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, Taylorís remainder formula.

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.