Mathematical modeling | Dynamical systems
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often bemodeled by linear systems. (Wikipedia).
Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar
From playlist Intro to Linear Systems
Solve Linear Systems of Equations
How to solve linear systems via matrices. We discuss consistent and inconsistent forms and show how to solve.
From playlist Intro to Linear Systems
Intro to Linear Systems: 3 Equations, 3 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 3 equations and 3 unknowns. Geometrically, we are looking at how three planes intersect. A linear system is a mathematical model of a system based on the use of a linear operator. Lin
From playlist Intro to Linear Systems
Intro to Linear Systems: 2 Equations, 3 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 3 unknowns. Geometrically, we are looking at how two planes intersect. A linear system is a mathematical model of a system based on the use of a linear operator. Line
From playlist Intro to Linear Systems
Linear Algebra: Systems of Linear Equations
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/
From playlist Basics: Linear Algebra
Solve a system of three equations with no solutions
👉Learn how to solve a system of three linear systems. A system of equations is a set of equations which are to be solved simultaneously. A linear equation is an equation whose graph is a straight line. The solution to a system of equations is a set of unique values of the variables for wh
From playlist Solve a System of Equations With Three Variables
Solve a system with three variables
👉Learn how to solve a system of three linear systems. A system of equations is a set of equations which are to be solved simultaneously. A linear equation is an equation whose graph is a straight line. The solution to a system of equations is a set of unique values of the variables for wh
From playlist Solve a System of Equations With Three Variables
Linear Algebra - Lecture 10 - Homogeneous Linear Systems
In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form.
From playlist Linear Algebra Lectures
When do linear systems have solutions?
How to determine the solution structure to a linear system of simultaneous equations. Several examples are discussed.
From playlist Intro to Linear Systems
Translating Inputs, Outputs, and Initial Conditions Between Linear and Nonlinear Dynamic Systems
In this video we discuss the nuances and differences between linear and nonlinear models. In particular, we show how to use equivalent inputs, outputs, and initial conditions for both systems. Topics and timestamps: 0:00 – Introduction 10:40 – Inputs 14:21 – Outputs 16:01 – Initial condi
From playlist Control Theory
Lecture 23 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood lectures on linear systems, focusing on linear time and variance systems. The Fourier transform is a tool for solving physical problems. In thi
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Linearizing a Simulink Model Using the Linear Analysis Tool and ‘linmod’
In this video we show how to linearize a non-linear Simulink model using numerical techniques. This approach is extremely powerful as it allows automatic generation of linear models of a complicated model about different trim/operating points. We investigate how to linearize using the Li
From playlist Working with Matlab
Deep Learning to Discover Coordinates for Dynamics: Autoencoders & Physics Informed Machine Learning
Joint work with Nathan Kutz: https://www.youtube.com/channel/UCoUOaSVYkTV6W4uLvxvgiFA Discovering physical laws and governing dynamical systems is often enabled by first learning a new coordinate system where the dynamics become simple. This is true for the heliocentric Copernican syste
From playlist Data-Driven Dynamical Systems with Machine Learning
Mod-05 Lec-24 General System and Diagonalizability
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
Kernel Learning for Robust Dynamic Mode Decomposition
In this video abstract, I present our new data-driven method for learning high-dimensional, nonlinear dynamical systems via kernel methods. This work is in collaboration with Profs Benjamin Herrmann, Beverley McKeon and Steve Brunton. The paper is available on arXiv: Title: Kernel Learni
From playlist Research Abstracts from Brunton Lab
This lecture is part of an online course on schemes, following chapter II of the book "Algebraic geometry" by Hartshorne. In this lecture we give some examples of linear systems of divisors, which are an older way of visualizing sections of an invertible sheaf by looking at the zeros of
From playlist Algebraic geometry II: Schemes
Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
This video illustrates the use of the Koopman operator to simulate and control a nonlinear dynamical system using a linear dynamical system on an observable subspace. From the Paper: Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for contro
From playlist Research Abstracts from Brunton Lab
Trimming and Linearization, Part 1: What Is Linearization?
Why go through the trouble of linearizing a model? To paraphrase Richard Feynman, it’s because we know how to solve linear systems. With a linear model we can more easily design a controller, assess stability, and understand the system dynamics. - Learn about linearization for model analys
From playlist Trimming and Linearization
Solving a system of three equations with infinite many solutions
👉Learn how to solve a system of three linear systems. A system of equations is a set of equations which are to be solved simultaneously. A linear equation is an equation whose graph is a straight line. The solution to a system of equations is a set of unique values of the variables for wh
From playlist Solve a System of Equations With Three Variables
Lecture 24 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on linear systems. The Fourier transform is a tool for solving physical problems. In this course the emphasis is on rela
From playlist Lecture Collection | The Fourier Transforms and Its Applications