Author | Arnold, Vladimir I. author |
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Title | Lectures on Partial Differential Equations [electronic resource] / by Vladimir I. Arnold |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-662-05441-3 |
Descript | X, 162 p. online resource |
1. The General Theory for One First-Order Equation -- 2. The General Theory for One First-Order Equation (Continued) -- 3. Huygensโ Principle in the Theory of Wave Propagation -- 4. The Vibrating String (dโAlembertโs Method) -- 5. The Fourier Method (for the Vibrating String) -- 6. The Theory of Oscillations. The Variational Principle -- 7. The Theory of Oscillations. The Variational Principle (Continued) -- 8. Properties of Harmonic Functions -- 9. The Fundamental Solution for the Laplacian. Potentials -- 10. The Double-Layer Potential -- 11. Spherical Functions. Maxwellโs Theorem. The Removable Singularities Theorem -- 12. Boundary-Value Problems for Laplaceโs Equation. Theory of Linear Equations and Systems -- A. The Topological Content of Maxwellโs 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.6. The History of Maxwellโs Theorem -- Literature -- B. Problems -- B.1. Material from the Seminars -- B.2. Written Examination Problems