In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing sequence of non-negative real numbers, the series converges if and only if the "condensed" series converges. Moreover, if they converge, the sum of the condensed series is no more than twice as large as the sum of the original. (Wikipedia).
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
The Cauchy--Riemann Equations (Remarks) | Complex Analysis, An Introduction
The purpose of this video is to give some insight into the Cauchy--Riemann criterion for a function to be holomorphic (or equivalently, analytic). The discussion is not formal but can be carried out in a formal manner. We show that the Cauchy--Riemann equations can be viewed as commuting o
From playlist Complex Analysis
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
C39 A Cauchy Euler equation that is nonhomogeneous
A look at what to do with a Cauchy Euler equation that is non-homogeneous.
From playlist Differential Equations
Find all Points for which the Cauchy Riemann Equations Hold
Find all Points for which the Cauchy Riemann Equations Hold Nice example of using the Cauchy Riemann Equations from complex variables.
From playlist Complex 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
Cauchy-Riemann Equations: Proving a Function is Nowhere Differentiable 1
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Using the Cauchy-Riemann Equations to prove that the function f(z) = conjugate(z) is nowhere differentiable. This is a straightforward application of the C.R. equations.
From playlist Complex Analysis
How Slow Can You Sum to Infinity? | Nathan Dalaklis
Series can often be intuitively misleading. When we are taking sums of even very small terms the series we are working with may still grow arbitrarily large, so how slowly can you sum to infinity, and what is the test to see if a series is going to converge or diverge? Here we talk about s
From playlist The First CHALKboard
Real Analysis | The Cauchy Condensation Test
We prove a series convergence test known as the Cauchy condensation test. This test is motivated by the classic proof of the divergence of the harmonic series. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-ma
From playlist Real Analysis
The computational theory of Riemann–Hilbert problems (Lecture 4) by Thomas Trogdon
Program : Integrable Systems in Mathematics, Condensed Matter and Statistical Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan Lecture Hall, ICT
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
The computational theory of Riemann–Hilbert problems (Lecture 2) by Thomas Trogdon
ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This program aims to address various aspects of integrability and its role in
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
C46 Solving the previous problem by another method
There are more ways than one to solve Cauchy-Euler equations. In this video I revert to the substitution method.
From playlist Differential Equations
The computational theory of Riemann–Hilbert problems (Lecture 3) by Thomas Trogdon
Program : Integrable systems in Mathematics, Condensed Matter and Statistical Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos. The next simplest topology ha
From playlist Toposes online
MIT 3.60 | Lec 24b: Symmetry, Structure, Tensor Properties of Materials
Part 2: Piezoelectricity (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
In this video, I figure out whether the crazy sum in the thumbnail converges or diverges. For this, I use the famous block test, also known as the Cauchy condensation test. Block Test: https://youtu.be/zNOXPUsMWMs Crazy Sum: https://youtu.be/5-D7g2xPhRc Series Playlist: https://www.youtu
From playlist Series
Complex Analysis 03: The Cauchy-Riemann Equations
Complex differentiable functions, the Cauchy-Riemann equations and an application.
From playlist MATH2069 Complex Analysis
Are you tired of all the convergence tests for series from calculus? Then this video is for you! Here I discuss the Block Test (or Cauchy Condensation Test), which is an important and clever way of testing for convergence for a series. Enjoy! Another Example: https://youtu.be/5-D7g2xPhRc
From playlist Series
Complex Analysis: Cauchy-Riemann Equations
From playlist Complex Analysis
The Unified Transform Method for linear evolution equations (Lecture 2) by David Smith
Program : Integrable systems in Mathematics, Condensed Matter and Statistical Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics