*My* summary of principal subject matter for the
second exam in Math 152, spring 2008

The exam will emphasize material discussed since the first exam, but
knowledge of older material will certainly be needed to do well. The
material tested is discussed in the
second section of the diary where there are a number of
examples. The text has further examples and supporting discussion.
- Quantities computed by definite integrals
- Arc length
- Surface area of surfaces obtained by revolving curves around an axis

- Taylor's Theorem
- Taylor polynomials
- Using the Error Bound coming from Taylor's Theorem

- Differential equations
- Initial value problem and verifying that a function is a solution
- Modeling using differential equations
- Separable differential equations
- Slope field (direction field) methods; asymptotic behavior including equilibrium solutions

- Sequences
- Convergence and divergence
- Sequences and continuous functions
- Bounded monotonic sequences converge

- Series
- Convergence and divergence
- Examples (geometric series, p-series)
- Absolute & conditional convergence
*Tests* for convergence: Comparison, Limit Comparison, Integral, Ratio, Root

- Power series and the radius of convergence and interval of
convergence

**
Maintained by **`
greenfie@math.rutgers.edu` and last modified 4/13/2008.