Please dont provide formulae simply. Provide the logic of origination of differential and integral calculus.
Try this, courtesy of YouTube: "Understand Calculus in 10 Minutes"
https://www.youtube.com/watch?v=WjJ-kpgps1c
These are ``scientific terms"-they refer to concepts in mathematics. There are many ways of defining them, that depend on the level of abstraction desired.
Introductory Real Analysis by Kolmogorov and Fomin is a useful reference.
Dear Rumani Dey
In a few words,
Integration of f(x) over a given domain finds areas under curves, and differentiation finds tangent lines to a given curve.
For some condition over f(x) the fundamental theorem of calculus states that if integral ∫f(x) = g(x), then the differentiation dg(x)/dx= f(x).
Ex: ∫xdx=x²/2+c, then d(x²/2+c)/dx = x.
One can find the complete information in an elementary real and mathematical analysis course. For a helpful application in calculus, see
http://wingdev.kr/zokbo/file/KAIST/Common/MAS101/thomas'%20calculus.pdf
copy and then google the above link.
Regards
Thank you Dr. Issam Kaddoura for the link , it is very helpful.
Thank you Dr. Karl Pfeifer and Dr. Stam Nicolis.
For all who still prefer TinyURL App, here is a link for the book suggested by colleague Issam Kaddoura:
https://tinyurl.com/2p8w9hjx
If you want to know more about numbers, continuums, differentiation, and integration, then dive into
Preprint Expert Hilbert space technology
A century ago scientists took more time to think than scientists do today. It was a period that many interesting facts about reality were discovered.
I have a feeling that a century ago people were subjected to fear of death by the world wars. Most inventions are due to military funding. Somehow people were accustomed to deep thinking and conscious speech which currently people lack.
I think that nationalism has killed many fruitful scientific projects. Many scientists left Europe.
Differentiation is a term used in calculus to refer to the change in, which properties experiences concerning a unit change in another related property.
Integration is a term used in calculus to refer to the formula and the procedure of calculating the area under the curve.
I suggest you to study:
Examples and Problems in Advanced Calculus: Real-Valued Functions
Book Examples and Problems in Advanced Calculus: Real-Valued Functions
Briefly, differentiation is the rate of change while integration is the accumulated sum.
Number systems own arithmetic that determines how numbers are distributed over space. A single line distributes all real numbers. Another single line or a three-dimensional space determines how spatial numbers are distributed by their arithmetic. Continuums obey the arithmetic of the underlying number system. Continuums can change. Differential calculus is the arithmetic of change.
Real number and spatial numbers mix into complex numbers and quaternions. Dynamic change of continuums can be described by complex differential calculus and by quaternionic differential calculus. In these situations, the real number part takes the role of progression.
It is best to consult the mathematicians, to give you full explanations.
Most physicists do not comprehend mathematicians because their methods differ.
Differentiation is used to study the small change of a quantity with respect to unit change of another. On the other hand, integration is used to add small and discrete data, which cannot be added singularly and representing in a single value.
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