Real numbers as Cauchy sequences don't work! | Real numbers and limits Math Foundations 114
This longish video lays out the various reasons why Cauchy sequences---as a basis for the theory of real numbers---don't work. Necessary viewing for all maths students! We really need to start addressing the logical weaknesses, rather than pretending that they are not there! Video Conten
From playlist Math Foundations
Cauchy principal value integral example. You learn in calculus courses that an improper integral is sometimes divergent, but in this video I show you how to make it (rigorously) equal to zero! This is widely used in distribution theory and Fourier analysis Subscribe to my channel: https:
From playlist Calculus
I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.
From playlist Differential Equations
Proof that the Sequence {1/n} is a Cauchy Sequence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Sequence {1/n} is a Cauchy Sequence
From playlist Cauchy Sequences
Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis
What are Cauchy sequences? We introduce the Cauchy criterion for sequences and discuss its importance. A sequence is Cauchy if and only if it converges. So Cauchy sequences are another way of characterizing convergence without involving the limit. A sequence being Cauchy roughly means that
From playlist Real Analysis
Cauchy Sequence In this video, I define one of the most important concepts in analysis: Cauchy sequences. Those are sequences which "crowd" together, without necessarily going to a limit. Later, we'll see what implications they have in analysis. Check out my Sequences Playlist: https://w
From playlist Sequences
Real Analysis - Part 64 - Cauchy Principal Value
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.
From playlist Real Analysis
If A Sequence is Cauchy in Space it's Component Sequences are Cauchy Proof
If A Sequence is Cauchy in Space it's Component Sequences are Cauchy Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Cauchy Sequences
Harmonic Functions -- Complex Analysis 9
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Complex Analysis
AKPotW: Cauchy's Mean-Value Theorem [Real Analysis]
If this video is confusing, be sure to check out our blog for the full solution transcript! https://centerofmathematics.blogspot.com/2018/03/advanced-knowledge-problem-of-week-3-29.html
From playlist Center of Math: Problems of the Week
Proof of the Cauchy-Schwarz inequality | Vectors and spaces | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/proof-of-the-cauchy-schwarz-inequality Proof of the Cauchy-Schwarz Inequality Watch the next lesson: https:
From playlist Vectors and spaces | Linear Algebra | Khan Academy
Tristan Riviere: The work of Louis Nirenberg on Partial Differential Equations
Original title of the lecture: "Exploring the unknown, the work of Louis Nirenberg on Partial Differential Equations" We had to shorten the title to fit Youtubes limitations of title length. Abastract: Partial differential equations are a central object in the mathematical modeling of na
From playlist Abel Lectures
Complex Analysis L06: Analytic Functions and Cauchy-Riemann Conditions
This video explores analytic complex functions, where it is possible to do calculus. We introduce the Cauchy-Riemann conditions to test for analyticity. @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in Complex Analysis
Taylor Series for Complex Valued Functions -- Complex Analysis 17
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Complex Analysis
11. Pseudorandom graphs I: quasirandomness
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao discusses a classic result of Chung, Graham, a
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Real numbers and Cauchy sequences of rationals (III) | Real numbers and limits Math Foundations 113
Motivated by Archimedes calculation of an approximate ratio of circumference to diameter of a circle, we introduce an Archimedean view on `real numbers": nested sequences of intervals whose sizes go to zero. If you are going to waffle about the existence of real numbers, this is at least a
From playlist Math Foundations
ME565 Lecture 2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions
ME565 Lecture 2 Engineering Mathematics at the University of Washington Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L02.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http
From playlist Engineering Mathematics (UW ME564 and ME565)
Complex Analysis L12: Examples of Complex Integrals
This video presents examples of how to use the various complex integration theorems to compute challenging complex integrals. @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in Complex Analysis
Real Analysis: Let {x_n} be a sequence of real numbers such that |x_n| is less than (3n^2-2)/(4n^3 + n^2 + 3). Prove that {x_n} is a Cauchy sequence.
From playlist Real Analysis