Differential systems | Partial differential equations | Differential topology
In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of the way a differential form restricts to a submanifold, and the fact that this restriction is compatible with the exterior derivative. This is one possible approach to certain over-determined systems, for example, including Lax pairs of integrable systems. A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system. To elaborate, a Pfaffian system is a set of 1-forms on a smooth manifold (which one sets equal to 0 to find solutions to the system). Given a collection of differential 1-forms on an -dimensional manifold , an integral manifold is an immersed (not necessarily embedded) submanifold whose tangent space at every point is annihilated by (the pullback of) each . A maximal integral manifold is an immersed (not necessarily embedded) submanifold such that the kernel of the restriction map on forms is spanned by the at every point of . If in addition the are linearly independent, then is-dimensional. A Pfaffian system is said to be completely integrable if admits a foliation by maximal integral manifolds. (Note that the foliation need not be regular; i.e. the leaves of the foliation might not be embedded submanifolds.) An integrability condition is a condition on the to guarantee that there will be integral submanifolds of sufficiently high dimension. (Wikipedia).
Introduction to Differential Inequalities
What is a differential inequality and how are they useful? Inequalities are a very practical part of mathematics: They give us an idea of the size of things -- an estimate. They can give us a location for things. It is usually far easier to satisfy assumptions involving inequalities t
From playlist Advanced Studies in Ordinary Differential Equations
Introduction to Differential Equation Terminology
This video defines a differential equation and then classifies differential equations by type, order, and linearity. Search Library at http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
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
A02 Independence of the solution set
The independence of a linear system. How to make sure that a set of solutions are not constant multiples of each other.
From playlist A Second Course in Differential Equations
Differential Equations | Variation of Parameters for a System of DEs
We solve a nonhomogeneous system of linear differential equations using the method of variation of parameters. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Systems of Differential Equations
B01 An introduction to separable variables
In this first lecture I explain the concept of using the separation of variables to solve a differential equation.
From playlist Differential Equations
How to graph the system of linear inequalities of one horizontal and one vertical
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
How to solve differentiable equations with logarithms
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
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Lecture 6, Systems Represented by Differential Equations | MIT RES.6.007 Signals and Systems
Lecture 6, Systems Represented by Differential Equations 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
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
Title: Rational Matrix Differential Operators and Integral Systems of PDEs
From playlist Fall 2017
Lec 2 | MIT Finite Element Procedures for Solids and Structures, Linear Analysis
Lecture 2: Analysis of continuous systems Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Linear Finite Element Analysis
Pre-recorded lecture 6: Constant normal forms, nilpotent Nijenhuis operators and Thompson theorem
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Nijenhuis geometry for ECRs: Pre-recorded Lecture 2 Part B
Pre-recorded Lecture 2 Part B: Nijenhuis geometry for ECRs Date: 9 February 2022 Lecture slides: https://mathematical-research-institute.sydney.edu.au/wp-content/uploads/2022/02/Prerecorded_Lecture2.pdf ---------------------------------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Mod-01 Lec-01 General Introduction
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
Analytically Solving Systems of Linear Ordinary Differential Equations
In this video we derive the analytical solution to a system of linear ordinary differential equations. This is also referred to as the linear time invariant (LTI) system or state space system. As such, this video describes the analytical solution to a linear state space system. In addit
From playlist Ordinary Differential Equations
Nijenhuis geometry for ECRs: Pre-recorded Lecture 2 Part A
Pre-recorded Lecture 2 Part A: Nijenhuis geometry for ECRs Date: 9 February 2022 Lecture slides: https://mathematical-research-institute.sydney.edu.au/wp-content/uploads/2022/02/Prerecorded_Lecture2.pdf ---------------------------------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Numerical Simulation of Ordinary Differential Equations: Integrating ODEs
In this video, I provide an overview of how to numerically integrate solutions of ordinary differential equations (ODEs). These solutions are known as trajectories, and provide a powerful computational tool for us to analyze nonlinear systems, where simple analytic techniques may not work
From playlist Engineering Math: Differential Equations and Dynamical Systems
Review of Linear Time Invariant Systems
http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Review: systems, linear systems, time invariant systems, impulse response and convolution, linear constant-coefficient difference equations
From playlist Introduction and Background