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Re: Definition needed !

  • To: mathgroup at
  • Subject: [mg33120] Re: Definition needed !
  • From: bghiggins at (Brian Higgins)
  • Date: Sun, 3 Mar 2002 17:15:24 -0500 (EST)
  • References: <a5t22h$65h$>
  • Sender: owner-wri-mathgroup at


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.



"max" <dpmbsn at> wrote in message news:<a5t22h$65h$1 at>...
> 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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