Worked-examples application in the teaching of functional analysis;

Application and research on functional analysis course;

A dynamic test of simple-supported-beam suffered from a number of crack damage scenarios is carried out to find out local crack damage location by functional analysis and function extremum theorem.

A functional analysis method to determine the position of a crack is proposed.

Since the concept of locally fine point, which is the generalized regular point, was introduced, many problems in nonlinear functional analysis have been solved, such as the conjugacy problem, the rank theorem in advanced calculus and so on.

In this paper some new advances in nonlinear functional analysis obtained by our research group are summarized.

In the present paper,on the basis of functional analytic methods,we first analyse the boundary value problems (BVP) of linear singular systems (LSS),several properties of LSS given.

The paper studies the finite difference schemes of a class of generalized highorder nonlinear wave equations with homogenerous boundary conditions, the convergence of finite difference schemes is verified by discrete functional analysis methods and prior estimation techniques.