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Ideas Re: Practical Projects using MV Calculus and Linear Algebra

  1. Dec 23, 2012 #1
    Hi everyone,

    I'm a grade 11 student in HS and am currently studying MV Calculus and Linear Algebra from distance learning through Stanford. Due to some problems, I'm going pretty slowly but I expect things to pick up soon. Anyway, I have an agreement with my school that if I complete a project that demonstrates my knowledge of the information taught in the aforementioned courses, they will give me credit-otherwise, I am screwed.

    Unfortunately, I have no clue what to do. My research experience and interests are mainly in various fields of biology and although our work is based on physics and mathematics principles, the actual experiments don't go indepth. I was originally planning to do something with general physics (last year, I explained special relativity w/ proofs for my physics class) but I've had no time to touch physics, as I'm buried with copious amounts of work. I am interested in learning more about programming and CS but again, I want to learn it properly and not sort of rush through to put something together.

    As such, do you guys have any suggestions with regards to a reasonable project that I could complete that demonstrated my knowledge in these fields? My proposal is due by Jan 7th. My teacher suggested fluid dynamics and someone else told me economics (?) but I'm not really sure how/if I could do that. Thanks- all opinions are very much welcome :)
  2. jcsd
  3. Dec 24, 2012 #2

    Stephen Tashi

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    If your main goal is to get academic credit for your online work, your primary problem involves the sociological question of approval, not any technical mathematical question.

    Who will judge your project? (Presumably, it won't be the members of physicforums, however fascinating their suggestions may be.) If your teacher or someone else has a significant vote in evaluating your project and they have a definite vision of a project, the safest bet is take their suggestions. Don't vary from them.

    If your advisors are making suggestions off the top of their heads, then you should investigate what kinds of projects have been approved for credit in the past for other students.

    Perhaps you are the first student doing this and perhaps none of you advisors knows multivariable calculus very well. Then you have great freedom in picking a topic. Is that the situation?

    Both the suggestions your were given involve learning subject matter outside of the the mathematics. Is that a requirement? (You say you are buried in work and that you don't want to spend time learning additional subjects.)
  4. Dec 24, 2012 #3
    Thanks for the response.
    Yep, basically. The people that will be evaluating me are undoubtedly intelligent; however, I think it's been a while since they've studied multivariable or linear algebra.

    No, it's not. I actually don't have a problem with learning new things, but I don't see the point of taking on a "sequential" subject or idea (that needs to be taught in a certain order to make sense) and rushing through it poorly just to finish this project.

    However, I will be devoting a large amount of time to learning general and organic chemistry for something else I absolutely need to do. As such, if I could do something involving math in these areas, I would be very happy to do it. I'm also ready to do studies of relatively 'isolated' topics that can be learnt without bypassing or skipping around important fundamentals. I'm just not sure where/what things to look at. If anyone has any ideas on a topic or idea that fits one of the above criteria, I'm all ears!
  5. Dec 24, 2012 #4
    For linear algebra, you could perhaps prove every statement of the invertible matrix theorem in front of the class, or perhaps do a case study of the Leontief consumption matrices and conditions under which they are invertible.

    For multivariable calculus, you could do a basic investigation of the Euler equations, equation of continuity, Bernoulli equations, Toricelli's principle, Navier-Stokes etc. That would be the fluid mechanics route. Under the economics route, you could study various production functions, differential equations governing supply and demad, incentive functions in social choice theory, tax/tariff/price floor/wage floor effects considered using calculus. You could even prove the general case of the law of comparative advantage.

    Could also go into chemistry, then you'd be able to supplement the research quite easily with an experiment. You could show the boiling point elevation of some common substances, such as water, olive oil etc. and then derive the boiling point elevation constant using chemical potentials.

  6. Dec 24, 2012 #5

    Stephen Tashi

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    Are there links to the Stanford material that the public can use? Your would-be advisors might see how to develop applications that are already mentioned in the courses.
  7. Dec 24, 2012 #6
    For my final project in MV calc this year I had to write a paper on the topic of curvature in 3-space, aka differential geometry. Might be more in-depth than what you'd want to pursue in a high school project (I had to do a LOT of research and scratch my head trying to figure it out), but as I recall the computations for gaussian/mean curvature in 3-space could be done using both linear A and multivariable calculus. Perhaps you could explore the overlap between both subjects and tie them into calculating the way something in 3-space curves. Use a computer algebra system to help with some of the computations though, they'll get messy.
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