Dynamical Systems and Differential Equations

Lec 27 | MIT 18.03 Differential Equations, Spring 2006

Order: Reorder
Duration: 50:25
Updated: 08 Aug 2013

Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commo...

http://wn.com/Lec_27_|_MIT_1803_Differential_Equations,_Spring_2006

Linearizing non-linear dynamic equations

Order: Reorder
Duration: 7:27
Updated: 17 Jul 2013

In this lecture, we go through the steps of linearizing non-linear differential equations about a given operating/equilibrium point. We will use the multi-va...

http://wn.com/Linearizing_non-linear_dynamic_equations

Multiagent Dynamical Systems

Order: Reorder
Duration: 56:46
Updated: 20 Jul 2013

I will show how to model multiagent systems using dynamical systems theory by deriving a class of macroscopic differential equations that describe mutual ada...

http://wn.com/Multiagent_Dynamical_Systems

Mythily Ramaswamy - Control of Differential Equations

Order: Reorder
Duration: 39:44
Updated: 08 Oct 2013

PROGRAM: RECENT TRENDS IN ERGODIC THEORY AND DYNAMICAL SYSTEMS DATES: Tuesday 18 Dec, 2012 - Saturday 29 Dec, 2012 VENUE: Department of Mathematics,Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara PROGRAM LINK: http://www.icts.res.in/program/ETDS2012 DESCRIPTION: "Dynamical Systems" is an exciting and very active field in mathematics that involves tools and techniques from many areas. A dynamical system can be obtained by iterating a function or letting evolve in time the solution of an equation. Even if the rule of evolution is deterministic, the long term behavior of the system is often chaotic. Different branches of "Dynamical Systems", in particular "Ergodic Theory", provide tools to quantify this chaotic behavior of the system and to predict it in an average. This program has been planned in two parts: 7 day Workshop (Dec 18-24, 2012) followed by 4 day Discussion Meeting (Dec 26-29, 2012). The aim is to bring together on one platform experts from around the world who are actively working in various sub-disciplines of Dynamical Systems. An important aspect of the program will be an emphasis on making it accessible to younger participants. The workshop will begin with lectures on basic Ergodic Theory followed by lectures on Topological Dynamics, Differentiable Dynamics and Symbolic Dynamics, including Cellular Automata. It will have a `problem and discussion' session every day. Many researchers from across the globe will be discussing their celebrated works in Ergodic Theory, Dynamical Systems and related areas during the four days of the Discussion Meeting. We will encourage young participants to present a short communication on their work in the presence of the eminent experts during the program.

http://wn.com/Mythily_Ramaswamy_Control_of_Differential_Equations

Lec 31 | MIT 18.03 Differential Equations, Spring 2006

Order: Reorder
Duration: 47:09
Updated: 31 Mar 2013

Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum. View the complete course: http://ocw.mit.edu/...

http://wn.com/Lec_31_|_MIT_1803_Differential_Equations,_Spring_2006

Taxonomy of Dynamic Systems

Order: Reorder
Duration: 9:40
Updated: 03 Jul 2013

An overview of the ways to classify dynamic systems (differential equations) based on continuity, linearity and time variance.

http://wn.com/Taxonomy_of_Dynamic_Systems

System Dynamics and Control: Module 3 - Mathematical Modeling Part I

Order: Reorder
Duration: 65:34
Updated: 18 Aug 2013

Discussion of differential equations as a representation of dynamic systems. Introduction to the Laplace Transform as a tool for solving differential equations.

http://wn.com/System_Dynamics_and_Control_Module_3_Mathematical_Modeling_Part_I

Logical Analysis of Hybrid Systems

Order: Reorder
Duration: 53:31
Updated: 30 Jul 2013

RI Seminar, February 18, 2011 Andre Platzer Assistant Professor, Computer Science Department, Carnegie Mellon University Hybrid systems model cyber-physical ...

http://wn.com/Logical_Analysis_of_Hybrid_Systems

Differential Equations, The Exponential Map Perspective - Lecture 7

Order: Reorder
Duration: 40:08
Updated: 25 Oct 2013

The seventh in a series of lectures which will examine differential equations from the perspective of the exponential map. The seventh lecture continues with very basic concepts from linear algebra. We are moving towards the Jordan Normal Form. The Jordan Normal Form puts a matrix into a form which is extremely easy to exponentiate. Differential equations, matrix theory, dynamical systems, exponential map, exponents, complex numbers, Taylor series, taylor polynomials, sequences, series, vector field, equilibrium, linearization, stable manifold, unstable manifold.

