ABC: Approach to the Basics of Calculus (Real line, sequences and series)

In the chapter Real line, sequences and series you will find:

1. The Real Line
   [Adams P1, Appendix III]
2. Sequences of Real Numbers
   [Adams 9.1]
3. Series
   [Adams 9.2-9.3]
4. Convergence Criteria
   [Adams 9.3-9.4]

Basic definitions of sequences and series of real numbers are give. Some necessary properties of sets of real numbers are a also given. These properties are necessary for understanding other topics in this Chapter. Concepts from this Chapter are used later for defining and proving many fundamental properties for functions of a real variable.

Learning outcomes

Student knows definitions of the area of a plane set and the Riemann integral. Student can give examples of functions that are Riemann integrable and of ones that are not. Student can apply standard integration methods, such as integration by parts and substitutions to obtain definite and indefinite integrals of elementary functions.