Contents -- Preface -- Introduction -- 1.1. Some Examples of Equations of Mathematical Physics -- 1.2. Classification of Second-Order Partial Differential Equations -- 1.3. Formulation of Problems of Mathematical Physics -- Hyperbolic Partial Differential Equations -- 2.1. The Cauchy Problem for the Equation of the Vibrating String -- 2.2. The Mixed Problem for the Equation of the Vibrating String -- 2.3. The Goursat Problem -- 2.4. The Riemann Method -- 2.5. The Cauchy Problem for the Wave Equation -- 2.6. An Inverse Problem for the WaveEquation -- 2.7.Inverse Spectral Problems -- 2.8. Inverse Scattering on the Line -- 2.9. The Cauchy Problem for the Korteweg - De Vries Equation -- Parabolic Partial Differential Equations -- 3.1. The Mixed Problem for the Heat Equation -- 3.2. The Cauchy Problem for the Heat Equation -- Elliptic Partial Differential Equations -- 4.1. Harmonic Functions and Their Properties -- 4.2. Dirichlet and Neumann Problems -- 4.3. The Green's Function Method -- 4.4. The Method of Upper and Lower Functions -- 4.5. The Dirichlet Problem for the Poisson Equation -- 4.6. The Method of Integral Equations -- 4.7. The Variational Method -- The Cauchy-Kowalevsky Theorem -- Exercises -- 6.1. Classification of Second-Order Partial Differential Equations -- 6.2. Hyperbolic Partial Differential Equations -- 6.3. Parabolic Partial Differential Equations -- 6.4. Elliptic Partial Differential Equations -- 6.5. Answers and Hints -- References -- Index.