Difference between revisions of "Calculus II"
(It was supposed to be a^x ((a^x)/(ln a)), not e^x. And you convert summations of series, not the series themselves into algebraic expressions. (I've inserted some of your changes, though.)) |
(Deleted "summations" (series are already sums)) |
||
| Line 4: | Line 4: | ||
==Overview== | ==Overview== | ||
| − | Lots of integration. Also some series | + | Lots of integration. Also some sequences and series. |
==What actually happens== | ==What actually happens== | ||
| − | After taking Calc I, you may think ''I know differentiation and integration, so what else is there to Calculus?'' Until you [[Multivariate Calculus|leave two dimensions]], it's just more integration. You learned how to integrate all polynomials (of base x) except x<sup>-1</sup> already, so now you'll learn x<sup>-1</sup>, more trig functions than you'll ever want to know, a<sup>x</sup>, integration by parts, and integration by substitution (if you didn't cover it in Calc I). Then you've got applications such as arc length and surface area/volume of a rotated curve. Finally, you'll play around with series for the last bit of the semester. You learn a lot of neat little tricks for turning series | + | After taking Calc I, you may think ''I know differentiation and integration, so what else is there to Calculus?'' Until you [[Multivariate Calculus|leave two dimensions]], it's just more integration. You learned how to integrate all polynomials (of base x) except x<sup>-1</sup> already, so now you'll learn x<sup>-1</sup>, more trig functions than you'll ever want to know, a<sup>x</sup>, integration by parts, and integration by substitution (if you didn't cover it in Calc I). Then you've got applications such as arc length and surface area/volume of a rotated curve. Finally, you'll play around with series for the last bit of the semester. You learn a lot of neat little tricks for turning series into algebraic expressions and figuring out if and when a series converges. |
Revision as of 19:32, 6 May 2006
Official Description
Calculus II (17-121)
Topics include sequences and series, approximations, techniques and applications of integration, and plane curves.
Overview
Lots of integration. Also some sequences and series.
What actually happens
After taking Calc I, you may think I know differentiation and integration, so what else is there to Calculus? Until you leave two dimensions, it's just more integration. You learned how to integrate all polynomials (of base x) except x-1 already, so now you'll learn x-1, more trig functions than you'll ever want to know, ax, integration by parts, and integration by substitution (if you didn't cover it in Calc I). Then you've got applications such as arc length and surface area/volume of a rotated curve. Finally, you'll play around with series for the last bit of the semester. You learn a lot of neat little tricks for turning series into algebraic expressions and figuring out if and when a series converges.
