To deliver you from the Preliminary Terrors

Excerpts

• To deliver you from the Preliminary Terrors

  (1) $d$ which merely means “a little bit of.”

• To deliver you from the Preliminary Terrors

  Thus $\ds\int dx$ means the sum of all the little bits of $x$; or $\ds\int dt$ means the sum of all the little bits of $t$.

• To deliver you from the Preliminary Terrors

  The word “integral” simply means “the whole.”

• To deliver you from the Preliminary Terrors

  Thus $dx$ means a little bit of $x$; or $du$ means a little bit of $u$. Ordinary mathematicians think it more polite to say “an element of,” instead of “a little bit of.” Just as you please.

• To deliver you from the Preliminary Terrors

  If you think of the duration of time for one hour, you may (if you like) think of it as cut up into $3600$ little bits called seconds. The whole of the $3600$ little bits added up together make one hour.

• To deliver you from the Preliminary Terrors

  The preliminary terror, which chokes off most fifth-form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning---in common-sense terms---of the two principal symbols that are used in calculating.

• To deliver you from the Preliminary Terrors

  Now any fool can see that if $x$ is considered as made up of a lot of little bits, each of which is called $dx$, if you add them all up together you get the sum of all the $dx$’s, (which is the same thing as the whole of $x$). The word “integral” simply means “the whole.”

• To deliver you from the Preliminary Terrors

  When you see an expression that begins with this terrifying symbol, you will henceforth know that it is put there merely to give you 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. That’s all.

Equations

Problems

No exercises in this chapter.