In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold. It is related to the concept of caustics in geometric optics. The ray's source may be a point (called the radiant) or parallel rays from a point at infinity, in which case a direction vector of the rays must be specified. More generally, especially as applied to symplectic geometry and singularity theory, a caustic is the critical value set of a Lagrangian mapping (π ○ i) : L ↪ M ↠ B; where i : L ↪ M is a Lagrangian immersion of a Lagrangian submanifold L into a symplectic manifold M, and π : M ↠ B is a Lagrangian fibration of the symplectic manifold M. The caustic is a subset of the Lagrangian fibration's base space B. (Wikipedia).
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
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
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
Calculus 2: Parametric Equations (1 of 20) What is a Parametric Equation?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a parametric equation. A parametric equation is an equation that expresses each variable of an equation in terms of another variable. Next video in the series can be seen at: https://
From playlist CALCULUS 2 CH 17 PARAMETRIC EQUATIONS
Math 101 Fall 2017 103017 Introduction to Cauchy Sequences
Definition of a Cauchy sequence. Convergent sequences are Cauchy. Cauchy sequences are not necessarily convergent. Cauchy sequences are bounded. Completeness of the real numbers (statement).
From playlist Course 6: Introduction to Analysis (Fall 2017)
C36 Example problem solving a Cauchy Euler equation
An example problem of a homogeneous, Cauchy-Euler equation, with constant coefficients.
From playlist Differential Equations
ECR Talk: "A tale of two (or more, integrable) billiards", Sean Gasiorek
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Week 2 (MATRIX): ECR Talk by Sean Gasiorek 14 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 Februar
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Covariance (1 of 17) What is Covariance? in Relation to Variance and Correlation
Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of
From playlist COVARIANCE AND VARIANCE
Shyuichi Izumiya: Caustics of world sheets in Lorentz-Minkowski 3-space
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
TU Wien Rendering #32 - Bidirectional Path Tracing, Multiple Importance Sampling
With a classical unidirectional path tracer, we'll have some scenes where it is difficult to connect to the light source, and therefore many of our computed samples will be wasted. What if we would start not only one light path from the camera, but one also from the light source, and conne
From playlist TU Wien Rendering / Ray Tracing Course
The Nature of Causation: The Counterfactual Theory of Causation
In this second lecture in this series on the nature of causation, Marianne Talbot discusses the counterfactual theory of causation. We have causal theories of reference, perception, knowledge, content and numerous other things. If it were to turn out that causation doesn’t exist, we would
From playlist The Nature of Causation
Light and Beyond (Lecture 3) by Rajaram Nityananda
SUMMER COURSES : LIGHT AND BEYOND SPEAKER : Rajaram Nityananda (Azim Premji University) DATE : 31 May 2020 to 28 June 2020 VENUE : Online Lectures and Tutorials This short and intensive advanced undergraduate level course starts with the understanding of light as an electromagnetic wave
From playlist Summer Course 2020: Light And Beyond
Caustic skeleton of the Cosmic Web - R. van de Weygaert - Workshop 1 - CEB T3 2018
Rien van de Weygaert (Kapteyn Astronomical Institute, Univ. Groningen) / 21.09.2018 Caustic skeleton of the Cosmic Web ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoinc
From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology
Caustic lenses are really weird
Get 100 free blades here: https://hensonshaving.com/stevemould when you buy a Henson razor with code stevemould Sometimes called caustics or free form lenses, these objects use clever maths to move light around to make images. Check out my video about Penrose Unilluminable Room: https://
From playlist Everything in chronological order
Introduction to Parametric Equations
This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
Roulettes: The Mathematics of Rolling
#SoME1 An introduction to the class of curves known as roulettes, created for the Summer of Mathematical Exposition (SoME) competition hosted by the YouTube channel 3Blue1Brown. The rules for SoME can be found at https://www.3blue1brown.com/blog/some1. This is my first time ever creating
From playlist Summer of Math Exposition Youtube Videos
What is General Relativity? Lesson 33: Math Break - The Cubic Equation
What is General Relativity? Lesson 33: Math Break-The Cubic Equation This is a lecture about the lesser known cousin of the quadratic equation: the cubic equation. The purpose of this lecture is to develop confidence regarding the roots of a cubic equation. All of the geodesics of the Sch
From playlist What is General Relativity?
Inverse problems in seismic/radar imaging
Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems URL: https://www.icts.res.in/program/IP2014 Dates: Monday 16 Jun, 2014 - Saturday 28 Jun, 2014 Description In Inverse Problems the goal is to determine the properties of the interior of an object from
From playlist Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems
Emergence of singularities from decoherence in a Josephson junction by Duncan H J O'Dell
Open Quantum Systems DATE: 17 July 2017 to 04 August 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore There have been major recent breakthroughs, both experimental and theoretical, in the field of Open Quantum Systems. The aim of this program is to bring together leaders in the Open Q
From playlist Open Quantum Systems
How to Prove a Sequence is a Cauchy Sequence Advanced Calculus Proof with {n^2/(n^2 + 1)}
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Prove a Sequence is a Cauchy Sequence Advanced Calculus Proof with {n^2/(n^2 + 1)}
From playlist Cauchy Sequences