Ordinary differential equations
In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations. For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that involve guessing and do not work for all inhomogeneous linear differential equations. Variation of parameters extends to linear partial differential equations as well, specifically to inhomogeneous problems for linear evolution equations like the heat equation, wave equation, and vibrating plate equation. In this setting, the method is more often known as Duhamel's principle, named after Jean-Marie Duhamel (1797–1872) who first applied the method to solve the inhomogeneous heat equation. Sometimes variation of parameters itself is called Duhamel's principle and vice versa. (Wikipedia).
C29 Variation of parameters Part 2
I continue with an explanation of the method of variation of parameters.
From playlist Differential Equations
C32 Example problem using variation of parameters
Another example problem using the method of variation of parameters.
From playlist Differential Equations
C33 Example problem using variation of parameters
Another example problem using the method of variation of parameters on second-order, linear, ordinary DE's.
From playlist Differential Equations
Free ebook http://tinyurl.com/EngMathYT I show how to solve differential equations by applying the method of variation of parameters for those wanting to review their understanding.
From playlist Differential equations
Differential Equations | Variation of Parameters.
We derive the general form for a solution to a differential equation using variation of parameters. http://www.michael-penn.net
From playlist Differential Equations
C28 Variation of parameters Part 1
We have already seen variation of parameters in action, but here we expand the method for use in second-order linear DE's, even with non-constant coefficients.
From playlist Differential Equations
Variation of Constants / Parameters
Download the free PDF http://tinyurl.com/EngMathYT A basic illustration of how to apply the variation of constants / parameters method to solve second order differential equations.
From playlist Differential equations
Variation of parameters to solve differential equations
Free ebook http://tinyurl.com/EngMathYT How to use the method of variation of parameters to solve second order ordinary differential equations with constant coefficients. Several examples are discussed.
From playlist Differential equations
C31 The same problem but using variation of parameters
In part 2 I finally solve the example problem using the method of variation of parameters.
From playlist Differential Equations
DeepMind x UCL | Deep Learning Lectures | 11/12 | Modern Latent Variable Models
This lecture, by DeepMind Research Scientist Andriy Mnih, explores latent variable models, a powerful and flexible framework for generative modelling. After introducing this framework along with the concept of inference, which is central to it, Andriy focuses on two types of modern latent
From playlist Learning resources
Linear Regression, Clearly Explained!!!
The concepts behind linear regression, fitting a line to data with least squares and R-squared, are pretty darn simple, so let's get down to it! NOTE: This StatQuest comes with a companion video for how to do linear regression in R: https://youtu.be/u1cc1r_Y7M0 You can also find example co
From playlist StatQuest
Dynamic Eigen Decomposition I: Parameter Variation in System Dynamics
Video 1 in a series about dynamic eigen decomposition (DED) theory and applications. Here we cover basic theoretical aspects of the DED as applied to a 2 degree of freedom mechanical oscillator with parameter variation. The surprising fact we uncover is that dynamic eigenvectors are preser
From playlist Summer of Math Exposition Youtube Videos
Stanford CS229: Machine Learning | Summer 2019 | Lecture 20 - Variational Autoencoder
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/ai Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
Juan Carlos De los Reyes: Bilevel learning approaches in variational image ....
In order to determine the noise model in corrupted images, we consider a bilevel optimization approach in function space with the variational image denoising models as constraints. In the flavour of supervised machine learning, the approach presupposes the existence of a training set of cl
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Topic Models: Variational Inference for Latent Dirichlet Allocation (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I
Working with Parameter Uncertainty | Robust Control, Part 4
Watch the first videos in this series: Robust Control, Part 1: What Is Robust Control? - https://youtu.be/A7wHSr6GRnc Robust Control, Part 2: Understanding Disk Margin - https://youtu.be/XazdN6eZF80 Robust Control, Part 3: Disk Margins for MIMO Systems - https://youtu.be/sac_IYBjcq0 The
From playlist Robust Control
DSI Seminar | Adaptive Contraction Rates and Model Selection Consistency of Variational Posteriors
In this DSI Seminar Series talk from June 2021, University of Notre Dame associate professor Lizhen Li discusses adaptive inference based on variational Bayes. Abstract: We propose a novel variational Bayes framework called adaptive variational Bayes, which can operate on a collection of
From playlist DSI Virtual Seminar Series
Seventh Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, December 2, 10:00am EDT Speaker: Martin Burger, FAU Title: Nonlinear spectral decompositions in imaging and inverse problems Abstract: This talk will describe the development of a variational theory generalizing classical spectral decompositions in linear filters and si
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
A18 Example problem using variation of parameters
An example problem using the method of variation of parameters to solve a non homogeneous system of differential equations.
From playlist A Second Course in Differential Equations
Variational Methods: How to Derive Inference for New Models (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I