When I study the properties of autonomous differential equation, they said that the solutions to the autonomous equations are monotonus functions.
I can't undestand what is monotonus function?
what about monotonic function?
what is the difference between monotonic function and monotonus function?
please explain with example
It was not needed to post this question in RG. A simple google or any standard book of mathematical physics could have given you the answer. Anyways,
A monotonic function is a function which is either entirely non-increasing or non-decreasing. A function is monotonic if its first derivative (which need not be continuous) does not change sign.
Monotonous and monotonic are same thing.
For more details, see attached links.
https://en.wikipedia.org/wiki/Monotonic_function
http://ndp.jct.ac.il/tutorials/infitut1/node14.html
I am afraid i cannot agree with Vicash.
monotonic function means increasing or decreasing function, while
monotonous means not interesting (Webster' s)
Greetings
@ Tadeusz
Not interesting implies none variation...i..e, either just increasing or just decreasing.
Monotonic functions correspond to increasing or decreasing functions. So, for each value of x, there is a unique value y (value of the function).
Monotonic function refers to increasing or decreasing function
When a function is increasing on its entire domain or decreasing on its entire domain, we say that the function is strictly monotonic, and we call it a monotonic function.
Certainly there are autonomous differential equations, whose solution is not monotonic:
x''(t) = - a * x(t).
So the possible meanings are monotonous, i.e. boring or monotone, i.e. boring again !?!
It may look like a linguistic question. Monotonous means boring, not interesting, flat. This term is not in math vocabulary.
Monotonic or monotone function (on an interval) is either nondecreasing or nonincreasing function.
Best,
Roman
Are you kidding me ? Mine was a joke! :-)
The real question was that the "solutions to the autonomous equations" can not be only "nondecreasing or nonincreasing functions". IMHO.
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