trying to be a mile wide AND a mile deep
From the Editor in Notices of the AMS Vol 43, Issue 10 (October 1996) was an essay on the need for mathematical literacy in the general public, beginning with Nixon’s use of the third derivative. A beginner’s guide to quadric surfaces (pdf), by me, for my calculus students and intended to supplement the textbook rather […]
Happy St. Patrick’s Day! Here, have an awkward flow chart.
In case it wasn’t clear from musings on series, these posts are collections of themed material that individually don’t make full posts. 1. There are many ways for a limit to fail to exist. It could be infinite, oscillate within a finite interval, completely devolve into radio static, or simply give you different values when […]
1. “Sufficiently large” is an important concept in sequences and series. In essence it means any crazy thing can happen for as long as it wants to happen, so long as there is a finite point after which the sequence or series starts behaving in a controlled/predictable way. A finite number of terms can’t affect […]
I like to present totally cooked-up examples demonstrating the reason for certain hypotheses or limitations in calculus, in the hope that they will help students remember and correctly apply the theorems more easily. Here are a few. Note that the sequence has limit 0 but the function oscillates. This is why you can use convergence […]
One of the main things students struggle with on exams is identifying the method to use on each problem. When they are learned in class, they are segregated by type, and their distinguishing features are not always highlighted. Here’s a brief cheat sheet on related rates and optimization. optimization related rates sample keywords maximize, minimize, […]