Lecture plan
This is only a tentative plan and still subject to changes.
The chapter numbers refer to the 10th edition of Kreyszig (references to the 9th edition in parentheses if they are different).
The video lectures refer (approximately) to the video lecture from 2011. Note that the content of the video lecture differs slightly from mine (I did not cover complex Fourier series and the application of the Laplace transform to PDEs). Moreover I covered the topics in a different order (notably, I started with Fourier series and discussed PDEs before the Fourier transformation).
| Week | Chapter | Content | ~ Video Lecture |
|---|---|---|---|
| 34 | 11.1 | Introduction. Periodic functions, trigonometric series, Fourier series. Euler's formula. Convergence of the Fourier series. | 10, 11, 12 |
| 35 | 11.2-11.4 (11.3-11.6) | Changes of the period. Symmetries, cosine and sine series. Application: "Forced oscillations." Approximation by trigonometric polynomials, Parseval's identity. | 13, 14, 16, 17 |
| 36 | 12.1-12.3 | Partial differential equations (PDEs). Wave equation. Separation of variables. | 24, 26, 27, 28, 29 |
| 37 | 12.4, 12.6 (12.4-12.5) | D'Alembert's solution of the one-dimensional wave equation. Heat equation. Laplace equation. | 29, 30, 26, 27, 28, 31 |
| 38 | 11.7, 11.9 | Fourier transform. | 19, 20, 21, 22, 23 |
| 39 | 12.7 (12.6), 6.1-6.2 | Solution of the heat equation using the Fourier transform. Laplace transform. | 31, 32, 2, 3, 4 |
| 40 | 6.2-6.5 | Laplace transform. | 4, 5, 6, 7, 8, 9 |
| 41 | 6.6-6.7; 19.1-19.2 | Laplace transform. Fixed point iterations for the solution of non-linear equations. | 10, 33, 34 |
| 42 | 19.2-19.3 | Newton's method. Secant method. Interpolation. | |
| 43 | 19.3, 19.5 | Interpolation. Numerical | |
| 44 | 20.1-20.3 | Numerical solution of linear equations. | |
| 45 | 21.1-21.3 | Numerical solution of ordinary differential equations (ODEs). | |
| 46 | 21.4 | Numerical solution of PDEs. | |
| 47 | 21.6 | Numerical solution of PDEs. |