       Re: Definition needed !

• To: mathgroup at smc.vnet.net
• Subject: [mg33120] Re: Definition needed !
• From: bghiggins at ucdavis.edu (Brian Higgins)
• Date: Sun, 3 Mar 2002 17:15:24 -0500 (EST)
• References: <a5t22h\$65h\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Max,

In Calculus a stationary point  or critical point  of a function is
values of the indpendent variables for which the first derivatives of
the function both exist  and vanish. Clearly a stationary point can be
a maximum, minimum or saddle point.

Qualitatively, a turning point occurs when a solution curve turns back
on itself as a parameter is varied. For example, the solution defined
by f(y,h)=y^2-h has a turning point at y=0,h=0. There is no real
solution for h<0 and two solutions for h>0. Turning points are
discussed in detail in bifurction theory. You can find a precise
mathematical description of a turning point in books on bifurcation
theory. e.g. Seydel's book  "From Equilibrium to Chaos: Practical
Bifurcation and Stability Analysis"  has a very readible account of
these matters.

Cheers,

Brian

"max" <dpmbsn at hotmail.com> wrote in message news:<a5t22h\$65h\$1 at smc.vnet.net>...
> I'm after a little clarification/support on a definition. The concern stems
> from certain sources using the terminlogy 'stationary point' and 'Turning
> point' as having the same meaning.
> My stance is that Stationary points can be Max, Min or Inflexion, whereas
> Turning points can only be used for Max or Min points.
> Your views will be welcomed
>
>
> Max

```

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