**Basics: **definition of convergence
for infinite series, absolute convergence, conditional convergence, interval
and radius of convergence for power series, Taylor series, parametric curves,
orientation of parametric curves.

**Convergence Tests**: Integral test, comparison test, limit comparison
test, alternating series test, ratio test, root test.

**Divergence Tests**: kth-term test, integral
test, comparison test, limit comparison test, ratio test, root test

**Remainder/Error
Estimations**: Integral test,
alternating series test,

**Elementary Taylor Series**: Geometric series, exponential function, sine and
cosine function, tangent inverse, logarithmic function.

**Techniques: **Deriving
new series from known ones: add/subtract, multiply/divide, differentiate/integrate.

**Application of Taylor Series:** Finding limits, approximating integrals.

**Elementary Parametric Curves:** Lines, circles, ellipse, trivial parameterization.

**Alternative Parameterizations:** Technique to reverse the orientations of parametric
curves.

**Calculus of Parametric Curves:** Position vectors, velocity vectors, tangent lines,
length of curves, surface areas of rotating solids.

**Partial Review Problems**: All homework, quiz, lecture
example problems, and sample exams.