Newton's method - Hewlett Packard

This is a discussion on Newton's method - Hewlett Packard ; I am an AP Calculus teacher with many successful years employing the 48G. Now using the 50G and I would like to know how to put Newton's method in the 50G. It was never a problem on the 48G, but ...

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  1. Newton's method

    I am an AP Calculus teacher with many successful years employing the
    48G. Now using the 50G and I would like to know how to put Newton's
    method in the 50G. It was never a problem on the 48G, but what worked
    for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
    f'(x) and also define f(x). Enter a numeric value, press N from the
    var list and the calc figures out the rest, then you can iterate as
    desired. When I do this on the 50, all I get is infinity for the
    answer, which apparently means the 50 doesn't recognize f(x) or if it
    does, it comes up with zero for its derivative. I don't know much
    about global/local variables or programming.....Thanks in advance for
    any help.

    Also, anyone else encountered the 50's bizarre treatment of odd
    fractional root functions and their graphs? For instance, after many
    many failed trials, the only way I have found to get the 50 to draw
    the entire graph of y=x^(5/3) is to graph y=x^2/cube root of x! This
    is pathetic, and I hope someone knows a much more elegant solution.
    Again, thanks in advance.

    Srock

  2. Re: Newton's method

    Since nobody of the experts seems to be online, let me give you a
    first hint
    in RPN notation, which is the only one I know:
    1) store your function to a variable F: e.g. 1-x^2 F STO>
    2) calculate the Newton formula and store it to the variable G:
    F F X delta / +/- X + G STO>
    3) enter a starting value and calculate the next value by:
    starting value X STO> G EVAL
    and so on

    Of course you can do all of these statements within a little program
    and hence get an iteration step by pressing one button

    Peter

  3. Re: Newton's method

    On Feb 15, 7:30*am, sr...@midland-7.org wrote:
    > I am an AP Calculus teacher with many successful years employing the
    > 48G. Now using the 50G and I would like to know how to put Newton's
    > method in the 50G.


    Forgive me for hijacking this discussion, but are you actually using
    the HP-50G in the classroom? Do you require your students to have
    50Gs also, or do they have a mix of HP and TI calcs?

  4. Re: Newton's method

    On Feb 15, 9:30 am, sr...@midland-7.org wrote:
    > I am an AP Calculus teacher with many successful years employing the
    > 48G. Now using the 50G and I would like to know how to put Newton's
    > method in the 50G. It was never a problem on the 48G, but what worked
    > for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
    > f'(x) and also define f(x). Enter a numeric value, press N from the
    > var list and the calc figures out the rest, then you can iterate as
    > desired. When I do this on the 50, all I get is infinity for the
    > answer, which apparently means the 50 doesn't recognize f(x) or if it
    > does, it comes up with zero for its derivative. I don't know much
    > about global/local variables or programming.....Thanks in advance for
    > any help.
    >
    > Also, anyone else encountered the 50's bizarre treatment of odd
    > fractional root functions and their graphs? For instance, after many
    > many failed trials, the only way I have found to get the 50 to draw
    > the entire graph of y=x^(5/3) is to graph y=x^2/cube root of x! This
    > is pathetic, and I hope someone knows a much more elegant solution.
    > Again, thanks in advance.
    >
    > Srock


    A fractional power is a root of a power. A "root" is an inverse
    function. I posted a discussion of the topic in the thread
    http://groups.google.com/group/comp....47e4b8ccb2c203
    ; the main message is at
    http://groups.google.com/group/comp....47e4b8ccb2c203
    If you'll look that over and it's still a problem, please reply to me
    offline and I'll be happy to help.
    To actually produce your graph, you need to disambiguate the root
    (inverse-function) process. There are a total of 3 roots to the
    problem. The branch which is positive for positive x transitions to a
    complex one if you pass from positive real x to negative real x along
    a path which avoids the origin. If instead you graph XROOT(3,x^5) you
    will get what you want.
    In other words, the CAS underpinnings of the HP50 exhibit what some
    might call excessive pedantic fussiness about function definitions but
    which others might applaud as deep congruence with the underlying
    structure of the complex plane.
    Irl

  5. Re: Newton's method

    On Feb 15, 5:30 pm, sr...@midland-7.org wrote:
    > I am an AP Calculus teacher with many successful years employing the
    > 48G. Now using the 50G and I would like to know how to put Newton's
    > method in the 50G. It was never a problem on the 48G, but what worked
    > for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
    > f'(x) and also define f(x). Enter a numeric value, press N from the
    > var list and the calc figures out the rest, then you can iterate as
    > desired. When I do this on the 50, all I get is infinity for the
    > answer, which apparently means the 50 doesn't recognize f(x) or if it
    > does, it comes up with zero for its derivative. I don't know much
    > about global/local variables or programming.....Thanks in advance for
    > any help.


