Скачать или смотреть CALCULUS VI Real Analysis Sequences

Description: This module introduces the foundational concept of sequences in real analysis, a cornerstone of rigorous mathematical reasoning. Students will explore the formal definition of a sequence, limits of sequences, and the criteria for convergence. Key topics include monotonic sequences, boundedness, the completeness property of the real numbers, and important theorems such as the Monotone Convergence Theorem and the Bolzano-Weierstrass Theorem.

keywords: sequence, limit of a sequence, convergent sequence, divergent sequence, bounded sequence, monotonic sequence, supremum, infimum, monotone convergence theorem, Bolzano-Weierstrass theorem, Cauchy sequence, completeness of ℝ, real numbers, epsilon-N definition, subsequence, convergence criteria, upper bound, lower bound, limit point, analysis, real analysis

picture design resources:
AlexAntropov86-Pixabay, geralt-Pixabay, 00rwullie-Pixabay, GDJ-Pixabay, mattiaverga-Pixabay, Pexels-Pixabay, JohnstonMartin-Pixabay, Yuri_B-Pixabay, Mikkehouse-Pixabay, nooneXY-Pixabay, YolGezer-Pixabay, CharlVera-Pixabay.

TIMESTAMPS:
00:00:05 Definition Of A Sequence
00:06:41 Limit Of A Sequence
00:11:45 Convergent & Divergent Sequences
00:13:34 Bounded & Monotonic Sequences
00:48:13 Bolzano-Weierstrass Theorem
01:00:01 Cauchy Sequence
01:04:59 The Completeness Of R