Results 1 to 9 of 9

Math Help - calculus defintion

  1. #1
    Newbie
    Joined
    Oct 2006
    From
    NCR
    Posts
    3

    calculus defintion

    what is a differential eqn?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Akanksha gupta View Post
    what is a differential eqn?
    It is an equation connecting a function with the independent variable, and its
    own derivative (or derivatives) so a first order Ordinary Differential Equation
    (ODE) is something like:

    f(x, y, y')=0

    a second order one is of the form:

    f(x, y, y', y'')=0,

    and so on for higher order.

    A Partial Differential Equation (PDE) is similar but there are multiple
    independent variables and also uses partial derivatives.

    Some examples of ODEs:

    1:

    y'' = - 3 y,

    or in standard form:

    y'' + 3 y = 0.

    2:

    y'' + x y' + x^2 y = sin(3 x),

    or in standard form:

    y'' + x y' + x^2 y - sin(3 x) = 0.

    RonL
    Last edited by CaptainBlack; October 8th 2006 at 08:34 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    There are two types of equations.

    (Abusing terminology)

    An algebraic equation asks to find all number that satisfies the equation.
    For example,
    x^5=1

    A functional equation asks to find all functions that satisfies the equation.
    For example,
    f(x+y)=f(x)f(y) for all numbers x,y
    Note we are not solving for a number but a function that has that property.
    (If you are interesting all exponential functions make that true.)
    The problem with functional equation is that there is almost no developed way to solve them. Thus,
    f(x+y)=f(x)f(y)
    Might have other solutions rather than exponentials (I do not know).


    So a differencial equation is a type of functional equation. Differencial equations are much easier to solve because they are "well-behaved" meaning a function behaves normal rather than going all over the place.
    It gets its name because the derivative appears there.
    -------
    Quote Originally Posted by CaptainBlank
    It is an equation connecting a function with the independent variable, and its
    own derivative (or derivatives) so a first order Ordinary Differential Equation
    (ODE) is something like.................
    And you blame me for being to complicated.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by [B
    Im[/B]PerfectHacker]

    Quote Originally Posted by CaptainBlank
    It is an equation connecting a function with the independent variable, and its
    own derivative (or derivatives) so a first order Ordinary Differential Equation
    (ODE) is something like.................
    And you blame me for being to complicated.
    Yes a general description of what constitutes a Differential Equation is
    complicated if you don't already know what a DE is, and that is why I gave
    some examples.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2006
    From
    NCR
    Posts
    3

    thanks

    Thanks for the explaination but i m not able to understand even a bit of it. may be i am a dumbo but can u explain it more properly. Please.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Akanksha gupta View Post
    Thanks for the explaination but i m not able to understand even a bit of it. may be i am a dumbo but can u explain it more properly. Please.
    An Ordinary Differential Equation (ODE) is an equation relating the derivative (and higher order derivatives for higher order ODEs) of a function to the values of the function and the independent variable.

    For example:

    dy/dx + 3 x y = f(x),

    for some function of f of x.

    RonL
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,739
    Thanks
    645
    Hello, Akanksha gupta!

    I must assume you know what a derivative is . . .


    What is a differential equation?

    Here's the baby-talk approach I've used in my classes . . .


    In algebra, we are asked to solve: .2x - 4 .= .-3

    We want a number x so that:
    . . if we double x and subtract 4, we get -3.
    And there are algebraic procedures for finding the solution (x = ).


    In Differential Equations, we can be given something like:

    . . . .dy
    . . 2 --- - 4y .= .-3
    . . . .dx

    We want a function y = f(x) so that:
    . . if we double the derivative of y and subtract 4 times y, we get -3.

    And there are procedures for solving this differential equation.

    Solution: . y .= .Ce^
    {2x} + .for any constant C.

    Follow Math Help Forum on Facebook and Google+

  8. #8
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Soroban View Post
    Hello, Akanksha gupta!

    I must assume you know what a derivative is . . .



    Here's the baby-talk approach I've used in my classes . . .


    In algebra, we are asked to solve: .2x - 4 .= .-3

    We want a number x so that:
    . . if we double x and subtract 4, we get -3.
    And there are algebraic procedures for finding the solution (x = &#189.


    In Differential Equations, we can be given something like:

    . . . .dy
    . . 2 --- - 4y .= .-3
    . . . .dx

    We want a function y = f(x) so that:
    . . if we double the derivative of y and subtract 4 times y, we get -3.

    And there are procedures for solving this differential equation.

    Solution: . y .= .Ce^
    {2x} + ¾ .for any constant C.

    Is that not what I said?
    -----------
    ~~~~~~
    -----------
    Is there such a thing as a functional-function equation?
    For example,
    f(x+y)=f(x)+f(y) where f:R--> R

    But are there cases where we have,
    L(x+y)=L(x)+L(y) where L:R(x)--->R(x)
    Where R(x) represents the set of functions f:R-->R

    The reason why I am asking this is because the Laplace Transform appears to do that. It transform a function into a function.
    ---------
    ~~~~~
    ---------
    This is to the user who asked the question. If you do not know what a derivative is then you cannot understand well what a differencial equation is.

    To add, differencial equations are useless to mathemations. Only for science and physics they are useful. Funny that mathemations developed them but never use them.
    Last edited by ThePerfectHacker; October 9th 2006 at 06:38 AM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2006
    From
    NCR
    Posts
    3
    Thanks it was intresting and sry if felt about the quote
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. unitary,close to it seflf defintion question
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: July 26th 2011, 03:16 AM
  2. Replies: 3
    Last Post: January 18th 2010, 10:44 AM
  3. Another Chi square - s^2 defintion
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 12th 2009, 11:00 PM
  4. Replies: 4
    Last Post: October 4th 2009, 09:21 AM
  5. Defintion of derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 3rd 2008, 07:41 PM

Search Tags


/mathhelpforum @mathhelpforum