tag:blogger.com,1999:blog-5303307482158922565.post5984002972123712402..comments2024-07-23T09:12:20.588-07:00Comments on Math Mama Writes...: What is Calculus? Part OneSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5303307482158922565.post-21810131653147329382013-11-02T09:54:22.439-07:002013-11-02T09:54:22.439-07:00Here's the link to the fascinating article Pat...Here's the link to the fascinating article Pat references above: http://www.maa.org/programs/maa-awards/writing-awards/the-lost-calculus-1637-1670-tangency-and-optimization-without-limits<br /><br />Thanks, Pat!Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-66688996054233202252013-11-01T00:59:22.357-07:002013-11-01T00:59:22.357-07:00Or?
I tell them it's about finding areas and...Or? <br /><br />I tell them it's about finding areas and volumes, and the powerful tool it uses is summation. The idea of infinitely close points from derivatives becomes the idea of infinitely thin slices.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-41228235011709482782013-11-01T00:10:39.199-07:002013-11-01T00:10:39.199-07:00Hi Sue, great topic of discussion. I just wondered...Hi Sue, great topic of discussion. I just wondered what you tell your students? Do you tell them that integral calculus is about infinite summations or about finding areas and volumes? Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-45946533025330568332013-10-31T20:45:07.424-07:002013-10-31T20:45:07.424-07:00Ecept that before the Mayor of Amsterdam, Johann H...Ecept that before the Mayor of Amsterdam, Johann Hudde, found tangents and maxima without limits. See "The Lost Calculus (1637-1670), Tangency and Optimization without Limits", by Jeff Suzuki in the MAA Mathematics Magazine, Dec, 2005. A virtual unknown of whom it is told, "Leibniz in particular was impressed with Hudde’s work, and when Johann Bernoulli proposed the brachistochrone problem, Leibniz lamented:<br />If Huygens lived and was healthy, the man would rest, except to solve your problem. Now there is no one to expect a quick solution from, except for the Marquis de l’Hˆopital, your brother [Jacob Bernoulli], and Newton, and to this list we might add Hudde, the Mayor of Amsterdam, except that some time ago he put aside these pursuits ."<br />By the way, Calculus teachers who dismiss l'Hoptial for puchasing Bernoulli's work might re-examine their position in light of such praise from Leibniz.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-5005861947684643802013-10-31T20:18:02.948-07:002013-10-31T20:18:02.948-07:00Sometimes it's the students who give us a grea...Sometimes it's the students who give us a great entryway...A student of mine asked me a great question. "Mr. Abdulla. I get the idea of average velocity, but what do you mean when you say something has a velocity of 2.5 m/s at exactly 2 seconds. I mean, at exactly at 2 seconds, like at that exact moment doesn't make any sense." To actually answer that question requires us to define a derivative much the way Leibniz did, if I remember correctlyMr. Abdullahttps://www.blogger.com/profile/05759785210972777854noreply@blogger.com