http://wn.com/Differential_Equations,_The_Exponential_Map_Perspective_Lecture_7

State Space Representation ( Dynamic Systems ) | Mechanical Engineering

Order: Reorder
Duration: 9:01
Updated: 04 Aug 2013

State Space Representation Dynamic Systems.

http://wn.com/State_Space_Representation_Dynamic_Systems_|_Mechanical_Engineering

Differential Equations: The Exponential Map Perspective - Lecture 1

Order: Reorder
Duration: 48:25
Updated: 06 Sep 2013

The first in a series of lectures which will examine differential equations from the perspective of the exponential map. The first lecture starts by considering real exponents, where several key exponent properties are assumed to be true for ALL REAL NUMBERS (this was not made clear in the lecture). From there, we derive several basic exponent properties that we know from basic algebra. We begin to study Taylor series, and will eventually define complex exponents using the exponential function. This will serve as a spring-board towards demonstrating the importance of the exponential function in mathematics, and the ideas will be used later on when we talk about the exponential of a matrix. Differential equations, matrix theory, dynamical systems, exponential map, exponents, complex numbers, Taylor series, taylor polynomials, sequences, series, vector field, equilibrium, linearization, stable manifold, unstable manifold. This lecture occurred on Sept. 5th, 2013.

http://wn.com/Differential_Equations_The_Exponential_Map_Perspective_Lecture_1

Differential Equations: The Exponential Map Perspective - Lecture 9

Order: Reorder
Duration: 37:29
Updated: 16 Nov 2013

The ninth in a series of lectures which will examine differential equations from the perspective of the exponential map. The ninth lecture discusses coordinates, and change of basis. We are moving towards the Jordan Normal Form. The Jordan Normal Form puts a matrix into a form which is extremely easy to exponentiate. Differential equations, matrix theory, dynamical systems, exponential map, exponents, complex numbers, Taylor series, taylor polynomials, sequences, series, vector field, equilibrium, linearization, stable manifold, unstable manifold.

http://wn.com/Differential_Equations_The_Exponential_Map_Perspective_Lecture_9

Fixed points and stability of a nonlinear system

Order: Reorder
Duration: 18:01
Updated: 11 Nov 2013

Find the fixed points and determines the linear stability of a system of two first-order nonlinear differential equations. Lecture notes at http://www.math.ust.hk/~machas/differential-equations.pdf

http://wn.com/Fixed_points_and_stability_of_a_nonlinear_system

Lecture 3

Order: Reorder
Duration: 53:18
Updated: 21 Sep 2013

The third in a series of lectures which will examine differential equations from the perspective of the exponential map. The third lecture develops the complex logarithm. This will serve as a spring-board towards demonstrating the importance of the exponential function in mathematics, and the ideas will be used later on when we talk about the exponential of a matrix. Differential equations, matrix theory, dynamical systems, exponential map, exponents, complex numbers, Taylor series, taylor polynomials, sequences, series, vector field, equilibrium, linearization, stable manifold, unstable manifold. This lecture occurred on Sept. 19th, 2013.

http://wn.com/Lecture_3

Modeling and control of dynamic systems - From electric vehicles to systems biology : Adachi's Group

Order: Reorder
Duration: 3:55
Updated: 15 Apr 2013

At the Adachi Laboratory, the theme of research is modeling and control. Control means actively changing a systems dynamics in a desired way. Control is util...

http://wn.com/Modeling_and_control_of_dynamic_systems_From_electric_vehicles_to_systems_biology_Adachi's_Group

Solving Differential Equations by LT part 2

Order: Reorder
Duration: 14:00
Updated: 07 Oct 2013

http://wn.com/Solving_Differential_Equations_by_LT_part_2

Solving Differential Equations by LT part 1

Order: Reorder
Duration: 10:01
Updated: 07 Oct 2013

http://wn.com/Solving_Differential_Equations_by_LT_part_1

Interactive Exploration of a Dynamical System

Order: Reorder
Duration: 5:47
Updated: 06 Oct 2013

Interactive Exploration of a Dynamical System Follow us on Twitter - https://twitter.com/ExcellentVideos Facebook - http://www.facebook.com/excellent.randomvideos Disclaimer !!! I have neither created this video nor own this video. As I liked this video and as it was under creative commons license I have shared this video For the source of the video, Please check http://vimeo.com/23839605 Description below is the exact copy of what was mentioned in the source A user interface for exploring systems of differential equations. Every variable is shown as a plot; every parameter has a knob that can be adjusted in realtime. This ubiquitous visualization and in-context-manipulation helps the user develop a sense for how the parameters of the system influence its behavior. Part of the Kill Math project: worrydream.com/KillMath By Bret Victor: worrydream.com

