Calculus and Analysis

[duff18-votailprof]

Which is the difference between calculus and analysis?

I'm taking a look at mathematics books in english and I'm a bit confused about this separation.

[jhooper3581]

Calculus and analysis

[duff18-votailprof]

I didn't notice your first, clarifier, reply
The difference that you underlined is evident from two books of Tom Apostol, named (surprise surprise) Calculus and Mathematical Analysis, the latter is deeper and more complete.
Thanks for your help

[gugo82]

"duff18":Just to increase my confusion, the programs of Calculus I and Calculus II of the Basic Sequence (I'm referring to the last link) are quite similar to those of Analisi 1 and Analisi 2 of my physics' course.
The same analogy seems to be appliable to the mathematics book that I found, I mean just looking at the summaries.

Yes, but what if you come to the theory behind?

I bet your Analisi 1 and 2 books are way better than any Calculus book, isnt' it?

[duff18-votailprof]

Just to increase my confusion, the programs of Calculus I and Calculus II of the Basic Sequence (I'm referring to the last link) are quite similar to those of Analisi 1 and Analisi 2 of my physics' course.
The same analogy seems to be appliable to the mathematics book that I found, I mean just looking at the summaries.

[gugo82]

One could say that Calculus is the "ground-state" of Analysis, in the sense that it concerns the most applicable (and therefore the most ancient) part of Mathematical Analysis.

In fact, a typical Calculus book contains nothing more but the most elementary facts of Differential and Integral Calculus which are applicable to solve exercises (for example, to study the graph of a function, the convergence of a series, etc...), spiced up with some proofs.
On the other hand, Analysis books usually heavily rely on theory; to better understand the differences, you can just make a comparison of Adams, Calculus: a complete course with Rudin, Principles of Mathematical Analysis...

To cut the long story short, Calculus is finalized to solve simple real-life problems (following the motto "more real-life practice and less theory"), while Analysis is a deep study of the theory which is behind elementary Calculus (and the motto is "more theory and more theoric practice").

[Camillo]

First look at this nice picture

http://web.mit.edu/

and this one
http://web.mit.edu/newsoffice/2010/cat- ... -1112.html


finally here some informations on Calculus I and II (MIT)

http://www-math.mit.edu/academics/under ... culus.html

[dissonance]

As far as I know, Anglo-Saxon univerisities have Calculus courses, typically in the first two years, which are kind of a blend of our "Analisi, Algebra lineare, Geometria". But I've never attended such a university... I don't know directly.