What Should I do for a Math Project?

[sheldonrocks97]

For my Calculus II class I need to do a math project for some extra credit. I talked to my professor and she says that the project can be about anything as long as it is about math.

Also, I wouldn't prefer to have a project that includes too much multivariable calculus, because I'm only in Calc II, but it if it has a little bit of it that's okay.

My favorite aspects of math are functions, integrals, limits, and equations (of lines or just solving them).

With that in mind what should I do for my project? I'm open to any suggestions you all my have.

 

[micromass]

Here are some things that come to mind:

Fourier series and the many applications it has to mathematics such as the Basel problel

Calculus in nonstandard analysis, this forms an alternative mathematics without limits

Metric spaces and a generalization of continuity and limits

Some complex analysis

Optimization problems with calculus of variations

Applying calculus to probability theory

 

[sheldonrocks97]

Here are some things that come to mind:

Fourier series and the many applications it has to mathematics such as the Basel problel

Calculus in nonstandard analysis, this forms an alternative mathematics without limits

Metric spaces and a generalization of continuity and limits

Some complex analysis

Optimization problems with calculus of variations

Applying calculus to probability theory

These are all pretty cool ideas. I'll look into them; thanks for the help.

 

[JaredEBland]

I feel like metric spaces might be a bit much for you since you're in calc II. They're awesome, and a great (and useful) property to have in a topological space, but probably a bit advanced for calculus II.

Applying calculus to probability theory will be cool, and you'll see it again in thermal physics.

What about multi-variable Taylor series? I know you don't want to do much with multi-variable calculus, but if you can play with two or three dimensional Taylor series it may be useful.

Fourier Series are really neat as well. Another thing is other infinite series representations. Fourier is for sine/cosine, but there are all sorts of other functions you can do. Learning about orthogonal functions on an interval and expanding series in Legendre polynomials is useful.

Why not try to track down some cool uses to the parametric functions you learn towards the end of calc II?

Using center of mass / volumes of revolution to find something like the moment of inertia about different axes are a cool application of Calc II techniques, but may require you delve a little bit into 3-D calculus.