Dynamical Systems and Differential Equations

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

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

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

Introduction to autonomous differential equations

Order: Reorder
Duration: 8:29
Updated: 09 Apr 2013

See http://mathinsight.org/autonomous_differential_equation_introduction for context.

http://wn.com/Introduction_to_autonomous_differential_equations

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

The stability of equilibria of a differential equation, analytic approach

Order: Reorder
Duration: 8:04
Updated: 15 Apr 2013

See http://mathinsight.org/stability_equilibria_differential_equation for context.

http://wn.com/The_stability_of_equilibria_of_a_differential_equation,_analytic_approach

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

Rotational Dynamic System Modeling Example

Order: Reorder
Duration: 6:40
Updated: 10 Jan 2014

This is a quick review of how to generate differential equations for a system having rotating disks, torsional stiffness and torsional damping.

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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

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

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

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 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

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

DYNAMIC SYSTEMS Firmenjubiläum 2013

Order: Reorder
Duration: 5:07
Updated: 06 Aug 2013

20 Jahre Kompetenz in industrieller Kennzeichnung -- DYNAMIC Systems feiert Geburtstag DYNAMIC Systems ist auf individuelle Komplettlösungen für automatisierte Kennzeichnungsaufgaben insbesondere für die Branchen Automotive, Elektronik/Telekommunikation, Chemie, Pharma/Medizin und Logistik spezialisiert. Das Produktspektrum umfasst Etiketten, Drucker, Barcode-Scanner, RFID-Lösungen, Beschriftungssysteme und Software. Mit integrierten und systemübergreifenden Konzepten bietet DYNAMIC Systems industrielle Kennzeichnung „aus einer Hand" und ist einer der führenden Systemanbieter auf dem Gebiet der industriellen Kennzeichnungssysteme im deutschsprachigen Raum. Seit 2010 agiert DYNAMIC Systems gemeinsam mit der Schwarz Druck GmbH in der DYNAMIC Holding GmbH, Wörthsee, www.dynamic-systems.de

http://wn.com/DYNAMIC_SYSTEMS_Firmenjubiläum_2013

Dynamical Systems

Order: Reorder
Duration: 101:13
Updated: 14 Aug 2013

Mathematics of Complexity lecture 3 Class description: We've all heard the buzzwords - chaos, fractals, networks, power laws. What do these terms mean in a r...

http://wn.com/Dynamical_Systems

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

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

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...

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How To: Find the Domain of a Function #1

Order: Reorder
Duration: 6:33
Updated: 13 Jan 2014

I hope you found this video useful, please subscribe for daily videos! WBM Foundations: Mathematical logic Set theory Algebra: Number theory Group theory Lie groups Commutative rings Associative ring theory Nonassociative ring theory Field theory General algebraic systems Algebraic geometry Linear algebra Category theory K-theory Combinatorics and Discrete Mathematics Ordered sets Geometry Geometry Convex and discrete geometry Differential geometry General topology Algebraic topology Manifolds Analysis Calculus and Real Analysis: Real functions Measure theory and integration Special functions Finite differences and functional equations Sequences and series Complex analysis Complex variables Potential theory Multiple complex variables Differential and integral equations Ordinary differential equations Partial differential equations Dynamical systems Integral equations Calculus of variations and optimization Global analysis, analysis on manifolds Functional analysis Functional analysis Fourier analysis Abstract harmonic analysis Integral transforms Operator theory Numerical analysis and optimization Numerical analysis Approximations and expansions Operations research Probability and statistics Probability theory Statistics Computer Science Computer science Information and communication Applied mathematics Mechanics of particles and systems Mechanics of solids Fluid mechanics Optics, electromagnetic theory Classical thermodynamics, heat transfer Quantum Theory Statistical mechanics, structure of matter Relativity and gravitational theory Astronomy and astrophysics Geophysics applications Systems theory Other sciences Category

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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