*My* summary of principal subject matter for the last
part of the semester in Math 151, fall 2007

- Important stuff from before the second exam, primarily methods of
computing derivatives, common functions, and mathematical
modeling. Also algebraic manipulation.
- Initial value problems for differential equations
- Antiderivatives and general solutions
- Initial conditions and specific solutions
- Simple modeling (such as velocity/acceleration problems)

- Definition of the definite integral
- Partitions and intermediate (sample) points
- Riemann sums
- Limiting behavior of Riemann sums

- Interpretation of the definite integral (signed area, accumulated
rate of change)
- FTC 1: the definite integral is the difference of antiderivative
values at the upper and lower limits
- FTC 2: differentiating a variable upper parameter in a definite
integral to get the integrand back
*(Watch out for logical confusion
about the variable in the parameter and the "dummy" variable of
integration!)*
- Substitution to get antiderivatives and to evaluate definite
integrals.
- Exponential growth and decay (Ce
^{kt})
- Area between two curves

**
Maintained by **`
greenfie@math.rutgers.edu` and last modified 12/6/2007.