Lectures on Partial Differential Equations

Chapter 1 The General Theory for One First-Order Equation

Chapter 2 The General Theory for One First-Order Equation (Continued)

Chapter 3 Huygens’ Principle in the Theory of Wave Propagation

Chapter 4 The Vibrating String (d’Alembert’s Method)

Chapter 5 The Fourier Method (for the Vibrating String)

Chapter 6 The Theory of Oscillations. The Variational Principle

Chapter 7 The Theory of Oscillations. The Variational Principle (Continued)

Chapter 8 Properties of Harmonic Functions

Chapter 9 The Fundamental Solution for the Laplacian. Potentials

Chapter 11 Spherical Functions. Maxwell’s Theorem. The Removable Singularities Theorem

Chapter 12 Boundary-Value Problems for Laplace’s Equation. Theory of Linear Equations and Systems