Equations of Mathematical Physics -- Application of the Theory of Plane Waves to the Lamb Problem -- On a New Method in the Plane Problem on Elastic Vibrations -- On Application of a New Method to Study Elastic Vibrations in a Space with Axial Symmetry -- On Vibrations of a Half-Plane and a Layer with Arbitrary Initial Conditions -- On a New Method of Solving Problems about Propagation of Vibrations -- Functionally Invariant Solutions of the Wave Equation -- General Theory of Diffraction of Waves on Riemann Surfaces -- The Problem of Propagation of a Plastic State -- On a New Problem of Mathematical Physics -- On Motion of a Symmetric Top with a Cavity Filled with Fluid -- On a Class of Problems of Mathematical Physics -- Computational Mathematics and Cubature Formulas -- Schwarz’s Algorithm in Elasticity Theory -- On Solution Uniqueness of Difference Equations of Elliptic Type -- On One Difference Equation -- Certain Comments on the Numeric Solutions of Integral Equations -- Certain Modern Questions of Computational Mathematics -- Functional Analysis and Computational Mathematics -- Formulas of Mechanical Cubatures in n-Dimensional Space -- On Interpolation of Functions of n Variables -- Various Types of Convergence of Cubature and Quadrature Formulas -- Cubature Formulas on the Sphere Invariant under Finite Groups of Rotations -- The Number of Nodes in Cubature Formulas on the Sphere -- Certain Questions of the Theory of Cubature Formulas -- A Method for Calculating the Coefficients in Mechanical Cubature Formulas -- On the Rate of Convergence of Cubature Formulas -- Theory of Cubature Formulas -- Convergence of Approximate Integration Formulas for Functions from L 2 (m) -- Evaluation of Integrals of Infinitely Differentiable Functions -- Cubature Formulas with Regular Boundary Layer -- A Difference Analogue of the Polyharmonic Equation -- Optimal Mechanical Cubature Formulas with Nodes on a Regular Lattice -- Constructing Cubature Formulas with Regular Boundary Layer -- Convergence of Cubature Formulas on Infinitely Differentiable Functions -- Convergence of Cubature Formulas on the Elements of -- The Coefficients of Optimal Quadrature Formulas -- On the Roots of Euler Polynomials -- On the End Roots of Euler Polynomials -- On the Asymptotics of the Roots of the Euler Polynomials -- More on the Zeros of Euler Polynomials -- On the Algebraic Order of Exactness of Formulas of Approximate Integration.

S.L. Sobolev (1908–1989) was a great mathematician of the twentieth century. His selected works included in this volume laid the foundations for intensive development of the modern theory of partial differential equations and equations of mathematical physics, and they were a gold mine for new directions of functional analysis and computational mathematics. The topics covered in this volume include Sobolev’s fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because they were published in journals that are difficult to access. Audience This book is intended for mathematicians, especially those interested in mechanics and physics, and graduate and postgraduate students in mathematics and physics departments.