Higher mathematics for physics and technology: mathematical methods of modern physics
Academy of Fundamental Medicine and Biology
The publication is intended for students, graduate students, teachers, researchers and individuals involved in self-education in the field of applied mathematics and physics. It outlines fundamental mathematical theories related to solving problems in semiconductor physics, molecular and atomic physics, solid state physics, condensed matter physics, nanotechnology, gas-tight films and materials.
The manual includes the general theory of equations of state and heat conduction, the hydrodynamic theory of gases and solutions, the theory of electrical and magnetic phenomena, the theory of the gravitational field, the mathematical theory of elasticity, the theory of stability, the theory of plasticity, the mechanics of a deformable solid and viscous body, the theory of thermal melting of metals and alloys, mathematical modeling in natural sciences and in technical calculations, methods for solving large systems of equations, geometric modeling.
Particular attention is paid to the applications of the theory of equations in the field of technical problems: their numerical solution in problems of dynamics, astronomy, climatology, physical chemistry, etc.
The book is intended for students of technical universities, engineers and scientists, and may also be useful for all those interested in mathematics and physics.
4th edition, revised
Series: Academy of Fundamental Medicine and Biology + PHYSICS
Annotation to the book:
The publication provides an overview of the main sections of mathematics and natural sciences dealing with the solution of problems in mechanics and physics and the solution of which is associated with research based on the use of the symplectic theory of manifolds and differential forms of equations. It is shown that the problems of mechanics and physics are also used in solving other problems. The presentation was not only conducted in chronological order, but all issues, including the most important ones, were considered from the particular to the general. The content of the presentations does not claim to be an exhaustive coverage of the material, and inaccuracies may be found in it.
The book discusses not only general issues that arise when solving differential equations and equations of mathematical physics, but also some particular issues that are especially important for solving problems in which it is necessary to ensure the reliability of the results obtained.