Thread: Advanced calculus

as you may recognize from my earlier posts, its based on calculus. I'm just wondering, after we learn all this basic integration and differentiation with trigonometry, log, integer variable;

when do we learn the surface and line, and volume integral, is it the higher calculus, exactly when do we interact with that? because im currently studied A-maths, (advanced maths) and it is very similar to what im going to face in my next two years (except it is going to have more chapters) , and surely it doesn't interact with this level of calculus, and mathematics. is it for when you are going for pure physics and maths in University?
anyone who is a mathematician for real in this forum who specializes in calculus, any advices would be great

thank you for your time, and would appreciate any advices.

Here in the states calculus usually lasts five quarters (three per year) or three semesters (two per year), or about a year and a half of university-level study.

During the final two quarters (or final semester) the more advanced topics to which you made reference are studied. That completes the calculus sequence required of all math, engineering and science majors (biology students may have different requirements).

This calculus sequence is taken during the first two years of university study and the student would typically have three semesters of physics and two of chemistry along with calculus. This is the typical minimun basic requirement and further study of these subjects will depend on the specific major elected by the student (math, chemistry, engineering, physics, etc.).

Hope that answers your question.

Oh, and by the way, while mathematics has an 's' at the end, the short name of "math" would not; that is, "maths" is not used.

Originally Posted by Ots

Oh, and by the way, while mathematics has an 's' at the end, the short name of "math" would not; that is, "maths" is not used.

It often is in Europe and Britain.

Originally Posted by Heinsbergrelatz

as you may recognize from my earlier posts, its based on calculus. I'm just wondering, after we learn all this basic integration and differentiation with trigonometry, log, integer variable;

when do we learn the surface and line, and volume integral, is it the higher calculus, exactly when do we interact with that? because im currently studied A-maths, (advanced maths) and it is very similar to what im going to face in my next two years (except it is going to have more chapters) , and surely it doesn't interact with this level of calculus, and mathematics. is it for when you are going for pure physics and maths in University?
anyone who is a mathematician for real in this forum who specializes in calculus, any advices would be great

thank you for your time, and would appreciate any advices.

Line integrals, surface integrals and such are usually taught as part of what is called "Advanced Calculus" in the U.S. which is a third or fourth year class for students who already have three semesters of calculus and another semester of linear algebra. It is also taught in classes on vector analysis, mathematical methods for physics and engineering and in classes on electromagnetic theory. To really do it right one studies manifolds and learns about the integration of forms.

You can find a nice introductory treatment in Spivak's Calculus on Manifolds.

Originally Posted by inow

Originally Posted by Ots

Oh, and by the way, while mathematics has an 's' at the end, the short name of "math" would not; that is, "maths" is not used.

It often is in Europe and Britain.

That may very well be true but that doesn't make it correct.

Originally Posted by Ots

Originally Posted by inow

Originally Posted by Ots

Oh, and by the way, while mathematics has an 's' at the end, the short name of "math" would not; that is, "maths" is not used.

It often is in Europe and Britain.

That may very well be true but that doesn't make it correct.

I agree, but the question was not one of right/wrong, but one of used/unused. 8)

Either way, it appears I may have accidentally derailed the thread, and that was never my intention. Sorry for the interruption, guys.

Originally Posted by inow

Originally Posted by Ots

Originally Posted by inow

Originally Posted by Ots

Oh, and by the way, while mathematics has an 's' at the end, the short name of "math" would not; that is, "maths" is not used.

It often is in Europe and Britain.

That may very well be true but that doesn't make it correct.

I agree, but the question was not one of right/wrong, but one of used/unused. 8)

Either way, it appears I may have accidentally derailed the thread, and that was never my intention. Sorry for the interruption, guys.

Ots is, typically, myopic. It is quite correct to use "maths", which is consistent with British useage. It just as correct as the use of "boot" for the American "trunk".

On the other hand, your compadres in Texas may give your some odd looks.

So it seems, ill have to face it anyway, whether it is now or later, because im thinking of continuing my study with calculus throughout my pre uni, and university.

anyway, thank you all for your facts, and advices, now i seem to get alittle idea of when im gonna clash in to it, and to Dr rocket, appreciate your offer for the book "Michael Spivak's Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus", ill try and get it, or borrow it from the local library.

Originally Posted by inow

Originally Posted by Ots

Originally Posted by inow

Originally Posted by Ots

Oh, and by the way, while mathematics has an 's' at the end, the short name of "math" would not; that is, "maths" is not used.

It often is in Europe and Britain.

That may very well be true but that doesn't make it correct.

I agree, but the question was not one of right/wrong, but one of used/unused. 8)

Either way, it appears I may have accidentally derailed the thread, and that was never my intention. Sorry for the interruption, guys.

Actually, in my myopic way I was giving H-berger some info for his/her use, as I have lived in Europe and speak several languages. Myopically though, of course.

H-berger

to ots;

i would appreciate it if you could address my user i.d. properly though it doesn't matter significantly. thank you