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
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.†