Course description

Purpose  The main idea is the acquaintance with additional concepts and methods of functional  analysis for successful decision of numerical mathematics typical problems.

Short description   The course includes the series of lectures and practical studies specified of some tasks realization by students. The main subjects of study are functional analysis principal concepts, associated with Lebesque and Sobolev spaces, generalized functions, embedding theorems, and their application for approximate schemes construction and analysis, typical ill-posed problems solution, the best approximation construction in various functional spaces.

Representation  In the process of  functional analysis study students become familiar not only with abstract concepts of spaces and linear operators. As a result of given course study every student must well interpret various functional spaces characteristics and motivation of their application in the process of mathematical problems statement, investigation and solution.

As a result students must

• know: special applications of various functional spaces, formulation of mathematical problems in the operator equations form, testing of lasts correctness;
• be master of: various methods for integral equations investigation and numerical solution, the best approximation construction in various functional spaces.