| 1. | 26. September (PDF) | Wave equation and its derivation. Separation of variables. |
| 2. | 3. Oktober (PDF) | Superposition principle. Wave equation. Fourier series and Fourier theorem. |
| 3. | 10. Oktober (PDF) | Heat equation. Nonzero boundary conditions and adiabatic conditions. |
| 4. | 17. Oktober (PDF) | Heat equation on an infinite bar. Heat equation on a solid ball. |
| 5. | 24. Oktober (PDF) | 2D and 3D equations. Double Fourier series and Fourier transform. |
| 6. | 31. Oktober (PDF) | Classification of second order PDEs. Types of boundary conditions. Laplace's equation. Sturm-Liouville problems. |
| 7. | 7. November (PDF) | Laplace's equation in polar coordinates and in cylindrical coordinates. Bessel equations and Bessel functions. |
| 8. | 14. November (PDF) | Laplace's equation in spherical coordinates. Spherical harmonics. Legendre equations and Legendre polynomials. |
| 9. | 21. November (PDF) | Application of complex analysis to Laplace's equation in 2D. Equipotential lines and lines of force. Conformal mapping. |
| 10. | 28. November (PDF) | Maximum principle for harmonic functions. Poisson's integral formula. |
| 11. | 5. December (PDF) | Integral representations. Definition of Green's functions. Distributions. Dirac delta. |
| 12. | 12. December (PDF) | Derivative of a distribution. Fundamental solutions. Use of Green's functions. Reflection principle. |
| 13. | 19. December (PDF) | Poisson's kernel vs. Green's function on a disk. Neumann problem for the Poisson equation. Neumann's functions. |