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If you have stretchable ropes, massive pulleys and air resistance, you'll need to be able to solve some complex differential equations which, in the North-Ameri

If you have stretchable ropes, massive pulleys and air resistance, you'll need to be able to solve some complex differential equations which, in the North-American context, would not be taught until 2nd year university. Yet, the simple concepts of conservation of energy and momentum can be taught using simple algebra at the high school level with these idealized systems. As for the deficit of practioners ... there are at least 10 times as many people getting a Ph.D. in Physics in Canada and the U.S. as there are positions ... so, no, there is no real shortage. (There is a shortage of qualified high school teachers though.)

learnstats2 12y ago
You absolutely don't need to solve complex differential equations for this purpose, unless you want a closed form. Let's be more imaginative: Numerical analysis of the same model would be fine for high school level and is likely to give a great and relevant insight into mechanics. Why is the closed form considered a prerequisite for a numerical approximation? Just because we ultimately end up at the latter, doesn't mean it should be taught in that order. I may be mistaken about the practitioners but I doubt many Physics PhDs are short of work. It certainly seems like employers want more of them.
- aroberge 12y ago
  Whether you find a closed form solution (and, for most realistic systems you will not) or you want to solve it numerically ... you still need to write a set of differential equations. Before you learn about differential equations, you need to have done some basic calculus. You can not teach high school students what differential equations are, how they describe mechanical systems, and how to solve them numerically. However, using the math they know, you can teach them to find solutions to idealized systems that illustrate conservation of energy and momentum which are fundamental physics concepts.
  - deleted 12y ago
    [deleted]
  - learnstats2 12y ago
    OK. I accept much of what you say. But it's perhaps not a coincidence that calculus and classical mechanics were invented at the same time in history - indeed, both were advanced significantly by the same person. Classical mechanics and calculus are two sides of the same coin. Fundamental Theorem of Calculus: <=1670 Principia Mathematica: >=1687 So which order do you prefer to teach them? In truth, HS math students do learn about differential equations, and easily have the capacity to apply them numerically. Some historical context and a little creativity in teaching could greatly help the understanding of both and benefit many students.

learnstats2 12y ago

You absolutely don't need to solve complex differential equations for this purpose, unless you want a closed form. Let's be more imaginative: Numerical analysis of the same model would be fine for high school level and is likely to give a great and relevant insight into mechanics. Why is the closed form considered a prerequisite for a numerical approximation? Just because we ultimately end up at the latter, doesn't mean it should be taught in that order. I may be mistaken about the practitioners but I doubt many Physics PhDs are short of work. It certainly seems like employers want more of them.

aroberge 12y ago
Whether you find a closed form solution (and, for most realistic systems you will not) or you want to solve it numerically ... you still need to write a set of differential equations. Before you learn about differential equations, you need to have done some basic calculus. You can not teach high school students what differential equations are, how they describe mechanical systems, and how to solve them numerically. However, using the math they know, you can teach them to find solutions to idealized systems that illustrate conservation of energy and momentum which are fundamental physics concepts.
- deleted 12y ago
  [deleted]
- learnstats2 12y ago
  OK. I accept much of what you say. But it's perhaps not a coincidence that calculus and classical mechanics were invented at the same time in history - indeed, both were advanced significantly by the same person. Classical mechanics and calculus are two sides of the same coin. Fundamental Theorem of Calculus: <=1670 Principia Mathematica: >=1687 So which order do you prefer to teach them? In truth, HS math students do learn about differential equations, and easily have the capacity to apply them numerically. Some historical context and a little creativity in teaching could greatly help the understanding of both and benefit many students.