Partial differential equations
An eikonal equation (from Greek εἰκών, image) is a non-linear (non-linear in x not in the unknown u) first-order partial differential equation that is encountered in problems of wave propagation. The classical eikonal equation in geometric optics is a differential equation of the form where lies in an open subset of , is a positive function, denotes the gradient, and is the Euclidean norm. The function is given and one seeks solutions .In the context of geometric optics, the function is the refractive index of the medium. More generally, an eikonal equation is an equation of the form where is a function of variables. Here the function is given, and is the solution.If , then equation becomes. Eikonal equations naturally arise in the WKB methodand the study of Maxwell's equations. Eikonal equations provide a link between physical (wave) optics and geometric (ray) optics. One fast computational algorithm to approximate the solution to the eikonal equation is the fast marching method. (Wikipedia).
On large time behavior of growth by birth and spread – Yoshikazu Giga – ICM2018
Partial Differential Equations Invited Lecture 10.7 On large time behavior of growth by birth and spread Yoshikazu Giga Abstract: This is essentially a survey paper on a large time behavior of solutions of some simple birth and spread models to describe growth of crystal surfaces. The mo
From playlist Partial Differential Equations
Paola Goatin: "A multi-population traffic flow model on networks accounting for vehicle automation"
Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop III: Large Scale Autonomy: Connectivity and Mobility Networks "A multi-population traffic flow model on networks accounting for vehicle automation" Paola Goatin - INRIA Sophia Antipolis-Méditerranée Abstract:
From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020
SIREN: Implicit Neural Representations with Periodic Activation Functions (Paper Explained)
Implicit neural representations are created when a neural network is used to represent a signal as a function. SIRENs are a particular type of INR that can be applied to a variety of signals, such as images, sound, or 3D shapes. This is an interesting departure from regular machine learnin
From playlist Papers Explained
Eugenia Saorin-Gomez - Inner parallel bodies & the Isoperimetric Quotient
Recorded 10 February 2022. Eugenia Saorin-Gomez of the Universität Bremen presents "Inner parallel bodies & the Isoperimetric Quotient" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The so-called Minkowski difference of convex bodies (compact and convex s
From playlist Workshop: Calculus of Variations in Probability and Geometry
Calculating e^A for a matrix A, explaining what this has to do with diagonalization, and solving systems of differential equations Check out my Eigenvalues playlist: https://www.youtube.com/watch?v=H-NxPABQlxI&list=PLJb1qAQIrmmC72x-amTHgG-H_5S19jOSf Subscribe to my channel: https://www.y
From playlist Eigenvalues
The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
Eigenvalues | Eigenvalues and Eigenvectors
In this video, we work through some example computations of eigenvalues of 2x2 matrices. Including a case where the eigenvalues are complex numbers. We do not discuss any intuition or definition of eigenvalues or eigenvectors, we simply carry out some elementary computations. If you liked
From playlist Linear Algebra
Find the Coefficient Matrix of a System to Determine Eigenvalues of a 2 by 2 Matrix
This video explains how to determine the coeifficient matrix for the system of equations to find the eigenvalues of a 2 by 2 matrix.
From playlist Eigenvalues and Eigenvectors
Eigenvalues + eigenvectors example
Free ebook http://tinyurl.com/EngMathYT I show how to calculate the eigenvalues and eigenvectors of a matrix for those wanting to review their understanding.
From playlist Engineering Mathematics
A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations
How to Find Eigenvectors Given Eigenvalues
This video explains who to find the eigenvectors that correspond to a given eigenvalue.
From playlist Eigenvalues and Eigenvectors
Ex: Find the Eigenvalues of a 3x3 Matrix
This video explains how to determine the eigenvalues of a given matrix. http://mathispower4u.com
From playlist Eigenvalues and Eigenvectors
2 to a matrix. I calculate two to the power of a matrix using tools from linear algebra, more precisely diagonalization and eigenvalues and eigenvectors. This is related to matrix exponentials and logarithms, which are used to solve systems of differential equations and decouple particles.
From playlist Eigenvalues
Peter van der Kamp: On CAC and Backlund transformations
Abstract: This talk summarizes joint work with D.J. Zhang, D.D. Zhang and X. Wei, on multi-component extensions of CAC systems, how to obtain auto-Backlund transformations from auto-Backlund transformations, and torqued ABS equations, see papers 33, 37, and 40 from https://wiskun.de/publi
From playlist Integrable Systems 9th Workshop
2 Equations 2 Unknowns. A High School Math Explainer
0:00 Intro 0:58 The substitution method 08:12 The like coefficients method 14:09 The determinant method 20:33 Discussion Equations: https://youtu.be/NtX98LNHO6k In algebra, a system of two equations with two unknowns can be solved by several different methods. This video covers algebraic
From playlist Summer of Math Exposition 2 videos
Progress in Symbolic Differential Equations
During this talk I will give an overview of recent developments, new features and improvements in Wolfram Language related to symbolic solutions of ordinary differential equations. I will begin by speaking about the recently introduced DSolve option IncludeSingularSolutions, which allows o
From playlist Wolfram Technology Conference 2022
(0.3.101) Exercise 0.3.101: Classifying Differential Equations
This video explains how to classify differential equations based upon their properties https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
(0.3) Lesson: Classifying Differential Equations
This video explains how to classify differential equations based upon their properties https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.
From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (5 of 35) What is an Eigenvector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show (in general) what is and how to find an eigenvector. Next video in this series can be seen at: https://youtu.be/SGJHiuRb4_s
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS