Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems.
The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method.
Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied mathematics, and researchers will benefit greatly from this book.

Translation Editor's PrefaceAuthor's Prefaces to the First and Third EditionsLecture 1. Derivation of the Fundamental Equations § 1. Ostrogradski's Formula § 2. Equation for Vibrations of a String § 3. Equation for Vibrations of a Membrane § 4. Equation of Continuity for Motion of a Fluid. Laplace's Equation § 5. Equation of Heat Conduction § 6. Sound WavesLecture 2. The Formulation of Problems of Mathematical Physics. Hadamard's Example § 1. Initial Conditions and Boundary Conditions § 2. The Dependence of the Solution on the Boundary Conditions. Hadamard's ExampleLecture 3. The Classification of Linear Equations of the Second Order § 1. Linear Equations and Quadratic Forms. Canonical Form of an Equation § 2. Canonical Form of Equations in Two Independent Variables § 3. Second Canonical Form of Hyperbolic Equations in Two Independent Variables § 4. CharacteristicsLecture 4. The Equation for a Vibrating String and its Solution by d'Alembert's Method § 1. D'Alembert's Formula. Infinite String § 2. String with Two Fixed Ends § 3. Solution of the Problem for a Non-Homogeneous Equation and for More General Boundary ConditionsLecture 5. Riemann's Method § 1. The Boundary-Value Problem of the First Kind for Hyperbolic Equations § 2. Adjoint Differential Operators § 3. Riemann's Method § 4. Riemann's Function for the Adjoint Equation § 5. Some Qualitative Consequences of Riemann's FormulaLecture 6. Multiple Integrals: Lebesgue Integration § 1. Closed and Open Sets of Points § 2. Integrals of Continuous Functions on Open Sets § 3. Integrals of Continuous Functions on Bounded Closed Sets § 4. Summable Functions § 5. The Indefinite Integral of a Function of One Variable. Examples § 6. Measurable Sets. Egorov's Theorem § 7. Convergence in the Mean of Summable Functions § 8. The Lebesgue-Fubini TheoremLecture 7. Integrals Dependent on a Parameter § 1. Integrals which are Uniformly Convergent for a Given Value of Parameter § 2. The Derivative of an Improper Integral with respect to a ParameterLecture 8. The Equation of Heat Conduction § 1. Principal Solution § 2. The Solution of Cauchy's ProblemLecture 9. Laplace's Equation and Poisson's Equation § 1. The Theorem of the Maximum § 2. The Principal Solution. Green's Formula § 3. The Potential due to a Volume, to a Single Layer, and to a Double LayerLecture 10. Some General Consequences of Green's Formula § 1. The Mean-Value Theorem for a Harmonic Function § 2. Behavior of a Harmonic Function near a Singular Point § 3. Behavior of a Harmonic Function at Infinity. Inverse PointsLecture 11. Poisson's Equation in an Unbounded Medium. Newtonian PotentialLecture 12. The Solution of the Dirichlet Problem for a SphereLecture 13. The Dirichlet Problem and the Neumann Problem for a Half-SpaceLecture 14. The Wave Equation and the Retarded Potential § 1. The Characteristics of the Wave Equation § 2. Kirchhoff's Method of Solution of Cauchy's ProblemLecture 15. Properties of the Potentials of Single and Double Layers § 1. General Remarks § 2. Properties of the Potential of a Double Layer § 3. Properties of the Potential of a Single Layer § 4. Regular Normal Derivative § 5. Normal Derivative of the Potential of a Double Layer § 6. Behavior of the Potentials at InfinityLecture 16. Reduction of the Dirichlet Problem and the Neumann Problem to Integral Equations § 1. Formulation of the Problems and the Uniqueness of their Solutions § 2. The Integral Equations for the Formulated ProblemsLecture 17. Laplace's Equation and Poisson's Equation in a Plane § 1. The Principal Solution § 2. The Basic Problems § 3. The Logarithmic PotentialLecture 18. The Theory of Integral Equations § 1. General Remarks § 2. The Method of Successive Approximations § 3.