*Preface*

*Academician S. L. Sobolev is a Founder of New Directions of Functional Analysis (by Yu. G. Reshetnyak)*

**Part I. Equations of Mathematical Physics**

1. Application of the Theory of Plane Waves to the Lamb Problem

2. On a New Method in the Plane Problem on Elastic Vibrations

3. On Application of a New Method to Study Elastic Vibrations in a Space with Axial Symmetry

4. On Vibrations of a Half-Plane and a Layer with Arbitrary Initial Conditions

5. On a New Method of Solving Problems about Propagation of Vibrations

6. Functionally Invariant Solutions of the Wave Equation

7. General Theory of Diffraction of Waves on Riemann Surfaces

8. The Problem of Propagation of a Plastic State

9. On a New Problem of Mathematical Physics

10. On Motion of a Symmetric Top with a Cavity Filled with Fluid

11. On a Class of Problems of Mathematical Physics

**Part II. Computational Mathematics and Cubature Formulas**

1. Schwarz’s Algorithm in Elasticity Theory

2. On Solution Uniqueness of Difference Equations of Elliptic Type

3. On One Difference Equation

4. Certain Comments on the Numeric Solutions of Integral Equations

5. Certain Modern Questions of Computational Mathematics

6. Functional Analysis and Computational Mathematics

7. Formulas of Mechanical Cubatures in *n*-Dimensional Space

8. On Interpolation of Functions of *n* Variables

9. Various Types of Convergence of Cubature and Quadrature Formulas

10. Cubature Formulas on the Sphere Invariant under Finite Groups of Rotations

11. The Number of Nodes in Cubature Formulas on the Sphere

12. Certain Questions of the Theory of Cubature Formulas

13. A Method for Calculating the Coefficients in Mechanical Cubature Formulas

14. On the Rate of Convergence of Cubature Formulas

15. Theory of Cubature Formulas

16. Convergence of Approximate Integration Formulas for Functions from L2^(*m*)

17. Evaluation of Integrals of Infinitely Differentiable Functions

18. Cubature Formulas with Regular Boundary Layer

19. A Difference Analogue of the Polyharmonic Equation

20. Optimal Mechanical Cubature Formulas with Nodes on a Regular Lattice

21. Constructing Cubature Formulas with Regular Boundary Layer

22. Convergence of Cubature Formulas on Infinitely Differentiable Functions

23. Convergence of Cubature Formulas on the Elements of L2^(*m*)

24. The Coefficients of Optimal Quadrature Formulas

25. On the Roots of Euler Polynomials

26. On the End Roots of Euler Polynomials

27. On the Asymptotics of the Roots of the Euler Polynomials

28. More on the Zeros of Euler Polynomials

29. On the Algebraic Order of Exactness of Formulas of Approximate Integration

*Index*