Higher order Calc project

In summary, the conversation suggests that there are several topics for a high school math project, including polar coordinates and integration, fractional derivatives, and series. Fractional calculus is considered to be a cool topic, but may not have as many practical applications as the other two. It is also mentioned that understanding basic calculus concepts on a deeper level may be a good project idea. Additionally, there is a resource provided for further information on the applications of fractional calculus.
  • #1
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I was wondering if there are any topics for calculus based or advanced high school math project that I can devote my whole semester to at school.
 
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  • #2
It depends of what you know about calculus. Some ideas are:

- polar coordinates and integration of polar curves
- fractional derivatives
- series and Taylor series

All of these should be quite ok for an interested high-school student...
 
  • #3
Hmm. Fractional calculus sounds pretty cool. But any cool applications associated with that?
 
  • #4
Hmm, I don't know any applications of fractional calculus. There might be some, but I think they're very complicated...

If you're looking for applications, then the other two topics sure have a lot of applications. But they might be less cool than fractional calculus :smile:
 
  • #5
Fractional calculus is possible for an advanced high school student to "discover", but probably not to "develop" the theory very much. Doing so, at the very least, requires some complex analytic properties of the Gamma function which we use as the meromorphic continuation of factorials onto the complex plane.

If you already know basic calculus, perhaps your project could be to write an essay that places some of those calculus concepts on a firmer, more rigorous groundwork (ie, introduce yourself to basic real analysis). Apostol's Calculus Vol.1 does this quite well.
 
  • #6
Is it possible to interpret fractional calculus in a physical sense like the first derivative is the rate of change, but if it's fractional, what does that represent?
 
  • #7
http://www.icp.uni-stuttgart.de/Jahresberichte/01/node2.html [Broken]

provides a good detailed explanation of the applications. It doesn't really look too hard though.
 
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1. What is the purpose of a "Higher order Calc project"?

A "Higher order Calc project" typically refers to a project or assignment in a higher level calculus course that involves the use of more advanced mathematical concepts and techniques. The purpose of such a project is to challenge students and further develop their understanding and application of calculus.

2. What topics are typically covered in a "Higher order Calc project"?

The topics covered in a "Higher order Calc project" can vary, but they often include topics such as multivariable calculus, vector calculus, differential equations, and advanced integration techniques.

3. How difficult are "Higher order Calc projects" compared to other calculus assignments?

"Higher order Calc projects" are typically more challenging than other calculus assignments, as they require a deeper understanding and application of advanced concepts. However, the difficulty level may vary depending on the specific project and the individual student's strengths and weaknesses.

4. Can "Higher order Calc projects" be completed individually or in groups?

This may vary depending on the instructor's preference, but "Higher order Calc projects" are often completed individually in order to assess each student's understanding and skills. However, some instructors may allow or even require students to work in groups on these projects.

5. How can "Higher order Calc projects" be beneficial for students?

"Higher order Calc projects" can be beneficial for students as they provide an opportunity to apply and deepen their understanding of advanced calculus concepts. They also help to prepare students for more challenging courses and real-world applications of calculus in fields such as engineering, physics, and economics.

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