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I Some questions from a numerical analysis book

  1. Jun 15, 2017 #1
    Last edited by a moderator: Jun 15, 2017
  2. jcsd
  3. Jun 15, 2017 #2

    BvU

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    Can't find what this is about ....
     
  4. Jun 15, 2017 #3

    DrClaude

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    This is a 300 page book. You will have to specify what you are talking about.
     
  5. Jun 15, 2017 #4
    Are we trying to find the roots with all these types of numerical methods ? or is it called finding something else ?
     
  6. Jun 15, 2017 #5

    DrClaude

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    Generally speaking, a numerical algorithm that allows you to solve a problem of the type ##\mathbf{F}(\mathbf{x}) = 0## is indeed called a root-finding algorithm.
     
  7. Jun 15, 2017 #6
    So what are we trying to do when we use numerical differentiation ? I don't think its called root finding ? is it ?
     
  8. Jun 15, 2017 #7

    DrClaude

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    No, it is called numerical differentiation.
     
  9. Jun 15, 2017 #8
    OK , thanks
     
  10. Jun 15, 2017 #9

    Mark44

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    A book on Numerical Analysis typically discusses techniques for solving equations, finding derivatives numerically, and calculating integrals numerically. It might also discuss techniques for finding matrix inverses, finding eigenvalues and eigenvectors of matrices, and other topics.
     
  11. Jun 15, 2017 #10
  12. Jun 15, 2017 #11

    Mark44

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    Really, though, @rosiekidcute, if you're struggling with basic concepts like fractions, factoring, and trig (as in recent threads), it's not very likely that you will understand topics in numerical analysis or partial differential equation.
     
  13. Jun 15, 2017 #12
    I keep thinking of naturally occurring things whenever i think of derivatives , differential equations and partial differential equations .Like electricity , magnetic field .
    I am always like if there is a derivative in a differential equation , how could have that happened ? what could have made it like that . Maybe i should stop thinking about it that way .Its just some rules , Maybe its my lack of experience .
     
  14. Jun 15, 2017 #13

    jbriggs444

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    No need to invoke electricity or magnetism. Consider Newton's second law for an object with a fixed mass: F=ma. Force equals mass times acceleration.

    That acceleration is a the first derivative of velocity. ##F=m \frac{dv}{dt}##.
    That velocity is the first derivative of position. ##F = m \frac{d^2x}{dt^2}##.
    If we are dealing with a mass on a spring, that force is also given by Hooke's Law: F = -kx.
    So we have ##-kx = m \frac{d^2x}{dt^2}##

    That's a differential equation. (A second order homogeneous linear differential equation. There is a straightforward crank-and-grind approach to solving those).
     
    Last edited: Jun 15, 2017
  15. Jun 15, 2017 #14
    Thanks ,

    function.png

    Same things right ?
     
  16. Jun 17, 2017 #15

    Mark44

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    No, these are different quantities: displacement, velocity, acceleration, and jerk.
     
  17. Jun 17, 2017 #16
    Right , sorry about that .
     
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