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: <email@example.com>
- 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