Thread: Fourier Series and Mandelbrot Set in trig?

I joined just for this ridiculous question. A friend of mine has asked of my help. She's in a Trig class at a community college, and I tutor at one myself. Having taken everything through Calc 3 and Differential Equations, I seemed like the guy to ask.

Well, her teacher has asked her to explain, create examples, and solve both Fourier Series and the Mandelbrot Set in her basic trig class. Apparently he's a calculus teacher primarily, and really doesn't pay attention to the actual coursework. It was assigned Friday afternoon to be turned in before the Monday morning final, of which they will be covered on the test. No examples given, nothing. It rather enrages me.

I cannot find anything online explaining either of these without calculus (and they're tough even for me), so given it's a trig forum, I'm appealing for help here. Is there a way of explaining these concepts to her without need of calculus?

Thanks in advance for looking it over, even if you can't help.

You should probably get some problems and post them. Fourier series are just a summation of periodic functions, usually trigonometric functions. If this is a pre-calculus class your just going to need trig-identities and nth term summation stuff.

See the issue is that there are no problems. They aren't covered in her book at all, and the teacher didn't go over them. It's something her teacher just decided "figure this out, explain it, and it'll be on your final." No explanations, nothing. I cannot find anything online to explain it in terms other than using integration.

The teacher is just looking for an explanation? If he did not give any problems, or teach anything on the subject he cant be looking for more than the following.

For Fourier Series use your knowledge of taylor series to explain approximations. Why do we use these approximations? Use this picture

File:Fourier Series.svg - Wikipedia, the free encyclopedia

to extend the idea of approximations to periodic functions. Why do we use trigonometric functions to approximate functions like this? What is the behavior of a summation of trigonmetric functions for some (Hint: oscillation)

For the Madelbrot Set

Explain complex numbers and the complex plane. Why did we extend the Reals?

Show what recursion is, and how we can define and obtain a function recursively. Maybe Newton's method will help here.

Go over boundedness and infinite behavior.

If the set of complex numbers about



are bounded, they form a Mandelbrot Set. What does a Mandelbrot Set form? How can you relate this to boundedness and recursion?