- #1
koustav
- 29
- 4
in a certain problem it was written Δθ=∂θ/∂x*Δx + ∂θ/∂y*Δy + ∂θ/∂z*Δz + infinitesimals of order higher than Δx,Δy and Δz.can anyone tell me what is "infinitesimals of order higher than Δx,Δy and Δz?"
Infinitesimals of order higher refer to quantities that are infinitely smaller than any nonzero real number but are still nonzero. These quantities are used in mathematical analysis and calculus to represent the behavior of functions at a specific point.
The main difference between infinitesimals of order higher and regular infinitesimals is that the former are considered to be nonzero whereas the latter are considered to be equal to zero. This distinction allows for more accurate calculations and better understanding of mathematical concepts.
Infinitesimals of order higher play a crucial role in the development of calculus and other mathematical theories. They allow for the precise definition of concepts such as limits, derivatives, and integrals, which are essential for solving complex mathematical problems.
Yes, infinitesimals of order higher are also used in physics, particularly in quantum mechanics, to model the behavior of particles at a subatomic level. They are also used in economics to describe the behavior of markets and in other fields to study complex systems and phenomena.
There has been some controversy surrounding the use of infinitesimals of order higher in mathematics, particularly in the 17th and 18th centuries. However, with the development of rigorous mathematical theories and the introduction of non-standard analysis, the use of infinitesimals of order higher has become widely accepted among mathematicians and scientists.