In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry. In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped, and `triangle inequality', regarded as an axiom, added. If one assumes the continuity axiom in addition, then, in the case of the Euclidean plane, we come to the problem posed by Jean Gaston Darboux: "To determine all the calculus of variation problems in the plane whose solutions are all the plane straight lines." There are several interpretations of the original statement of David Hilbert. Nevertheless, a solution was sought, with the German mathematician Georg Hamel being the first to contribute to the solution of Hilbert's fourth problem. A recognized solution was given by Ukrainian mathematician Aleksei Pogorelov in 1973. In 1976, Armenian mathematician Rouben V. Ambartzumian proposed another proof of Hilbert's fourth problem. (Wikipedia).
Explanation of fourth-order Runge Kutta
From playlist A Second Course in Differential Equations
C49 Example problem solving a system of linear DEs Part 1
Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.
From playlist Differential Equations
C56 Continuation of previous problem
Adding a bit more depth to the previous problem.
From playlist Differential Equations
A first example problem solving a linear, second-order, homogeneous, ODE with variable coefficients around a regular singular point.
From playlist Differential Equations
C14 Example problem with a third order linear DE with constant coefficients
Example problem solving a third-order linear, homogeneous, ODE with constant coefficients.
From playlist Differential Equations
Fourth Order Cauchy Euler Differential Equation xy^(4) + 10y''' = 0
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Fourth Order Cauchy Euler Differential Equation xy^(4) + 10y''' = 0
From playlist Differential Equations
Solving a Fourth Order Linear Homogeneous Differential Equation
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Solving a Fourth Order Linear Homogeneous Differential Equation
From playlist Differential Equations
Math Major Examples -- Number Theory #4
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From playlist Number Theory
13F Example Problems for Euclidean n Space
Some example problems in Euclidean n-Space.
From playlist Linear Algebra
C47 Example problem solving a Cauchy Euler equation
The last problem solved in this section, before we move on to another technique for linear differential equations.
From playlist Differential Equations
Nonlinear algebra, Lecture 5: "Nullstellensätze ", by Bernd Sturmfels
This is the fifth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Hilbert’s Nullstellensatz is a classical result from 1890, which offers a characterization of the set of all polynomials that vanish on a given v
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
This video illustrates the use of the Koopman operator to simulate and control a nonlinear dynamical system using a linear dynamical system on an observable subspace. From the Paper: Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for contro
From playlist Research Abstracts from Brunton Lab
Jim Bryan : Curve counting on abelian surfaces and threefolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Andreas LÄUCHLI - Numerical Hamiltonian truncation approach to the \phi^4 theory in 1+1d and beyond
https://indico.math.cnrs.fr/event/2435/
From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”
A Strangely Deep Problem about Sequences
This video goes over a fun little problem from A Hilbert Space Problem Book by Paul Halmos. It's a simple problem to understand, and the solution to it is surprisingly deep. It allows us to introduce the idea of a Reproducing Kernel Hilbert Space through what are called Generating Function
From playlist Summer of Math Exposition Youtube Videos
Distributional Aspects of Hecke Eigenforms - Raphael Steiner
Short talks by postdoctoral members Topic: Distributional Aspects of Hecke Eigenforms Speaker: Raphael Steiner Affiliation: Member, School of Mathematics Date: October 2, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Nonlinear algebra, Lecture 10: "Invariant Theory", by Bernd Sturmfels
This is the tenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Mod-01 Lec-06 Introduction to Inner Product Spaces
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Separation of variables and the Schrodinger equation
A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
Pascal Auscher: On representation for solutions of boundary value problems for elliptic systems (2)
In order to extend the first order approach to BVP with Lp data in the sense of Kenig-Pipher, we need to extend our semigroups to Lp setting. Unfortunately, our semigroups are seldom bounded on all of Lp. They turn out to be bounded on some abstract Hardy spaces associated to a first order
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"