Timeline for Why do we teach calculus students the derivative as a limit?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2016 at 6:13 | comment | added | Tom Copeland | Look at Morse and Feshbach's Methods for Theoretical Physics for an intuitive explanation of the form of the Schrodinger equation for the wave function for a free particle. | |
| Jan 29, 2011 at 22:27 | comment | added | Pete L. Clark | ...the equation gives a law governing the behavior of some object over time, and the solution to the equation tells you what the consequences of that law are for the behavior of the object. In particular, my favorite example is m x'' = - kx. To solve this equation without writing down Hooke's Law, a picture of a spring, carefully explaining the physical significance of the minus sign...what a disservice that would be! By making it physical, you give the student a chance to use her intuition: "Well, if I were forced to satisfy this differential equation, what would I do?" | |
| Jan 29, 2011 at 22:21 | comment | added | Pete L. Clark | ...The irony of this for me personally is that I haven't taken a physics class since high school, so all the physics I now know is that which comes up when explaining closely related topics in mathematics. For instance, if I am supposed to talk about first order differential equations, I feel compelled to talk at least a little about second order differential equations, especially those of the form F(x) = c x'', because this is the best motivation I know as to what solving differential equations means and why it's important:... | |
| Jan 29, 2011 at 22:18 | comment | added | Pete L. Clark | I agree that there should be at least somewhat more physics in calculus courses than their currently is. To do it otherwise seems like another example of the decortication of calculus: the subject takes place in a certain intellectual context and as a response to certain scientific problems. A lot of students get really worried when you talk physics though, since they think you're expecting them to have some outside knowledge that they in fact don't have... | |
| Oct 19, 2010 at 14:11 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Sep 27, 2010 at 12:00 | comment | added | Thierry Zell | Interesting answer. I must stress the connections with Physics than I realized, since a student asked me just last week if I taught Physics also. You mention that we tend to only test the algebraic part of calculus; clearly, we should put our money where our mouth is. Because I emphasize the theory, I make sure there are at least some non-algebraic questions on my tests (you can make up some easy ones). If a prof thinks that the audience can only handle the algebraic stuff, I'm ok with it, but then you should be teaching only that. | |
| Sep 27, 2010 at 6:29 | history | answered | Theo Johnson-Freyd | CC BY-SA 2.5 |