This textbook provides for study the main branches of mathematical physics in the volume recommended for engineering and technical specialties of higher educational estsblishments. The authors took into consideration the great experience gained by training students of the specialty «Dynamics and Strength of Machines» at the NTU «KhPI» Department of Applied Mathematics for 40 years. The publication offers only theoretical lectural material as well as some necessary additions that help to understand the above in more depth. The solutions of some equations and the basic types of equations of classical mathematical physics are given in details. Among the solution methods, the main attention is paid to Fourier’s and D'Alembert’s methods and the method of Green's functions. Not only precision methods for solving mathematical physics problems, but also approximate ones are considered.
In particular, one of the most effective modern approximate methods based on the use of variational methods and the R-functions theory is described. This method is known as a variational-structural method or a method of R-functions (international abbreviation — RFM). In order to understand this method the R-functions theory and the POLE-RL programming system are briefly presented, that enables to solve boundary value problems of mathematical physics in a domain of complicated shape under various types of boundary conditions.
The material is presented in the way to help students to master mathematical methods and use them confidently in the future. For this purpose solutions of lots of problems are given. Every section contains theoretical material and detailed solutions of problems and sums. Almost every section is supplemented with laboratory works to check up the level of mastered material. These laboratory works are designed for individual work and contain 25 variants of tasks.
One of the features of this publication is the availability of the necessary information to use the MAPLE system as one of the known systems that increases the effectiveness of scientific research and relieves the research engineer from routine work related to computation.
The textbook can be useful for students as well as for lecturers, graduate students and researchers who face the necessity to solve partial differential equations in their practical work