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<!DOCTYPE html>
<meta charset="utf-8">
<title>To deliver you from the Preliminary Terrors | Calculus Made Easy</title>
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<style>
body{counter-reset:h1 1}
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<h1><br>To deliver you from the Preliminary Terrors</h1>
<p class="a rotatedFloralHeartBullet">
<p>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.
<p>These dreadful symbols are:
<p>(1) $d$ which merely means “a little bit of.”
<p>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. But you will find that
these little bits (or elements) may be considered to be
indefinitely small.
<p>(2) $\int$ which is merely a long $S$, and may be called
(if you like) “the sum of.”
<p>Thus $\int dx$ means the sum of all the little bits
of $x$; or $\int dt$ means the sum of all the little bits
of $t$. Ordinary mathematicians call this symbol “the
integral of.” 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.” 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.
<p>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.
<p>That's all.
<br>
<hr>
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