Timeline for Calculus Teaching: Is it possible or desirable to give a severely abbreviated treatment of series convergence tests?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2014 at 4:28 | history | edited | Ricardo Andrade |
added top level tag describing subject
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| Feb 5, 2014 at 3:58 | history | edited | Andrés E. Caicedo |
edited tags
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| Jul 12, 2013 at 23:14 | comment | added | The User | Out of curiosity because I do not know the system well: Am I right that skipping most of the proofs is normal in US calculus lectures? | |
| Jul 12, 2013 at 22:05 | comment | added | KConrad | I had a meeting yesterday with some engineering faculty at my school to discuss what parts of the first-year calculus curriculum are useful to their 0undergraduate students, and they (the faculty) had no interest in all those convergence tests. They'd much rather students see Fourier series than spend 2 weeks (?) on bazillion convergence tests for power series. | |
| Jul 12, 2013 at 21:19 | answer | added | Amir Asghari | timeline score: 0 | |
| Jul 12, 2013 at 19:00 | comment | added | Matt | I'm at a top tier public university and due to the quarter system (Calc I, II, III happen in Fall, Winter, Spring so only over a year) we don't cover any of the series convergence tests. | |
| Jul 12, 2013 at 18:30 | comment | added | Yemon Choi | I think the main issue would be whether subsequent courses have your course down as a prerequisite where they are supposed to learn "sequences and series". If not, then fine; if so, then probably consultation with the lecturers of those other courses is in order | |
| Jul 12, 2013 at 16:54 | answer | added | Margaret Friedland | timeline score: 5 | |
| Jul 12, 2013 at 16:02 | comment | added | Aaron Hoffman | It seems that there are a small number of big ideas: (1) The geometric series can be explicitly summed; (2) Whether or not a series converges is a property of its tail; (3) If the tail of a series which is known to converge/diverge (in practice the geometric series) dominates/(is dominated by) the tail of some other series, then that series necessarily converges/diverges. It seems to me that if you can get these points across you will have done your students a great service. Caveat: I have no experience trying this in practice and am not a scholar of education. | |
| Jul 12, 2013 at 15:26 | comment | added | Gerald Edgar | This is a course without proofs, primarily for non-math majors? You don't think subsequent physics or engineering courses will want them to know those tests? Then: go for it... (No, I have no experience doing that.) | |
| Jul 12, 2013 at 15:21 | answer | added | Charles Staats | timeline score: 4 | |
| Jul 12, 2013 at 14:47 | history | edited | The User |
that is more about teaching than about pedagogy
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| Jul 12, 2013 at 14:25 | review | Close votes | |||
| Jul 12, 2013 at 16:57 | |||||
| Jul 12, 2013 at 14:16 | comment | added | François G. Dorais | Frank, for CW questions, you now need to flag the moderators. There is still a button to make your answers CW. | |
| Jul 12, 2013 at 14:15 | history | made wiki | Post Made Community Wiki by François G. Dorais | ||
| Jul 12, 2013 at 14:09 | comment | added | stankewicz | Do the topics you've discussed as being skipped here tend to get covered in the multivariable calculus class? | |
| Jul 12, 2013 at 13:58 | comment | added | Frank Thorne | Did the "Community Wiki" option disappear? I would have clicked the button, but it no longer seems to exist. | |
| Jul 12, 2013 at 13:58 | history | asked | Frank Thorne | CC BY-SA 3.0 |