Introduction (solving physical problems with mathematics);

The intersection of mathematics and physics refers to some parts of physics that are studied by specific mathematical methods. The corresponding mathematical method is also called mathematical physics method.

The development of mathematics and physics has always been inseparable. Many mathematical theories are developed on the basis of physical problems; Many mathematical methods and tools are usually only applied in physics.

Mathematical theories and methods aimed at studying physical problems. It discusses the mathematical model of physical phenomena, studies the mathematical solution of physical problems established in the model, explains and foresees physical phenomena, or modifies the original model according to physical facts. The study of physical problems has always been closely related to mathematics. In Newtonian mechanics, the motions of particles and rigid bodies are described by ordinary differential equations, and solving these equations becomes an important mathematical problem in Newtonian mechanics. /kloc-since the 0/8th century, many partial differential equations have been summarized in the theory of continuum mechanics, heat transfer and electromagnetic field, which are collectively called mathematical and physical equations. At the beginning of the 20th century, the study of mathematical physics equations began to become the main content of mathematical physics. Since then, based on the needs of plasma physics, solid state physics, nonlinear optics, space technology and nuclear technology, many new partial differential equation problems have appeared, such as isolated wavelets, discontinuous solutions, bifurcation solutions and inverse problems, which further enriched the contents of mathematical and physical equations. Since the 20th century, due to the update of physics content, mathematical physics has taken on a new look. With the in-depth study of electromagnetic theory and gravitational field, people's concept of time and space has undergone fundamental changes. This makes the geometry of Minkowski space and Riemannian space become the necessary mathematical theory of Einstein's special relativity and general relativity. Global differential geometry is also needed when discussing large-scale spatio-temporal structure. The emergence of quantum mechanics and quantum field theory enriches mathematical physics. The symmetry revealed in physical objects makes group theory very useful. The crystal structure is given by several subgroups of Euclidean space motion group. Various representations of orthogonal groups and Lorentz groups play an important role in discussing many physical problems with spatio-temporal symmetry. The study of the internal symmetry of the interaction between elementary particles leads to the emergence of Young-Mills theory. This theory is based on gauge potential, which is the connection on fiber bundle studied by mathematicians. Topological invariants about fiber bundles have also begun to play a role in physics. Microscopic physical objects are often random. In classical statistical physics, it is necessary to deeply study the statistical laws of various stochastic processes. With the development of computer, many problems in mathematical physics can be solved by numerical calculation. Computational mechanics and computational physics developed from this play an increasingly important role. The development of science shows that the content of mathematical physics is getting richer and richer, and the ability to solve physical problems is getting stronger and stronger. The study of mathematical physics also greatly promotes mathematics and is the source of new ideas, new objects, new problems and new methods in mathematics.