012407 - Lecture 2 Evolutionary Process What is(or what...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
01/24/2007: Lecture 2 Evolutionary Process: What is (or, what will we mean by) an "evolutionary process?" The word "evolution" comes up a lot in science and engineering (e.g. RLC circuit with sources.) From a vector x whose entries are capacitor voltages and inductor currents we can generically write an ODE: = + Dxt Axt Et = Dxt dxdt E(t) is a vector of functions dependent on sources This equation governs the time-"evolution" of state variables (ie, entries in x(t)) If you have nonlinear stuff, get: ( )= ( ( ), ( ) ) Dx t f x t E t -> which is a non-linear ODE. Dynamical Systems Theory studies things like this. In Newtonian physics, similarly, for a system of N particles – let: x i = position of particle i p i = momentum of particle i then (m i = mass of pt. i) = × ( ) Dxit 1mi pi t = ( ) Dpit fi t <-- net force on particle I (can depend on {xj, pj} and our "exogenous" forces.)
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern