Thread: few differential equations and general maths questions ...??

  1. #1
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    few differential equations and general maths questions ...??

    we had this computer oriented numerical methods at college , and i am still trying to follow it ...

    it was a difficult subject ... and i was trying to narrow it down ...

    it had lot of maths related questions ... and we never had the proper texts or notes to follow it properly ...

    so i decided to collect and make some notes from online resources to narrow it down ...

    now it sorts of looks a bit like all these ...




    http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf

    http://www.ce.utexas.edu/prof/mckinn...s_Indirect.pdf

    http://www.ce.utexas.edu/prof/mckinn...FixedPoint.pdf

    http://www.ce.utexas.edu/prof/mckinn..._Bisection.pdf

    http://www.ce.utexas.edu/prof/mckinn...s_3_Newton.pdf

    http://www.mathsisfun.com/algebra/sy...equations.html

    http://www.sosmath.com/soe/SE211105/SE211105.html


    few differential equations and general maths questions ...??-32_wannaplay2-jpg




    could somebody help me with initial steps for programming the solution for such an equation ??

  2. #2
    and the hat of int overfl Salem's Avatar
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    How about you post just one question, rather than your entire reading list on us.
    If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
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    This could be a case where the students don't need to understand how the methods or algorithms are derived or exactly how they work, but only how to convert a method into a program. There can be situations where the underlying methods won't work, and without understanding the methods, this could be a problem, but it's common for these type of classes to focus on just coding of methods as opposed to fully understanding the methods.

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    rcgldr

    This could be a case where the students don't need to understand how the methods or algorithms are derived or exactly how they work, but only how to convert a method into a program. There can be situations where the underlying methods won't work, and without understanding the methods, this could be a problem, but it's common for these type of classes to focus on just coding of methods as opposed to fully understanding the methods.
    there was this parts in a text book , where equations and its numerical methods to find approximate roots were described ...

    but the programming part of it was very weak ....






    Salem

    How about you post just one question, rather than your entire reading list on us.



    i am sorry , i am a bit new to differential equations and programming ...


    few differential equations and general maths questions ...??-differential_equation_examples_33-png


    how do i solve this with a programming language ??
    Last edited by delta; 06-20-2016 at 03:20 AM.

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    Quote Originally Posted by delta View Post
    how do i solve this with a programming language ??
    To actually solve such equations (if it can be solved), you'd probably want something like matlab (expensive if not a student), or you can use the wolframalpha web site math solver. I'm not sure how you'd use a numerical method for the equation shown. Typically numerical methods are used for real life situations, like reentry where the force related to gravity and aerodynamic drag vary during the re-entry. given initial conditions, like velocity and position. A simple example would be

    d2(x) / (dt)​2 = -x

    or

    x'' = -x

    which is a sine (or cosine) wave (assuming real numbers only), where initial condition is stated, and numerical methods used to predict velocity and position over time.
    Last edited by rcgldr; 06-20-2016 at 11:13 AM.

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    may i re arrange a few things for one last time ? so that the steps involved in finding the solution of such a question with a programming language like c , looks a bit more appropriate ...

    few differential equations and general maths questions ...??-differential_equation_examples_33-png

    few differential equations and general maths questions ...??-32_wannaplay2-jpg



    first i think it is important to identify the type of equation , that we are dealing with ...

    there is at least this much types of numerical methods associated with a differential equations itself ...


    Solution by Taylor's series
    Picard's method of successive approximations
    Euler's method
    Modified Euler's Method
    Runge-Kutta method
    Predictor-Corrector Methods
    Adams-Moulton Method
    Milne's method
    i think we are trying to find the solution of the differential equations with its associated numerical methods to find approximate roots of the equations ...

    in the case of a polynomial for example...

    a solution of a polynomial equation is also called a root of the polynomial ...

    a value for the variable that makes the polynomial zero

    if you can't find an exact expression, then you can use numerical methods to get approximations ...

    with numerical methods you can choose how close to zero you want, and it will give you a value that's at least that close ...



    it is also important to identify the types of solutions that can be applied to an equation depending on the type of equation ...



    http://www.ce.utexas.edu/prof/mckinn...Eqs_Direct.pdf

    http://www.ce.utexas.edu/prof/mckinn...s_Indirect.pdf

    http://www.ce.utexas.edu/prof/mckinn...FixedPoint.pdf

    http://www.ce.utexas.edu/prof/mckinn..._Bisection.pdf

    http://www.ce.utexas.edu/prof/mckinn...s_3_Newton.pdf

    http://www.mathsisfun.com/algebra/sy...equations.html

    http://www.sosmath.com/soe/SE211105/SE211105.html


    the next step would be to use the appropriate numerical methods or the appropriate algorithm on the equation to find its approximate roots ...








    rcgldr

    To actually solve such equations (if it can be solved), you'd probably want something like matlab (expensive if not a student), or you can use the wolframalpha web site math solver. I'm not sure how you'd use a numerical method for the equation shown. Typically numerical methods are used for real life situations, like reentry where the force related to gravity and aerodynamic drag vary during the re-entry. given initial conditions, like velocity and position. A simple example would be

    d2(x) / (dt)​2 = -x

    or

    x'' = -x

    which is a sine (or cosine) wave (assuming real numbers only), where initial condition is stated, and numerical methods used to predict velocity and position over time.

    thanks a lot for those replies rcgldr ,

    trying to see an overall picture of all these things was a bit hard ...

    i will try to improve this little by little , with all these information's in my mind ...

    that was my attempt to narrow it down a little bit more ...
    Last edited by Salem; 06-21-2016 at 02:46 AM. Reason: URL fix

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