06.01.2019: One Chapter of Math – Calculus Made Easy: Chapter 1

Today’s soundtrack is Victory Christian Centre: Majesty, a live worship album that wears its influence on its sleeve (pun intended).

So here we are! Today, I’m starting on the first chapter of Silvanus P. Thompson’s classic book, Calculus Made Easy. The book was originally published in 1919, but has since been revised twice: once in 1945 and once in 1998.

Right away, Thompson uses humour to make the reader feel at ease, opening the prologue with a Simian proverb: “‘What one fool can do, another can'” (Thompson, 1998, p. 35). He upbraids the writers of mathematics textbooks as having a “desire to impress […] with their tremendous cleverness” (Thompson, 1998, p. 38), as they seem to try to find the hardest way to solve a given problem. Thompson claims that he is himself “a remarkably stupid fellow [who] had to unteach [himself] the difficulties” (p. 38) and now wants to share the tricks that he uses to make the easy calculations easy and the difficult ones not quite so hard.

In beginning the first chapter, Thompson says that there are two symbols that we will use often in calculus. They are d and ∫. The former “merely means ‘a little bit of'” (Thompson, 1998, p. 39); the latter (which is called the integral symbol) may be called “‘the sum of'” (Thompson, 1998, p. 39). “Thus,” says Thompson (1998), “∫dx means the sum of all the little bits of x” (p. 39).

So whenever we see “an expression that begins with this terrifying symbol [( ∫ ), we] will henceforth known that it is put there merely to give [us] instructions that you are now to perform the operation (if you can) of totalling up all the little bits that are indicated by the symbols that follow” (Thompson, 1998, p. 40).

That’s it for today! Next time, I’ll be reading the second chapter.

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