New answers tagged

4 votes

Explaining difference between improper integrals that converge and diverge

As Sue VanHattum suggests, it makes sense to shift gears to series first, for simplicity. I would also do two examples of series with decreasing terms, one where it's obvious that it converges, and ...
user avatar
  • 41
9 votes

Explaining difference between improper integrals that converge and diverge

I'd say: Don't trust your eyes, especially not when infinity is concerned and you are plotting in one small region. Sure, they look fairly similar when you are plotting over $[1,10]$. $1/(1+x)$ in ...
user avatar
  • 4,774
6 votes
Accepted

Explaining difference between improper integrals that converge and diverge

Perhaps it's easier for students to see the reason for these results when you are looking at infinite series. Does the course you teach include this? (If not, you can still do it and set up a diagram ...
user avatar
  • 17.3k
4 votes

Explaining difference between improper integrals that converge and diverge

To me (a dumb troll), the way to intuitively think about it is 0 versus infinity. Infinity makes things huge. Zero makes them small. So, if you have an asymptotic approach you have a huge (to ...
user avatar
  • 57
2 votes

Why is differential calculus often presented before integral calculus?

I have come to realize another very practical reason for teaching differentiation before integration. In most applications of integration we are splitting something (area, volume, arclength, work, etc)...
user avatar
4 votes

Multivariable Calculus Project Ideas

I have 3d printing as an extra-credit option for some projects, which are usually framed as a (fictional) business person looking for math equations to use specifically so they can then 3d print their ...
user avatar
  • 41
0 votes

Unusual applications of integration

One that you see (saw) in chem classes was the "cut and weigh" method of integrating area under the peak for strip chart recorders. https://books.google.com/books?id=igR_jsqfcowC&pg=...
user avatar
1 vote

Unusual applications of integration

Something you can do to generate more diverse problems is to combine the problem types from your textbook. You can also be explicit about the kind of work you want them to show you, and make it clear ...
user avatar
2 votes

How does one tutor an A-level student past the derivative paradox?

I'm not sure how I missed this question when it was first posted, and it already has many answers, but I feel there are some important things that still need to be said to address your specific ...
user avatar
8 votes
Accepted

Is "Annular Ring" redundant?

I argue that annular ring is not redundant because in common use annulus and ring are not synonyms. Put another way, not all rings are annular. The adjective annular is used to emphasize that the ring ...
user avatar
  • 5,083
4 votes

Is "Annular Ring" redundant?

Perhaps "formally redundant", depending on who you ask. As in the many comments. But/and a certain amount of redundancy can be good, if it saves time and confusion. "Let me repeat that ...
user avatar
  • 13.5k

Top 50 recent answers are included