The next step in calculus.

[Cogman]

this last school year I finished High school calculus, and as strange as it sounds, I actually enjoyed it. The major part of this level of calculus was finding the areas betwean a graph and the axis of the graph, finding derivitives, and doing rotationals. So whats next? Is it going to deal a lot with multiple variables, or is it going to deal mainly with finding volumes.

Dont know how highly technical this is, but I guess you guys can throw in your favorite forumlas and explain where they come from and such to spice it up a bit

 

[Kibbo]

Dude,

You have yet to discover the beauty of Integration. Some of the calculations are a bit inelegant, and it's not quite as universal as Derivation, but it is soooo useful.

 

[Cogman]

integration? I believe That I already have learned about integration, how else could I find the area of a rotation, or find the area betwean a graph the axises.?

Unless there is more to intigration then im realizing.

 

[Mday]

Calculus is not a HS course. So, unless you took AP Calc AB or BC, or whatever they call it now, we dont know what you know.

Calc 1 = intro to calc, differentiation and integration
Calc 2 = integration techniques and infinite series
Calc 3 = multivariable calculus
Then following the DIRECT calculus route you have
Real Analysis = imagine your first month of calc 1 be an indepth course, and lasting 3 months, further exploring continuity or the lack there of
Complex Analysis = what happens when 'i' becomes part of the equation? and further into the realm of continuity with respect to the complex plane. if continuity is pretty before, yielding super duper nice results, continuity in the complex world is even more so. that is, continuity with respect to differentiation and integration.

There are graduate levels of real and complex analysis.

Then there is calculus on steroids (not really): TENSORS.

Then there are side courses related to the above:
Ordinary differential equations
Partial differential equations
Topology (wavering on whether it should be mentioned)
Differential Geometry (wavering on whether it should be mentioned)