http://wn.com/Interactive_Exploration_of_a_Dynamical_System

Differential Equations: The Exponential Map Perspective - Lecture 6

Order: Reorder
Duration: 38:20
Updated: 18 Oct 2013

The sixth in a series of lectures which will examine differential equations from the perspective of the exponential map. The sixth lecture introduces very basic concepts from linear algebra. We are moving towards the Jordan Normal Form. The Jordan Normal Form puts a matrix into a form which is extremely easy to exponentiate. Differential equations, matrix theory, dynamical systems, exponential map, exponents, complex numbers, Taylor series, taylor polynomials, sequences, series, vector field, equilibrium, linearization, stable manifold, unstable manifold. This lecture occurred on Sept. 19th, 2013.

http://wn.com/Differential_Equations_The_Exponential_Map_Perspective_Lecture_6

Equation of Tangent Plane to a Surface at a Point Example #1

Order: Reorder
Duration: 6:07
Updated: 10 Jul 2013

I hope you found this video useful, please subscribe for daily videos! WBM Foundations: Mathematical logic Set theory Algebra: Number theory Group theory Lie...

http://wn.com/Equation_of_Tangent_Plane_to_a_Surface_at_a_Point_Example_1

Lecture 2 | Introduction to Linear Dynamical Systems

Order: Reorder
Duration: 65:52
Updated: 11 Aug 2013

Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on linear functions for the course, Introduction to Linear ...

http://wn.com/Lecture_2_|_Introduction_to_Linear_Dynamical_Systems

System Dynamics Modeling & Analysis Lecture - 2007-09

Order: Reorder
Duration: 89:02
Updated: 16 Jul 2012

This is the 9. lecture in IE 602 System Dynamics Modeling & Analysis course of Spring 2007 in Bogazici University. The lecture is given by Prof. Yaman Barlas...

http://wn.com/System_Dynamics_Modeling_Analysis_Lecture_2007-09

Simulink tutorial: Second Order Dynamic System

Order: Reorder
Duration: 5:52
Updated: 05 Jun 2013

This tutorial shows how to create a 2nd order system in Simulink. The code can be found in the tutorial section in http://www.eeprogrammer.com/. More enginee...

http://wn.com/Simulink_tutorial_Second_Order_Dynamic_System

Branches of Mathematics

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Applied mathematics

Related Topics

Lec 27 | MIT 18.03 Differential Equations, Spring 2006

Linearizing non-linear dynamic equations

Multiagent Dynamical Systems

Mythily Ramaswamy - Control of Differential Equations

Lec 31 | MIT 18.03 Differential Equations, Spring 2006

Taxonomy of Dynamic Systems

System Dynamics and Control: Module 3 - Mathematical Modeling Part I

Logical Analysis of Hybrid Systems

Differential Equations, The Exponential Map Perspective - Lecture 7

State Space Representation ( Dynamic Systems ) | Mechanical Engineering

Differential Equations: The Exponential Map Perspective - Lecture 1

Differential Equations: The Exponential Map Perspective - Lecture 9

Fixed points and stability of a nonlinear system

Lecture 3

Make changes yourself !

Lec 27 | MIT 18.03 Differential Equations, Spring 2006

Linearizing non-linear dynamic equations

Multiagent Dynamical Systems

Mythily Ramaswamy - Control of Differential Equations

Lec 31 | MIT 18.03 Differential Equations, Spring 2006

Taxonomy of Dynamic Systems

System Dynamics and Control: Module 3 - Mathematical Modeling Part I

Logical Analysis of Hybrid Systems

Differential Equations, The Exponential Map Perspective - Lecture 7

State Space Representation ( Dynamic Systems ) | Mechanical Engineering

Differential Equations: The Exponential Map Perspective - Lecture 1

Differential Equations: The Exponential Map Perspective - Lecture 9

Fixed points and stability of a nonlinear system

Lecture 3

Modeling and control of dynamic systems - From electric vehicles to systems biology : Adachi's Group

Solving Differential Equations by LT part 2

Solving Differential Equations by LT part 1

Interactive Exploration of a Dynamical System