trying to be a mile wide AND a mile deep
The key to the equations of lines and planes in three dimensions is that, in each case, we need a point to locate the object in space, and a vector to tilt it at the correct angle. In each case, however, the kind of vector that unambiguously gives the direction of the object is different. […]
To work with factorial in series, you often simply need the ratio test. However, sometimes the ratio test doesn’t give a tractable fraction. In those cases it is good to remember the definition of factorial, in particular the fact that n! = n·(n-1)!, and that tests for convergence typically have conditions that need only hold […]
In a number of tests for series convergence and divergence, you locate or calculate a quantity and draw conclusions based on its value. Here’s a table of which values give what conclusions, for five such tests. Note that the table assumes the series is of the correct form for the test to apply at all […]
1. There is no one multiplication for vectors. You can define multiplication-like operations; some give scalars (dot product and other inner products) and some give vectors (cross product). Nicely, these behave like regular products when it comes to vector-valued functions: the product rule applies when you differentiate (though you must maintain ordering with cross product!). […]
This is a page I made for my statistics students in Spring of 2010. I can’t guarantee it’s perfectly accurate with a current version of Excel because I don’t have Excel on my current computer, but I assume it should still be very close. In all of the below, “data” (“x-data”, “y-data”) stands in for […]
1. Drawing causation conclusions Ski and snowboard sales tend to rise and fall together, but sales of one don’t lead to sales of the other – they are both tied to an outside factor. Throughout grade school, mathematical skills correlate positively to height. Height doesn’t make you good at math, but older children are on […]