This is a supplementary video to the Real Analysis series. It connects the topic of series with the uniform convergence of sequence of functions.
Weierstrass M-Test
The Weierstrass M-test, sometimes also called the Weierstrass majorant criterion, is named after the German mathematician Karl Weierstraß and after the constants in the theorem that are often denoted by $M$.
Content of the video:
00:00 Intro
00:28 Comparison for series of functions
00:56 Theorem about Weierstrass M-Test
03:19 Uniform convergence explanation
05:00 Proof of Weierstrass M-Test
09:46 Application of Weierstrass M-Test
11:25 Credits
We will apply this theorem in the Complex Analysis series and also in a technical part of the Fourier Transform series, where we will show the convergence of so-called Fourier series.