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
6 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2013 at 19:33 | comment | added | Charles Staats | Oh--one other note: I can attest from my experience that basically skipping sequences and going straight to series does seem to work. | |
| Jul 12, 2013 at 19:31 | comment | added | Charles Staats | I would note that I think it's important to be able to address why the series always diverges outside the radius of convergence, since this can be counterintuitive in many examples (e.g., when $f(x) = 1/(1-x)$, it's intuitive that the series diverges for $x \ge 1$ but not for $x < -1$). But this example can be done using the ratio test, along with some rough explanation that the divergence is necessary because the summands keep getting bigger rather than smaller. | |
| Jul 12, 2013 at 19:26 | comment | added | Charles Staats | Actually, I was in a similar situation--the course I was teaching was specifically targeted at students with poor precalculus backgrounds. However, at my university, which is known for being very theoretical in all respects, proofs are heavily emphasized even at this level. So, for instance, by this point in the course, my students more or less understood how to do a very (very!) basic epsilon-delta proof even if they could not add fractions. | |
| Jul 12, 2013 at 16:12 | comment | added | Frank Thorne | Thanks Charles. The level of our students is such that I feel I should skip most or all of the proofs. Especially since there is a separate honors section of calculus. | |
| S Jul 12, 2013 at 15:21 | history | answered | Charles Staats | CC BY-SA 3.0 | |
| S Jul 12, 2013 at 15:21 | history | made wiki | Post Made Community Wiki by Charles Staats |