    The problem is that the value of X is being substituted into F(X)
    before the derivative is evaluated, which makes the derivative 0. One
    way around the problem is to define your Newton function as:

    << -> X << 'X-F(X)/d1F(X)' ->NUM >> >>

    -wes

  6. Re: Newton's method

    On Mar 6, 8:53*pm, Irl wrote:
    > On Feb 15, 9:30 am, sr...@midland-7.org wrote:
    >
    >
    >
    >
    >
    > > I am an AP Calculus teacher with many successful years employing the
    > > 48G. Now using the 50G and I would like to know how to put Newton's
    > > method in the 50G. It was never a problem on the 48G, but what worked
    > > for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
    > > f'(x) and also define f(x). Enter a numeric value, press N from the
    > > var list and the calc figures out the rest, then you can iterate as
    > > desired. When I do this on the 50, all I get is infinity for the
    > > answer, which apparently means the 50 doesn't recognize f(x) or if it
    > > does, it comes up with zero for its derivative. I don't know much
    > > about global/local variables or programming.....Thanks in advance for
    > > any help.

    >
    > > Also, anyone else encountered the 50's bizarre treatment of odd
    > > fractional root functions and their graphs? For instance, after many
    > > many failed trials, the only way I have found to get the 50 to draw
    > > the entire graph of y=x^(5/3) is to graph y=x^2/cube root of x! This
    > > is pathetic, and I hope someone knows a much more elegant solution.
    > > Again, thanks in advance.

    >
    > > Srock

    >
    > A fractional power is a root of a power. A "root" is an inverse
    > function. I posted a discussion of the topic in the threadhttp://groups.google.com/group/comp.sys.hp48/browse_frm/thread/9bc57d...
    > ; the main message is athttp://groups.google.com/group/comp.sys.hp48/msg/6347e4b8ccb2c203
    > If you'll look that over and it's still a problem, please reply to me
    > offline and I'll be happy to help.
    > To actually produce your graph, you need to disambiguate the root
    > (inverse-function) process. There are a total of 3 roots to the
    > problem. The branch which is positive for positive x transitions to a
    > complex one if you pass from positive real x to negative real x along
    > a path which avoids the origin. If instead you graph XROOT(3,x^5) you
    > will get what you want.
    > In other words, the CAS underpinnings of the HP50 exhibit what some
    > might call excessive pedantic fussiness about function definitions but
    > which others might applaud as deep congruence with the underlying
    > structure of the complex plane.
    > Irl- Hide quoted text -
    >
    > - Show quoted text -


    Thanks very much!

  7. Re: Newton's method

    On Mar 7, 11:50*am, Wes wrote:
    > On Feb 15, 5:30 pm, sr...@midland-7.org wrote:
    >
    > > I am an AP Calculus teacher with many successful years employing the
    > > 48G. Now using the 50G and I would like to know how to put Newton's
    > > method in the 50G. It was never a problem on the 48G, but what worked
    > > for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
    > > f'(x) and also define f(x). Enter a numeric value, press N from the
    > > var list and the calc figures out the rest, then you can iterate as
    > > desired. When I do this on the 50, all I get is infinity for the
    > > answer, which apparently means the 50 doesn't recognize f(x) or if it
    > > does, it comes up with zero for its derivative. I don't know much
    > > about global/local variables or programming.....Thanks in advance for
    > > any help.

    >
    > The problem is that the value of X is being substituted into F(X)
    > before the derivative is evaluated, which makes the derivative 0. *One
    > way around the problem is to define your Newton function as:
    >
    > << -> X << *'X-F(X)/d1F(X)' ->NUM >> >>
    >
    > -wes


    Thanks!

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