Preface

1. Main Problems of Mathematical Physics

Main concepts and notations

Concepts and assumptions from the theory of functions and functional analysis

Main equations and problems of mathematical physics

2. Methods of Potential Theory

Fundamentals of potential theory

Using the potential theory in classic problems of mathematical physics

Other applications of the potential method

Eigenfunction Methods

Eigenvalue problems

Special functions

3. Eigenfunction method

Eigenfunction method for problems of the theory of electromagnets phenomenon

Eigenfunction method for problems in the theory of oscillations

4. Methods of Integral Transforms

Main integral transformations

Using integral transforms in problems of oscillation theory

Using integral transforms in heat conductivity problems

Using integral transformations in the theory of neutron diffusion

Application of integral transformations to hydrodynamic problems

Using integral transforms in elasticity theory

Using integral transforms in coagulation equation

5. Methods of Discretisation of Mathematical Physics Problems

Finitedifference methods

Variational methods

Projection methods

6. Splitting Methods for applied problems of mathematical physics

7. Methods for Solving NonLinear Equations References

Continuity and differentiability of nonlinear mappings

Adjoint nonlinear operators

Convex functionals and monotonic operators

Variational method of examining nonlinear equations

Minimising sequences

The method of the steepest descent

The Ritz method

The NewtonKantorovich method

The GalerkinPetrov method for nonlinear equations

Perturbation method

Applications to some problem of mathematical physics

Index
