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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
by 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 agoOK. 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.