Differential operators | Multivariable calculus
In differential equations, the Laplace invariant of any of certain differential operators is a certain function of the coefficients and their derivatives. Consider a bivariate hyperbolic differential operator of the second order whose coefficients are smooth functions of two variables. Its Laplace invariants have the form Their importance is due to the classical theorem: Theorem: Two operators of the form are equivalent under gauge transformations if and only if their Laplace invariants coincide pairwise. Here the operators are called equivalent if there is a gauge transformation that takes one to the other: Laplace invariants can be regarded as factorization "remainders" for the initial operator A: If at least one of Laplace invariants is not equal to zero, i.e. then this representation is a first step of the used for solvingnon-factorizable bivariate linear partial differential equations (LPDEs). If both Laplace invariants are equal to zero, i.e. then the differential operator A is factorizable and corresponding linear partial differential equation of second order is solvable. Laplace invariants have been introduced for a bivariate linear partial differential operator (LPDO) of order 2 and of hyperbolic type. They are a particular case of generalized invariants which can be constructed for a bivariate LPDO of arbitrary order and arbitrary type; see Invariant factorization of LPDOs. (Wikipedia).
Differential Equations | The Laplace Transform of a Derivative
We establish a formula involving the Laplace transform of the derivative of a function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Laplace transform of 1/sqrt(t), *SPEED RUN*
laplace transform of 1/sqrt(t), L{1/sqrt(t)}, laplace transform examples, laplace transform lessons, blackpenredpen
From playlist Properties of Laplace Transform (Nagle's Sect7.3)
Laplace Transform of 1 (Using the Definition)
Laplace Transform of 1 using the definition. Have a wonderful day! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Than
From playlist Laplace Transforms
3 Properties of Laplace Transforms: Linearity, Existence, and Inverses
The Laplace Transform has several nice properties that we describe in this video: 1) Linearity. The Laplace Transform of a linear combination is a linear combination of Laplace Transforms. This will be very useful when applied to linear differential equations 2) Existence. When functions
From playlist Laplace Transforms and Solving ODEs
Introduction to Laplace Transforms
Introduction to Laplace Transforms A full introduction. The definition is given, remarks are made, and an example of finding the laplace transform of a function with the definition is done.
From playlist Differential Equations
Differential Equations | Laplace Transform of a Piecewise Function
We find the Laplace transform of a piecewise function using the unit step function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Introduction to Laplace Transforms
This video introduces the Laplace transform of a function and explains how they are used to solve differential equations. http://mathispower4u.com
From playlist Laplace Transforms
C79 Linear properties of the Laplace transform
The linear properties of the Laplace transform.
From playlist Differential Equations
Sun-Yung Alice Chang: Conformal Invariants and Differential Equations
This lecture was held at The University of Oslo, May 24, 2006 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2006 1. “A Scandinavian Chapter in Analysis” by Lennart Carleson, Kungliga Tekniska Högskolan, Swed
From playlist Abel Lectures
Differential Equations: Lecture 7.1 Definition of the Laplace Transform
This is a real classroom lecture on Differential Equations. I covered section 7.1 which is on the Definition of the Laplace Transform. I hope this video is helpful to someone. If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel
From playlist Differential Equations Full Lectures
Alice Chang: Conformal Geometry on 4-manifolds
Abstract: In this talk, I will report on the study of integral conformal invariants on 4-manifolds and applications to the study of topology and diffeomorphism type of a class of 4-manifolds. The key ingredient is the study of the integral of 2 of the Schouten tensor which is the part of i
From playlist Abel in... [Lectures]
Emmy Noether Lecture: Conformal geometry on 4-manifolds — Sun-Yung Alice Chang — ICM2018
Conformal geometry on 4-manifolds Sun-Yung Alice Chang Abstract: In this talk, I will report on the study of a class of integral conformal invariants on 4-manifolds and applications to the study of topology and diffeomorphism type of a class of 4-manifolds. The key ingredient is the study
From playlist Special / Prizes Lectures
Lecture 20, The Laplace Transform | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 20, The Laplace Transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
Laplace Transform an intuitive approach
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From playlist Fourier and Laplace
Interaction between invariant structures for shape analysis - Kimmel - Workshop 2 - CEB T1 2019
Ron Kimmel (Technion) / 12.03.2019 Interaction between invariant structures for shape analysis. A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilari
From playlist 2019 - T1 - The Mathematics of Imaging
Dalimil Mazáč - Bootstrapping Automorphic Spectra
I will explain how the conformal bootstrap can be adapted to place rigorous bounds on the spectra of automorphic forms on locally symmetric spaces. A locally symmetric space is of the form H\G/K, where G is a non-compact semisimple Lie group, K the maximal compact subgroup of G, and H a di
From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory
Gergely Harcos - A glimpse at arithmetic quantum chaos
slides for this talk: https://www.msri.org/workshops/801/schedules/21771/documents/2987/assets/27969 Introductory Workshop: Analytic Number Theory February 06, 2017 - February 10, 2017 February 07, 2017 (11:00 AM PST - 12:00 PM PST) Speaker(s): Gergely Harcos (Central European Universit
From playlist Number Theory
Werner Müller : Analytic torsion for locally symmetric spaces of finite volume
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From playlist Topology
Separation of Variables - Laplace Eq Part 1
We use Separation of Variables to solve the Laplace Equation, including boundary conditions.
From playlist Mathematical Physics II Uploads
Resurgence and Partial Theta Series by David Sauzin
Title: Resurgence and Partial Theta Series Speaker: David Sauzin (Institute of Celestial Mechanics and Computation of the Ephemerides, Paris) Date: Friday, 05th August, 2022 Time: 11:00 am (IST) Venue: Hybrid Mode - Offline: Madhava Lecture Hall
From playlist Seminar Series