June 07, 2018 Thursday
Bedtime Story
Functional in Mathematical Analysis
Tonight we shall continue with what
Lagrange had to personally saw about geometry, as you would recall from last
night that he was dazzled with the beauty of analysis/calculus.
“I cannot say whether I will still be doing
geometry ten years from now.
It also seems to me that the mine has maybe
already become too deep and unless one finds new veins it might have to be
abandoned.
Physics and chemistry now offer a much more
glowing richness and much easier exploitation.
Also, the general taste has turned entirely
in this direction, and it is not impossible that the place of Geometry in the
Academies will someday become what the roles of Chairs of Arabic at the
universities is now.”
Can you believe that!
Comparing geometry to an obsolete Arabic
language and claiming that it has no future potential!
How wrong sometimes even the greatest can
get when it comes to foretelling the future.
Even as a Lagrange taught calculus, he was
not the ideal professor for an engineering perspective as he was less inclined
in the applications of his mathematics and his teaching tended to be more
abstract.
It is evident that he was a true
mathematician, least interested in the war applications of the subject that he
loved so much.
By about this age, perhaps when he was 18
that he started working on calculus of variations that is a branch of the wide
field of mathematical analysis that uses small changes in functions and
functionals to find their maxima and minima.
I had written quite a bit on functions in
my bedtime stories but what on earth is this strange term called ‘functional’
in mathematics?
Well, functional in mathematical analysis
is a kind of mapping where a space is transformed into real or imaginary
numbers.
In this process, some defined space is
mapped into real numbers R or sometimes complex numbers.
In some cases the input can be a function,
and then in that case the functional can be a function of function.
So if an argument x0 is mapped
into a function
x0 ↦
Here x0 is the argument that
goes into the function
Then the functional would be
f ↦
Here x0 is a parameter, meaning it
will help define that function
The beginning of this fascinating study of
mathematical analysis began in 1687 when Newton in his Principia published the
Minimum Resistance Problem.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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