# Here is where the calculus begins.

#### hhtt

##### Senior Member
Is translation of "Here is where the calculus begins" "Hier beginnt das Kalkül"?

Context is of course mathematics, its field relevant to limits, integrals, derivatives, differential equations. "Here is where the calculus begins" was from introductory part from a calculus text. After the author starts explain limits.

Thank you.

• Kalkül normally has a different meaning in German. Ordinarily we call calculus Infinitesimalrechnung.

Hier beginnt die Infinitesimalrechnung.

EDIT: The word Kalkül is most often used in the expression "das passt (mir) (nicht) ins Kalkül" (it (doesn't) go(es) according to (my) plans). But Duden has a definition I wasn't aware of: "durch ein System von Regeln festgelegte Methode, mit deren Hilfe bestimmte mathematische Probleme systematisch behandelt und automatisch gelöst werden können (z. B. Verfahren zur Auflösung linearer und quadratischer Gleichungen)"

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Ordinarily we call calculus Infinitesimalrechnung.

Are you sure that it is always written adjacant? Is it also "Infinitesimal Rechnung"?

Are you sure that it is always written adjacant? Is it also "Infinitesimal Rechnung"?
Yes, in German we normally compound nouns. If you must, you could write "Infinitesimal-Rechnung" -- but I see no good reason for that.
The separation of the noun as in Infinitesimal Rechnung is a bad habit that has started with the internet and with the orthography reform in the early 2000s. You get more - and sometimes better - search results with Infinitesimal Rechnung than with Infinitesimalrechnung. I consider that a systemic flaw in their search algoritm.

But Duden has a definition I wasn't aware of: "durch ein System von Regeln festgelegte Methode, mit deren Hilfe bestimmte mathematische Probleme systematisch behandelt und automatisch gelöst werden können (z. B. Verfahren zur Auflösung linearer und quadratischer Gleichungen)"

"Kalkül" is used in different parts of math, but not for "calculus"="Infinitesimalrechnung" - at least not in our time. So it is a "false friend". Another example is the "Lambda-Kalkül" used in logic. It has nothing to do with the calculus of Newton.

"Infinitesimalrechnung" is related to Newton's calculus.

This name is seldom used today. For very long times there where doubts about the foundations.

We had the name "Analysis" (related to Leibniz) in maths at the university. It avoids the "infinitely small" sizes and replaced them by limits.

Only recently there were a proof that the "Infinitesimalrechnung" is correct.

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Ich empfinde auch Analysis als das moderne Wort, das sehr gut engl. calculus entspricht. Das soll nicht bedeuten, dass Infinitesimalrechnung als Ausdruck falsch oder ungeeignet wäre, aber zumindest aus naturwissenschaftlicher Sicht ist mir Analysis als Ausdruck geläufiger und gefühlt zumindest auch umfassender.

Analysis ist das, was ich sagen würde, wenn ich Integral- und Differentialrechnung meine.

Thank you, Kajjo.

Is translation of "Here is where the calculus begins" "Hier beginnt das Kalkül"?

Context is of course mathematics, its field relevant to limits, integrals, derivatives, differential equations. "Here is where the calculus begins" was from introductory part from a calculus text. After the author starts explain limits.

Thank you.
If it is not directly related to Newton's calculus, I would propose "Analysis", too.

But by reasons of intonation and rhythm I would use: "Hier fängt die Analysis an."
"Hier beginnt die Analysis." is correct, too.

What kind of text is it?

Analysis ist das, was ich sagen würde, wenn ich Integral- und Differentialrechnung meine.
Wie wird das ausgesprochen?

Here you should use Infinitesimalrechnung because of analysis is used later in the book.

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