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Here in Brasil math is "divided" on fundamental, average and superior, where superior is the math that you learn on universities, like calculus, integrals, limits, derivates, etc.

My question is really simples, and it's about "high math". You that studied in universities or faculties will know it by definitions...

What the order that I need to study that high math subjects (calculus, integrals, limits, derivates, etc)?



PS: "What subject area do you want to learn? Or what area(s) look interesting to you?"

I'm interested in the "default" area, it is, when you join the university at some exact science courses like electronics, electric, computing sciences, etc, you will learn math. I don't know what you learn in that "math". I heard some terms, like calculus or limits and derivates, but I don't know a "sequence" to self-learn that subjects...

What the math subjects and/or what's the order, from first to last, to learn it?

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What subject area do you want to learn? Or what area(s) look interesting to you? In short, one might say "there exist many roads". For instance, with the teaching of calculus "today" what Arturo wrote does seem generally the case, but historically things differed, and there does exist a rather notable calculus text (Tom Apostol's Calculus) where the study of integration precedes that of differentiation. Much of linear algebra doesn't require calculus, but usually people learn linear algebra after, or along with, calculus these days. – Doug Spoonwood Aug 14 '11 at 23:12
You might find it useful to examine some university course catalog. Pick a university you know and look at their math courses. – Adam Saltz Aug 15 '11 at 0:36
The order depends on the major and the university. Generally speaking, in the U.S., single-variable Calculus tends to be the first "advanced math course", though many universities have several versions (some for the "hard sciences", some for life sciences, some for business school, etc). But this is very different, e.g., in Mexico, and I would expect it to be very different in Brasil as well. – Arturo Magidin Aug 15 '11 at 2:31

"Calculus" is divided into two parts, "Differential calculus" and "Integral calculus". Derivatives are studied in differential calculus, integrals are studied in Integral calculus. Limits are usually part of differential calculus. So the subjects you list are not distinct, they are all part of the same subject: Calculus.

That said, within Calculus one usually learns one-variable limits first, then single-variable differential calculus (which includes derivatives of real valued functions of real variable), then single-variable integral calculus (which includes integrals of real valued functions of real variables).

Then you study multi-variable calculus, going over the same order (limits, derivatives, integrals).

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