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Mathematical Physics


Basic concept of mathematical physics:

In this chapter we will demonstrate the various aspects Of the importance of mathematics in the elaboration of knowledge In Physics; Use dimensional analysis to evaluate the functional dependencies between The greatness; Discuss issues of similarity and scale in Physical phenomena; Estimate the order of magnitude Present in our daily experience and to evaluate The error in experimental measurements and calculate its Propagation in the calculation of derived quantities.

The opening sentence of this chapter was dictated by one of the greatest Physicists of the twentieth century, Richard Phillips Feynman. There is a bit of In this statement, after all, the main purpose of physics is The full understanding of natural phenomena, but certainly the Ability of a physical theory to provide a numerical result Which can be verified experimentally, is an evaluation criterion Used to check whether the theory is correct or not. A physical theory is a purely intellectual construction, which obviously takes into account the natural phenomena previously observed, aiming not only to explain what is already known, But also to provide elements that guide us to phenomena not yet observed.

As an intellectual construction, physical theories require language Adequate to allow its development and transmission properly. The mathematical language has been shown the most suitable for the purpose of the elaboration of physical theories. Richard Phillips Feynman, Physical North American, Was born in 1918 in New York. Doctor in Physics from MIT (Massachusetts Institute of Technology). He participated, during the second war World, Project Manhattan, which Produced for the United States of America, First atomic bomb. Won the Prize Nobel for his work in quantum theory of Fields, developing The electrodynamics Quantum theory, which The electromagnetism of Maxwell with the mechanics Quantum theory. She was active in Physical community to the Death in 1988 due to A cancer.

This "discovery", while it seems to us so obvious, is reasonably History of human civilization. Although we have the use of mathematical language for the treatment of some physical problems in antiquity, for example, in some Works of Archimedes, we can mark the beginning of the Modern theory of physical theories with mathematical language from the works of Galileo and Isaac Newton.

The first and most basic use of mathematical language in physics is the numerical treatment of physical quantities. In describing Natural phenomena, we must deal with certain quantities, Such as length, time, speed, temperature, electric charge, Etc., will characterize the state of the analyzed system. When we perform an experiment, we will have a sequence of numbers, which will correspond to the numerical values ??of Evaluated in the system. It is through behavior and the variation of these various numbers, as well as the interrelation among them, that we can infer general laws about the operation of a particular physical system. Once these laws, known as empirical laws, have been established, we can Use them to predict the behavior of quantities even in situations not yet tested by experiments.

With the help of more sophisticated mathematical tools, we can still mix these empirical laws and derive new laws that should operate purely on the basis of experimental evidence and rules of mathematical reasoning. Finally, we can also elaborate a more general theoretical framework, from of first principles that allow us to infer all empirical laws Known within a given context, from the Pure and simple manipulation of mathematical objects with nature totally abstract. An example of physical theory is Newton's theory of gravitation, which, within a single context, allows us to derive all the laws concerning the fall of bodies, but also to obtain precisely the laws of Kepler on the movement of the planets.

Importance of mathematical physic:

 Physics is one of the natural sciences that has contributed most to the development and well-being of man, because thanks to his study and research it has been possible to find in many cases a clear and useful explanation to the phenomena that appear in our daily life. The word physical comes from the Greek word physique whose meaning is nature. It is the Science that is in charge of studying natural phenomena, in which there are no changes in the composition of matter.

Physics has undergone a great development thanks to the efforts of notable scientists and researchers who, by inventing and perfecting instruments, apparatus and equipment, have made man sharpen his senses by detecting, observing and analyzing phenomena.

When the philosophy of the Greeks was born, physics was born properly. The word philosophy (from Greek Phil's lover and Sophia wisdom) means love of wisdom, this term was applied for the first time to the activity of certain Greek thinkers, who in the sixth century BC, reflected on natural phenomena, origin and Nature of life, beings and things.

Philosophy is born in Ionia on the coast of Asia Minor, and it is Miletus, Ephesus and Samos, some of the villages where we find the first thinkers, with their philosophy, called philosophy of nature or philosophy of physics, since physical means nature. In this philosophy of nature, the observation of nature, bodies and being occupied the forefront of studies, although they also think of the spirit and of being as a whole. Among the first naturalistic philosophers are Thales of Miletus, Anaximander and Anaximenes. By this same period they appear Leucippus and Demócrito, who expose the Atomist Theory, according to which the matter is formed of small particles called atoms.

In century IV AC Appears Aristotle who begins to study the fall of the bodies. In the second century of our era appears Ptolemy who studies the reflection of light. From this period, physics advances slowly through hundreds of years. Almost 1,500 years later Galileo appears that studies the movement of the pendulum and reaffirms the Heliocentric Planetary Theory along with Nicholas Copernicus.

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