2cos2x+ ... +b1sinx+b2sin2x+ ...}

I only need to find the first three terms, so its just a0+a1cosx+b1sinx.

a0 is defined as [itex]\frac{1}{\pi}[/itex][itex]\intf(x)dx[/itex] definite integral from -π/2 to π/2.

a1 is defined as [itex]\frac{2}{\pi}[/itex][itex]\int\f(x)cos(2πx/π)dx[/itex] definite integral from -π/2 to π/2.

b1 is defined as [itex]\frac{2}{\pi}[/itex][itex]\int\f(x)sin(2πx/π)dx[/itex] definite integral from -π/2 to π/2.For a0, my antiderivative was -log(cos(x)). After substitution, a0=0.

For a1, my antiderivative was log(cos(x))-(1/2)cos(2x). After substitution, a1=0.

I have not done b1 yet. Am I being trolled?

Does this ave something to do with the fact that tan(x) is undefined at those two interval points? Am I going in the wrong direction?
 
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  • #2
If a function is odd, can it have cosine terms?
If a function is even, can it have sine terms?
 
  • #4
Sorry, I didn't mean to repost. I was trying to change the red font and it reposted. Sorry.
 

FAQ: Fourier Series - Am I Crazy or is My Teacher Tricking Me?

What is a Fourier Series?

A Fourier Series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It is used to analyze and express a periodic function in terms of its fundamental frequency and its harmonics.

How is a Fourier Series used in science?

Fourier Series are commonly used in physics, engineering, and other scientific fields to understand and model periodic phenomena, such as sound waves, electrical signals, and vibrations. They are also used in signal processing and data analysis to extract useful information from complex signals.

Why is it confusing to learn about Fourier Series?

Fourier Series can be confusing because they involve complex mathematical concepts and require a good understanding of trigonometry and calculus. Additionally, the application of Fourier Series can vary depending on the specific problem, which can add to the confusion.

Am I crazy if I don't understand Fourier Series?

No, you are not crazy. Fourier Series can be challenging to grasp, and it is normal to have difficulty understanding them at first. With practice and patience, you can develop a better understanding of Fourier Series and their applications.

Is my teacher tricking me by teaching Fourier Series?

No, your teacher is not tricking you. Fourier Series are a fundamental concept in mathematics and have numerous practical applications in science and engineering. Understanding Fourier Series can help you analyze and interpret complex signals, which is a valuable skill in many scientific fields.

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