The first part of this course (Chapter 7) is to study several techniques of integration that are commonly
used in calculus such as integration by parts, partial fractions, and trigonometric substitutions. Also, we
study the topic of improper integrals.
The second part (Chapter 9) studies infinite sequences, their limits and some results concerning
convergence and divergence of sequences. Also, this part studies infinite series and their convergence
using the concept of limits. We study various convergence tests such as the integral test, p-test, the
divergence test, comparison test, limit comparison test, root test, ratio test, and the alternating series test.
Power series and Taylor series of functions are studied at the end of this chapter.
The Third part (Chapter 10) is devoted to studying the parametric equations and the polar coordinate
system. We learn about graphing functions in the polar coordinate system, as well as, studying
derivatives, slopes, areas and arc length of functions.
Finally, in the fourth part (Chapters 11) we introduce the topic of vectors in 2-dim and 3-dim real spaces
including the dot product of vectors.