THE DEVELOPMENT OF STUDENTS APPLIED MATHEMATICAL THINKING IN TEACHING INVERSE AND ILL-POSED PROBLEMS

Abstract

In the article the author draws the reader’s attention to the fact that, while mastering the process of learning the theory and methodology of inverse and ill-posed problems, students not only form the fundamental knowledge in the field of inverse and ill-posed problems, applied and computational mathematics, mathematical modeling of processes and phenomena, but also develop one of the most important component of mathematical ability creative and applied mathematical thinking.It is emphasized that the search for solutions to inverse and ill-posed problems, students acquire profound knowledge in such scientific fields as seismology, gravimetry, magnetometry, Geophysics, astrophysics, imaging, electrodynamics, atmospheric optics, quantum scattering theory and other scientific fields. When teaching inverse and ill-posed problems, students also learn the mathematical methods, which are not included in the content of traditional mathematics applied and computational mathematics, and can only be purchased in the teaching of special courses. Among them, spectral analysis, the method of Volterra operator equations, Sobolev method, method of scales of Banach spaces of analytic functions, the method of integral geometry, the method of tensor analysis, methods of computational mathematics and other mathematical methods.

Keywords

• обучение обратным и некорректным задачам
• прикладное математическое мышление
• прикладная математика
• вычислительная математика
• студент