Posted by MathOnNapkins

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Don't be a pussy. Take the BC Calculus exam. It's not just about not paying for college, it's proving how much you kick ass.

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Posted by Collegeboard BC Criteria that I haven't covered in class

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+ Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration.

# + Numerical solution of differential equations using Euler's method.
# + L'Hôpital's Rule, including its use in determining limits and convergence of improper integrals and series.

+ Solving logistic differential equations and using them in modeling.

IV. *Polynomial Approximations and Series
A. *Concept of Series

A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence or divergence.
B. *Series of constants

* + Motivating examples, including decimal expansion.
* + Geometric series with applications.
* + The harmonic series.
* + Alternating series with error bound.
* + Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series.
* + The ratio test for convergence and divergence.
* + Comparing series to test for convergence or divergence.

C. *Taylor Series

* + Taylor polynomial approximation with graphical demonstration of convergence. (For example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve.)
* + Maclaurin series and the general Taylor series centered at x = a.
* + Maclaurin series for the functions ex, sin x, cos x, and 1/(1-x).
* + Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series.
* + Functions defined by power series.
* + Radius and interval of convergence of power series.
* + Lagrange error bound for Taylor polynomials.

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Posted by MathOnNapkins

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The BC boils down to this...

most of the additional material is on series and convergence of series. L'hopital's rule is something I'd think you would have already covered anyway. Euler's method must have been added in the time since I took the test. But it's not extremely hard to understand anyway. I would say the hardest part of BC is figuring out how to find an interval or radius of convergence. The other stuff is relatively simple. Velocity? 1st Derivative. Acceleration? 2nd Derivative. (of a paremetric curve anyway).

The more obscure material is on curvature and stuff in 3 dimensions but it boils down to memorizing formulas.

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