In this video, I prove a very neat result about fixed points and give some cool applications. This is a must-see for calculus lovers, enjoy! Old Fixed Point Video: https://youtu.be/zEe5J3X6ISE Banach Fixed Point Theorem: https://youtu.be/9jL8iHw0ans Continuity Playlist: https://www.youtu
From playlist Calculus
Paul Shafer:Reverse mathematics of Caristi's fixed point theorem and Ekeland's variational principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Caristi's fixed point theorem is a fixed point theorem for functions that are controlled by continuous functions but are necessarily continuous themselves. Let a 'Caristi
From playlist Workshop: "Proofs and Computation"
What is the max and min of a horizontal line on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
The Lawvere fixed point theorem
In this video we prove a version of Lawveres fixed point theorem that holds in Cartesian closed categories. It's a nice construction that specializes to results such as Cantors diagonal argument and prove the the power set of a set is classically always larger than the set itself. https:/
From playlist Logic
Fixed points and stability: one dimension
Shows how to determine the fixed points and their linear stability of a first-order nonlinear differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org
From playlist Differential Equations
Find the max and min of a linear function on the closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Extreme Value Theorem Using Critical Points
Calculus: The Extreme Value Theorem for a continuous function f(x) on a closed interval [a, b] is given. Relative maximum and minimum values are defined, and a procedure is given for finding maximums and minimums. Examples given are f(x) = x^2 - 4x on the interval [-1, 3], and f(x) =
From playlist Calculus Pt 1: Limits and Derivatives
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
How to determine the absolute max min of a function on an open interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Fixed points in digital topology
A talk given by Chris Staecker at King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on October 11 2019. This is the second in a series of 3 talks given at KMUTT. Includes an introduction to graph-theoretical ("Rosenfeld style") digital topology, and some basic results a
From playlist Research & conference talks
Axioms for the fixed point index of an n-valued map
A research talk I gave at KU Leuven Kulak in Kortrijk, Belgium on June 4, 2019, at the conference on Nielsen Theory and Related Topics. The first 20 minutes is mostly about the Euler characteristic, and should be understandable to all mathematicians. The audience was other researchers in t
From playlist Research & conference talks
Piotr Przytycki: Torsion groups do not act on 2-dimensional CAT(0) complexes
We show, under mild hypotheses, that if each element of a finitely generated group acting on a 2-dimensional CAT(0) complex has a fixed point, then the action is trivial. In particular, all actions of finitely generated torsion groups on such complexes are trivial. As an ingredient, we pro
From playlist Geometry
Intro to Nielsen fixed point theory
A talk given by Chris Staecker at King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on October 10 2019. Covers basic definitions and results of Nielsen fixed point theory, plus a few minutes about Nielsen-type theories for coincidence and periodic points. Should be und
From playlist Research & conference talks
Proving Brouwer's Fixed Point Theorem | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra. Tweet at us! @pbsinfinite Facebook: facebook.com/pbs
From playlist An Infinite Playlist
Group theory 4: Lagrange's theorem
This is lecture 4 of an online course on mathematical group theory. It introduces Lagrange's theorem that the order of a subgroup divides the order of a group, and uses it to show that all groups of prime order are cyclic, and to prove Fermat's theorem and Euler's theorem.
From playlist Group theory
The Hartman-Grobman Theorem, Structural Stability of Linearization, and Stable/Unstable Manifolds
This video explores a central result in dynamical systems: The Hartman-Grobman theorem. This theorem establishes when a fixed point of a nonlinear system will resemble its linearization. In particular, hyperbolic fixed points, where every eigenvalue has a non-zero real part, will be "str
From playlist Engineering Math: Differential Equations and Dynamical Systems
Visual Group Theory, Lecture 5.4: Fixed points and Cauchy's theorem
Visual Group Theory, Lecture 5.4: Fixed points and Cauchy's theorem We begin with a small lemma stating that if a group of prime order acts on a set S, then the number of fixed points is congruent to the size of the set, modulo p. We need this result to prove Cauchy's theorem, which says
From playlist Visual Group Theory
Act globally, compute...points and localization - Tara Holm
Tara Holm Cornell University; von Neumann Fellow, School of Mathematics October 20, 2014 Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing inte
From playlist Mathematics
Banach fixed point theorem & differential equations
A novel application of Banach's fixed point theorem to fractional differential equations of arbitrary order. The idea involves a new metric based on the Mittag-Leffler function. The technique is applied to gain the existence and uniqueness of solutions to initial value problems. http://
From playlist Mathematical analysis and applications
Fixed and Periodic Points | Nathan Dalaklis
Fixed Points and Periodic points are two mathematical objects that come up all over the place in Dynamical systems, Differential equations, and surprisingly in Topology as well. In these videos, I introduce the concepts of fixed points and periodic points and gradually build to a proof of
From playlist The New CHALKboard