Calculus 2, part 2 of 2: Sequences and series

Calculus 2, part 2 of 2: Sequences and seriesSingle variable calculusS1. Introduction to the courseYou will learn: about the content of this course; you will also get a list of videos form our previous courses where the current topics (sequences and series) were discussed. S2.

Number sequences: a continuation from Calc1p1You will learn: more about sequences, after the introduction given in Calc1p1 (Section 5): in this section we repeat some basic facts from Calc1p1: the concept of a sequence and its limit, basic rules for computing limits of both determinate and indeterminate forms; these concepts are recalled, and you also get more examples of solved problems. S3. Weierstrass' Theorem: a continuation from Calc1p1You will learn: here we continue (after Calc1p1) discussing monotone sequences and their convergence; the main tool is Weierstrass' Theorem, also called "Monotone Convergence Theorem"; after repetition of some basic facts, you will get a lot of solved problems that illustrate the issue in depth.

S4. Using functions while working with sequencesYou will learn: in this section we move to the new stuff: a functional approach to sequences, that we weren't able to study in Calc1p1, as the section about sequences came before the section about functions (in the context of limits and continuity); how to use (for sequences) the theory developed for functions (derivatives, l'Hôpital's rule, etc). S5.

New theorems and tests for convergence of sequencesYou will learn: various tests helping us computing limits of sequences is some cases: Stolz-Cesàro Theorem with some corollaries, the ratio test for sequences; we will prove the theorems, discuss their content, and apply them on various examples. S6. Solving recurrence relationsYou will learn: solving linear recursions of order 2 (an introduction; more will be covered in Discrete Mathematics).