On Jul 12, 10:50 pm, "Linus Utopia" <linus_uto...@gmail.com> wrote:

"Eric Gisse" <jowr...@gmail.com> wrote in message
news:1184292390.619167.157010@x35g2000prf.googlegroups.com...

On Jul 12, 5:33 pm, "Linus Utopia" <linus_uto...@gmail.com> wrote:

How to detect turning points in curves
If you take a look at the following plot,

What condition always holds at a turning point?

Please don't say the "1st derivative=0"...

This is about numerical discrete data analysis, not the theoretical world...

In other words Linus, you either slept through calculus and partial
differential equations, or the concept of a "point of inflection" was
beyond your grasp.

You also seem to confuse what you call "discrete data analysis" with
calculus and partial differential equations, which indeed form the
basis of the mathematical abstratction that lead us to "theoretical
physics".

My friend, listen to what Eric says to you, because if you falsely
believe that the derivative is a product of "discrete data analysis",

On Jul 12, 10:50 pm, "Linus Utopia" <linus_uto...@gmail.com> wrote:

"Eric Gisse" <jowr...@gmail.com> wrote in message

news:1184292390.619167.157010@x35g2000prf.googlegroups.com...

On Jul 12, 5:33 pm, "Linus Utopia" <linus_uto...@gmail.com> wrote:

How to detect turning points in curves

Hi all,

If you take a look at the following plot,

http://img63.imageshack.us/img63/5050/gggyt1.jpg

You will agree with me that there are two turning points.

But is there a systematic way to let computer detect the turning points
automatically and programmatically?

What condition always holds at a turning point?

[...]

Please don't say the "1st derivative=0"...

This is about numerical discrete data analysis, not the theoretical world...- Hide quoted text -

- Show quoted text -

In other words Linus, you either slept through calculus and partial
differential equations, or the concept of a "point of inflection" was
beyond your grasp.

You also seem to confuse what you call "discrete data analysis" with
calculus and partial differential equations, which indeed form the
basis of the mathematical abstratction that lead us to "theoretical
physics".

My friend, listen to what Eric says to you, because if you falsely
believe that the derivative is a product of "discrete data analysis",
then you need to back and review the concepts taught in chapters 1 and
2 of your Calculus 101 course. Dust off your old copies of "Taylor" or
"Thomas", or a current text in vogue, and re-read the introductory
chapters, since you evidently missed them the first time around. Until
you've learned them, you cannot possibly grasp the concepts of
integral calculus, or how calculus is applied in a 3-dimensional
world!

Not to be sarcastic, but you really need to learn to crawl before you
try to run! :-)
If you can't read the language, it's very difficult to discern the
plot of the book!

Now it can get confusing to beginners where the point of inflection,
the turning point is, of a curve in 3-dimensions, because you must
simultaniously consider dx/dt, dy/dt, and dz/dt simultaneously, and
they may not all equal "0" at the same moment. Usually they don't.
It's sometimes hard to visualize. Unfortunately, that's the situation
in 3-dimensional space. Then to farther complicate the issue, it makes
a great deal of difference what reference frame that you chose to
employ, and sometimes that becomes a mathematically abstraction, such
as using a Hamiltonian, or other transform frame. The concept here is
that you use a referernce or transform frame that makes the soluton of
the differential equation solvable within that frame, then you map or
back-transform that solution to an x,y,z reference frame, or any other
that you can mentally visualize. The trick is finding a reference
frame of transform that renders the resulting differential equation
solvable. The following steps involve only turning a crank.

EE's tend to prefer Laplace tranforms, physicists seem to prefer
Hamiltonians and others. There are actually quite a few. My knowledge
of theoretical analysis is becoming rather dated since it is circa
1970, so Eric is a far better current source. Still, my methods help
to place man on the moon, and allow vehicles from earth to orbit
distant planets, so their is something to be said for it. Just think
about this: How many points of infelction encounted on the flight of a
space probe launched from earth with a goal of orbiting one of Mar's
moons? That is, how many times does the trajectory change slope,
direction, and velocity?

That's why you will never learn anything about physics from coffee
table books sold to the public at places like "Barnes & Noble". On a
more positive closing note, even a bricklayer or accountant has access
to real information today. Here's a secret that I will share with you
that I have with some of my close friends, including one very bright
guy and an excellent craftsman, who make his living as a professional
tile guy. Hopefully, Eric will agree with me on this --> First click
on the website of any noted science or techological university, say
Cal Tech or MIT, or whatever. Most of these websites will provide
descriptions of all of their courses, what their goal is, and the text
utilized in the course. You write the name of the text down, and go to
a bookseller like Amazon.com and search for that book. Typically
Amazon will first offer you a brand new copy of the text, but you
don't need that because likely only the problem sets have changed from
past editions (basic physics doen't change frequently). They will then
provide you with a list of "used" copies available, which are often
50% or more less expensive than the current edition. Buy one of these.
Read each chapter at least 3-times, and then work all of the problem
sets. This may on something like calculus or differential equations, 6-
months to a year, working the problems at least 3 entire evening each
week. (It like going to college, except for the partys and the
expense.) When you complete the equivalent of one course, and if you
run into dead-end questions, ask one of the more trusted and reliable
posters here for help by email (email because it avoids reponses by
the crackpots who now seem to dominate the posts on sci.physics).
Next, move on to the next subject (based on the curiculum of the
college that you are trying to tuition-free track.)

Figure about 3-5 years of study to gain a BS level education in math
or physics, but other than the cost of the textbooks, it will not have
cost you a dime.

Remember that tile guy that I mentioned? He is still laying tile for
his day living (which he is extremely good at, to minimize). He now
uses his computer to do visualizatons of protraits, and convert them
to fine mosaic tile bathroom floors at about $60,000 each. He also no
earns a consulting income from multiple local technical schools
teaching physics, although he never graduated from highschool. In
fact, he does better than me, even though I hold several college
degrees. Unfortunatly, he cannot still play the pipe organ. It's a
matter of priorities!

Take or discard this information for what you find it worth. Realize
that you are quite fortunate to live in the age of the Internet. I
provides very exceptional educational opportunities. Use it or lose
it.

Harry C.- Hide quoted text -

- Show quoted text -

EE's tend to prefer Laplace tranforms, physicists seem to prefer
Hamiltonians and others. There are actually quite a few. My knowledge
of theoretical analysis is becoming rather dated since it is circa
1970, so Eric is a far better current source. Still, my methods help
to place man on the moon, and allow vehicles from earth to orbit
distant planets, so their is something to be said for it. Just think
about this: How many points of infelction encounted on the flight of a
space probe launched from earth with a goal of orbiting one of Mar's
moons? That is, how many times does the trajectory change slope,
direction, and velocity?

Take or discard this information for what you find it worth. Realize
that you are quite fortunate to live in the age of the Internet. I
provides very exceptional educational opportunities. Use it or lose
it.

Harry C.