Partial differential equations | Generalized functions

Fundamental solution

In mathematics, a fundamental solution for a linear partial differential operator L is a formulation in the language of distribution theory of the older idea of a Green's function (although unlike Green's functions, fundamental solutions do not address boundary conditions). In terms of the Dirac delta "function" δ(x), a fundamental solution F is a solution of the inhomogeneous equation LF = δ(x). Here F is a priori only assumed to be a distribution. This concept has long been utilized for the Laplacian in two and three dimensions. It was investigated for all dimensions for the Laplacian by Marcel Riesz. The existence of a fundamental solution for any operator with constant coefficients — the most important case, directly linked to the possibility of using convolution to solve an arbitrary right hand side — was shown by Bernard Malgrange and Leon Ehrenpreis. In the context of functional analysis, fundamental solutions are usually developed via the Fredholm alternative and explored in Fredholm theory. (Wikipedia).

Video thumbnail

Differential Equation - 2nd Order Linear (4 of 17) The Fundamental Theory

Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce and explain the Fundamental Theory for the solution to 2nd order linear homogeneous differential equations. Next video in the series can be seen at: http://youtu.be/oItnzOZsayA

From playlist DIFFERENTIAL EQUATIONS 9 - 2nd ORDER INTRODUCTION

Video thumbnail

Find the particular solution given the conditions and second derivative

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Video thumbnail

How to solve a differentialble equation by separating the variables

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Video thumbnail

Particular solution of differential equations

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Video thumbnail

Extended Fundamental Theorem of Calculus

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples

From playlist Calculus

Video thumbnail

Find the particular solution with exponential and inverse trig

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Video thumbnail

Solve the general solution for differentiable equation with trig

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Differential Equations

Video thumbnail

Solve the particular solution differentiable equations by separating the variables

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Video thumbnail

How to solve a separable differential equation

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Video thumbnail

Joel Hass - Lecture 2 - Algorithms and complexity in the theory of knots and manifolds - 19/06/18

School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro

From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects

Video thumbnail

Lec 29 | MIT 18.03 Differential Equations, Spring 2006

Matrix Exponentials; Application to Solving Systems. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.03SC Differential Equations, Fall 2011

Video thumbnail

CTNT 2022 - Grothendieck’s section set and the Lawrence–Venkatesh method (by Alex Betts)

This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2022 - Conference lectures and special guest lectures

Video thumbnail

Marina Poulet, Université Claude Bernard Lyon 1

December 9, Marina Poulet, Université Claude Bernard Lyon 1 Zariski-dense subgroups of Galois groups for Mahler equations

From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra

Video thumbnail

Visualizing the Fundamental Theorem of Algebra // Math Minute [#48]

The Fundamental Theorem of Algebra is a statement about the relationship between the number of solutions a polynomial has and the degree of that polynomial. Namely, a polynomial will have the same number of solutions as its degree (once we count something called multiplicities). Subscrib

From playlist Math Minutes

Video thumbnail

[ANT09] Stacking oranges

In this video, we see how Pell's equation can be used to solve higher-order equations over the integers. We see another example of the importance of understanding which numbers are squares modulo each prime. The question was originally posed by Lucas: Nouvelles Annales de Mathématiques, s

From playlist [ANT] An unorthodox introduction to algebraic number theory

Video thumbnail

Mod-05 Lec-28 General Systems Continued and Non-homogeneous Systems

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

Video thumbnail

Variation of Parameters to Solve a Differential Equation (Second Order)

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! THE VIDEO ENDS ABRUPTLY, BUT THERE WAS NOTHING IMPORTANT THERE :) Variation of Parameters to Solve a Differential Equation (Second Order). In this video, I gi

From playlist All Videos - Part 1

Video thumbnail

2023 Number Challenge: Pell's Equation with d=2023

Check out other 2023 Number Challenges from this list. Share with your friends!! https://www.youtube.com/playlist?list=PLXpXgWDr4HM7KKeX7CaQIu4tfPRJ2HiUM Please subscribe to the channel. In this video, we study Pell's equation when d=2023. We use two methods: 1. With continue continu

From playlist Math Problems with Number 2023

Video thumbnail

Variation of Parameters to Solve a Differential Equation (Second Order) , Ex 2

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Variation of Parameters to Solve a Differential Equation (Second Order) , Ex 2. In this video, I use variation of parameters to find the solution of a differe

From playlist All Videos - Part 1

Video thumbnail

Find the particular solution differential equations

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give

From playlist Solve Differential Equation (Particular Solution) #Integration

Related pages

Signal processing | Functional analysis | Fredholm alternative | Bessel function | Marcel Riesz | Indicator function | Identity element | Biharmonic equation | Sides of an equation | Impulse response | Green's function | Screened Poisson equation | Fredholm theory | Parametrix | Mathematics | Dirac delta function | Distribution (mathematics) | Convolution | Bessel potential | Boundary element method