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

1. Important stuff from before the second exam, primarily methods of computing derivatives, common functions, and mathematical modeling. Also algebraic manipulation.
2. Initial value problems for differential equations
1. Antiderivatives and general solutions
2. Initial conditions and specific solutions
3. Simple modeling (such as velocity/acceleration problems)
3. Definition of the definite integral
1. Partitions and intermediate (sample) points
2. Riemann sums
3. Limiting behavior of Riemann sums
4. Interpretation of the definite integral (signed area, accumulated rate of change)
5. FTC 1: the definite integral is the difference of antiderivative values at the upper and lower limits
6. 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!)
7. Substitution to get antiderivatives and to evaluate definite integrals.
8. Exponential growth and decay (Cekt)
9. Area between two curves