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| Preface to the Second Russian Edition 1.The General Theory for One First-Order Equation. Literature 2.The General Theory for One First-Order Equation（Continued） Literature 3.Huygens’Principle in the Theory of Wave Propagation. 4.The Vibrating String（d’Alembert’S Method） 4.1.The General Solution 4.2.Boundary—Value Problems and the Cauchy Problem 4.3.The Cauchy Problem for an Infinite String.d’Alembert’S Formula 4.4.The Semi—Infinite String 4.5.The Finite String.Resonance 4.6.The Fclurier Method 5.The Fourier Method（for the Vibrating String） 5.1.Solution of the Problem in the Space of Trigonometric Polynomials. 5.2.A Digression 5.3.F0rmulas for Solving the Problem of Section 5.4.The General C8.se 5.5.Fourier Series 5.6.Convergence of Fourier Series 5.7.Gibbs’Phenomenon 6.The Theory of Oscillations.The Vlariational Principle Literature 7.The Theory of Oscillations.The Variational Principle （Continued） 8.Properties of Harmonic Functions 8.1.Consequences of the Mean—Value Theorem 8.2.The Mean.VaJue Theorem in the MultidimensionaI Case 9.The Fundamental Solution for the Laplacian.Potentials 9.1.Examples and Properties. 9.2.A Digression.The Principle of Superposition 9.3.Appendix.An Estimate of the Single—Layer Potential 10.The Double-Layer Potential. 10.1.Properties of the Double—Layer Potential、 11.Spherical Functions.Maxwell’S Theorem.The Removable Singularities Theorem. 12.Boundary—Value Problems for Laplace’S Equation.Theory of Linear Equations and Systems 12.1.F0ur Boundary—Value Problems for Laplace’S Equation. 12.2.Existence and Uniqueness of Solutions 12.3.Linear Partial Differential Equations and Their Symbols A.The Topological Content of Maxwell’S Theorem on the Multifield Representation of Spherical Functions A.1.The Basic Spaces and Groups A.2.Some Theorems of Real Algebraic Geometry A.3.From Algebraic Geometry to Spherical Functions A.4.Explicit Formulas. A.5.Maxwell’S Theorem and CP2/conj≈S4 A.6.The History of Maxwell’S Theorem Literature B.Problems B.1.Material from the Sereinars B.2.Written Examination Problems |
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