Maths and physics tutor | Mathematics:

The importance of mathematics for addressing situations in physics is presented by understanding that mathematics is the language for formulating the empirical laws of nature.

A large part of mathematics is determined by the understanding and definition of relationships between objects.  And physics is a typical example of this.

Mathematics.?

 

Maths and physics tutor: link

It is generally considered to be a relation of great intimacy, and some mathematicians have described

This science as "an essential tool for physics" refers to physics as "a rich source of inspiration".  It refers to physics as "a rich source of inspiration" as "an essential tool for science". and a rich source of physics knowledge".

Mathematics is the language of nature. which is found in the ideas of Pythagoras: and the belief that "numbers dominate the world" and that "everything is numbers".

These views were also expressed by Galileo Galilei:"The book of nature is written inm

Mathematical language".

It took a long time in the history of mankind when one came to know that mathematics is useful and important in the understanding of nature.?

Aristotle thought that the depth of nature could never be described by the abstract simplicity of mathematics.?

 

Galileo recognized and used the power of mathematics in the study of nature, which allowed his discoveries to herald the birth of modern science.

Materialists, in their study of natural phenomena, have two ways of progressing:

Method of use and observation

Method of mathematical reasoning.

Mathematics in Mechanical Scheme.?

 

The mechanical scheme treats the Universe as a whole as a dynamic system, subject to laws of motion that are essentially Newtonian.

The role of mathematics in this scheme is to represent the laws of motion by means of equations.

The key idea in this application of mathematics to physics is that equations representing the laws of motion should be simplified.

This method of simplicity is very restricted;  Fundamentally applied to the laws of motion, not to all natural phenomena in general.

 

The discovery of the theory of relativity made it necessary to revise the principle of simplicity.  Probably one of the fundamental laws of motion is the law of gravity.

Quantum Mechanics:

Quantum mechanics and pure mathematics are a vast area requiring introduction into physical theory, and the entire domain is associated with noncommutative multiplication.

One can hope in the future that the mastery of pure mathematics will be joined with fundamental advances in physics.

Static Mechanics and Dynamic Systems Ergodic Theory

A more advanced example that demonstrates the deep and fruitful relationship between physics and mathematics is that physics can develop new mathematical concepts, methods and principles.

This is demonstrated by the historical development of static mechanics and ergodic theory.

For example, the stability of the solar system was an old problem investigated by great mathematicians after the 18th century.

 

It was one of the main inspirations for the study of periodic movements in systems of bodies, and in dynamic systems in particular through Poincaré's work in celestial mechanics and Birkhoff's investigations in general dynamical systems.

Differential Equations, Complex Numbers and Quantum Mechanics

It is well known that since Newton's time, differential equations have been one of the main links between mathematics and physics, both important developments in analysis and the consistency and fruitful formulation of physical theories.

It is perhaps less well known that important concepts of functional analysis arose in the study of quantum theory.

Reference

1, Klein F, 1928/1979, The Development of Mathematics in the 19th Century, Brookline MA: Mathematics and Science Press.

2, Boniolo, Giovanni;  Budinich, Paolo;  Trobok, Mazda, ed.  (2005). The role and philosophical aspects of physics and mathematics.  Dordrecht: Springer.  ISBN 9781402031069.

3, Proceedings of the Royal Society (Edinburgh) Vol 59, 1938–39, Part II pp.  122-129.

Mehra J., 1973 "Einstein, Hilbert and the Theory of Gravity", in The Physician's Concept of Nature, J.  Mehra (eds.), Dordrecht: d.  Riedel..

4, Feynman, Richard P (1992).  "The relation of mathematics to physics".  The Law of Physical Law (reprint ed.).  London: Penguin Books.  pp.  35-58.  ISBN 978-0140175059.

Arnold, V.I., Aves, A., 1967, Problems Ergodix de la Mécanique Classic, Paris: Gauthier Villar