Udemy – Calculus 2, part 2 of 2: Sequences and series 2025-4

Udemy – Calculus 2, part 2 of 2: Sequences and series 2025-4 Downloadly IRSpace

Apr 18, 2025 - 19:55 Updated: Aug 17, 2025 - 19:14

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Udemy – Calculus 2, part 2 of 2: Sequences and series 2025-4

Calculus 2, part 2 of 2: Sequences and series, You 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. You 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. You 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. You will learn: more (than in Calc1p1) about the relationships between monotonicity, boundedness, and convergence of number sequences; subsequences and their limits; limit superior and limit inferior (reading material only: Section 3.6 on pages 50-55 in the UC Davis notes); Bolzano-Weierstrass Theorem; fundamental sequences (sequences with Cauchy property), their boundedness and convergence; construction of the set of real numbers with help of equivalence classes of fundamental sequences of rational numbers; the definition of complete metric spaces.

What you’ll learn

How to solve problems concerning sequences and series (illustrated with 378 solved problems) and why these methods work.
Various ways of defining number sequences: with help of a descriptive definition, an explicit (closed) formula, a recursive definition.
Limits of number sequences, both finite and infinite (repetition and continuation of the topic introduced in Calc1p1).
Arithmetic on extended reals (repetition and continuation of the topic introduced in Calc1p1).
Dealing with indeterminate forms (repetition and continuation of the topic introduced in Calc1p1).
Standard limits, comparing infinities (repetition and continuation of the topic introduced in Calc1p1).
Squeeze Theorem for sequences (repetition and continuation of the topic introduced in Calc1p1).
Weierstrass’ Theorem for sequences (repetition and continuation of the topic introduced in Calc1p1).
Functions defined for all positive arguments and their role in examining number sequences (monotonicity, limits).
Solving recurrence relations: closed formula for linear recurrences of order two (with or without initial conditions).

Who this course is for

University and college students wanting to learn Single Variable Calculus (or Real Analysis)
High school students curious about university mathematics; the course is intended for purchase by adults for these students

Specificatoin of Calculus 2, part 2 of 2: Sequences and series

Publisher : Udemy
Teacher : Hania Uscka-Wehlou , Martin Wehlou
Language : English
Level : All Levels
Number of Course : 273
Duration : 60 hours and 36 minutes

Content of Calculus 2, part 2 of 2: Sequences and series

Calculus 2, part 2 of 2_ Sequences and series

Requirements

Calculus 1: Limits and continuity (or equivalent)
Calculus 1: Derivatives with applications (or equivalent)
Calculus 2: Integrals with applications (or equilvalent)
You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody’s advantage if you ask your questions on the forum.

Udemy – Calculus 2, part 2 of 2: Sequences and series 2025-4