The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. It is further extensible to stochastic systems by using the Ito integral. The aim of this method is towards a unified theory for the solution of partial differential equations (PDE); an aim which has been superseded by the more general theory of the homotopy analysis method. The crucial aspect of the method is employment of the "Adomian polynomials" which allow for solution convergence of the nonlinear portion of the equation, without simply linearizing the system. These polynomials mathematically generalize to a Maclaurin series about an arbitrary external parameter; which gives the solution method more flexibility than direct Taylor series expansion. (Wikipedia).
LU Decomposition Using Elementary Matrices
This video explains how find the LU Decomposition of a square matrix using elementary matrices. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Matrix Equations
Solve a System of Linear Equations Using LU Decomposition
This video explains how to use LU Decomposition to solve a system of linear equations. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Matrix Equations
How to integrate by partial fractions
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to integrate by the method of partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is a fraction such that the numerator
From playlist A second course in university calculus.
Jean Ecalle: Taming the coloured multizetas
Abstract: 1. We shall briefly describe the ARI-GARI structure; recall its double origin in Analysis and mould theory; explain what makes it so well-suited to the study of multizetas; and review the most salient results it led to, beginning with the exchanger adari(pal∙) of double symmetri
From playlist Dynamical Systems and Ordinary Differential Equations
Ex: Setting Up Partial Fraction Decomposition
This video provides several examples of how to set up the fractions in order to perform partial fraction decomposition. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Performing Partial Fraction Decomposition
Integration Using Partial Fraction Decomposition Part 1
This video shows how partial fraction decomposition can be used to simplify and integral. This video only shows linear factors. Part 1 of 2 Site: http://mathispower4u.com
From playlist Integration Using Partial Fractions
Computational Physics Lecture 11, LU Decomposition and Matrix Inversion
In this lecture, we discuss the LU decomposition method for systems of linear algebraic equations. We then describe how to calculate the inverse of a matrix using this method. We also introduce the concept of the matrix condition number. Finally, we describe a simple iterative method for i
From playlist Nazarbayev: PHYS 270 - Computational Physics with Ernazar Ab
Using Elimination to Solve Systems
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
LU Decomposition - Shortcut Method
This video explains how to find the LU Decomposition of a square matrix using a shortcut involving the opposite of multipliers used when performing row operations. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Matrix Equations
Empirical Mode Decomposition (1D, univariate approach)
Introduction to the Empirical Mode Decomposition - EMD - (one-dimensional, univariate version), which is a data decomposition method for non-linear and non-stationary data. This video covers the main features of the EMD and the working principle of the algorithm. The EMD is briefly compar
From playlist Summer of Math Exposition Youtube Videos
Martin J. Gander: Multigrid and Domain Decomposition: Similarities and Differences
Both multigrid and domain decomposition methods are so called optimal solvers for Laplace type problems, but how do they compare? I will start by showing in what sense these methods are optimal for the Laplace equation, which will reveal that while both multigrid and domain decomposition a
From playlist Numerical Analysis and Scientific Computing
Partial Fraction Decomposition (Part 2)
Partial fraction decomposition is when a rational expression is written as the sum of simpler fractions. This video is part 2 - it will explain how to complete the proper decomposition form to find the partial fractions of a rational function. Partial fractions are very helpful in Calculu
From playlist Pre-Calculus / Trigonometry
Virginie Ehrlacher - Multi-center decomposition of molecular densities: a mathematical perspective
Recorded 04 May 2022. Virginie Ehrlacher of the École Nationale des Ponts-et-Chaussées presents "Multi-center decomposition of molecular densities: a mathematical perspective" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: The aim of this talk is
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
6. Singular Value Decomposition; Iterative Solutions of Linear Equations
MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: James Swan This is the last lecture on solving linear algebra. It began in recapping what students already learned in eigenvalues, eigenvectors, and eig
From playlist MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015
Mod-01 Lec-18 L U decomposition
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Deep Learning Lecture 7.3 - TICA, TCCA and time-autoencoders
Learning Slow Manifolds with Markovian methods: - time-lagged canonical correlation analysis (TCCA) - time-lagged independent component analysis (TICA) - time-autoencoders
From playlist Deep Learning Lecture
Jean Kossaifi: "Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch" Jean Kossaifi - Nvidia Corporation Abstrac
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Lecture 9 | Convex Optimization II (Stanford)
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd concludes his lecture on primal and dual decomposition methods. This course introduces topics such as subgradient, cutting-plane, and ellipsoid method
From playlist Lecture Collection | Convex Optimization
Solving a system of equations with infinite many solutions
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium