Lectures on Partial Differential Equations      V.I.Arnold

  1. The General Theory for First-Order Equation
  2. Continued
  3. Huygen's Principle in the Theory of Wave Propagation
  4. The Vibrating String(d'Alembert's Method)
  5. The Fourier Method(for the Vibrating String)
  6. The Theory of Oscillations   The Variational Principle
  7. Continued
  8. Properties of Harmonic Functions
  9. The Fundamental Solution for the Lapacian   Potentials
  10. The Double-Layer Potential
  11. Spherical Functions , Maxwell's Theorem   The Removable Singularies Theorem
  12. Boundary-Value Problems for Lapalce's Equation   Theory of Linear Equations and Systems

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  1. The Topological Content of Maxwell's Theorem on the Multifield Representation of Spherical Functions
  2. Problems