## Calculus: finding volume of revolution: the disc method

The tutor gives an example of the disc method for finding volume of revolution. Usually, the disc method is preferred when the graph is revolved about the x axis. Example: Find the volume generated, x=7 to x=10, when y=-(x-9)2+5 is …

## Calculus: integration by parts: ∫exsinxdx

The tutor shows how to integrate exsinxdx by parts. I’ve written a couple of posts on integration by parts: here and here. The method is used on products, and depends on choosing one function to integrate, then differentiating the other: …

## Microsoft Excel: how to make a square grid for graphing

The tutor explains how, on Excel, to make a grid useful for displaying a graph. In these days of software availability, one would expect making squares on a page to be obvious. Here’s the easiest way I know: In Excel, …

## Number theory: congruence: another problem from Underwood Dudley

The tutor investigates a problem involving the remainder of a power. On page 48 of his Elementary Number Theory, second edition, Underwood Dudley requests the remainder when 20012001 is divided by 26. Solution: 2001 mod 26 = 25 ⇒ 2001 …

## Number theory: another problem from Dudley’s Elementary Number Theory

The tutor investigates a problem involving composite numbers. For problem 4b, page 19, of his Elementary Number Theory (second edition), Dudley invites the reader to prove there are infinite n such that both 6n-1 and 6n+1 are composite. (Composite means …

## Calculus: integration by parts: how to integrate xsinx

The tutor shows an essential example of integration by parts. Back in my July 23 post, I show the formula for integration by parts as ∫uv’=uv-∫vu’ Let’s consider the example ∫xsinxdx Integration by parts is used to integrate a product …

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## Math: linear congruences

The tutor solves a system of linear congruences. Back in my post from March 25, 2014, I explain that “mod” means remainder: for instance, 7 mod 3 = 1. Two numbers that, divided by a number n, give the same …

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## jsDraw2DX Test

The tutor tests graphics with the jsDraw2DX library. jsDraw2DX is a graphics library for JavaScript. I’d call it object-oriented: for programmers used to that style, it may be very intuitive. The tilted text above was generated from the following code: …

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## Calculus: the formula for integration by parts

The tutor shows the motivation behind the integration by parts formula. Integration by parts is a reversal of the product rule (see my post here). If we start with the product rule as (uv)’=uv’ + u’v then we integrate both …

## Psychology: the jnd (just noticeable difference)

The tutor brings up a curiosity from psychology. Around 1860, a scientist named Gustav Fechner was interested in how physical input becomes mental experience – how sensation leads to perception. One of Fechner’s angles for studying that connection was the …

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