# Lecture plan

**This is only a tentative plan which will be updated continuously.**

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 order in which the different topics were discussed in 2011 differs from my lecture. Also, there will probably be small differences in content. That is, it is possible that some of the topics discussed in 2011 will not be part of this year's lecture and *vice versa*. Be aware of these differences in particular when preparing for the exam!

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; 19.1-19.2 | Laplace transform. Fixed point iterations for the solution of non-linear equations. Newton's method in one dimension. | 10, 33, 34 |

42 | 19.2-19.3, Notes | Convergence order. Secant method. Newton's method in higher dimensions. Interpolation. | 35, 36, 37 |

43 | 19.3, 19.5 | Numerical integration. Numerical solution of linear equations: Gauss elimination and Gauss elimination with partial pivoting. | 37, 38, 39, 40, 41 |

44 | 20.1-20.3 | Numerical solution of linear equations: Matrix decompositions, Jacobi method, Gauss-Seidel method. Numerical solution of ordinary differential equations (ODEs): explicit Euler method. | 41, 42, 43, 44, 45 |

45 | 21.1, 21.3, 21.4 | Numerical solution of ODEs: convergence order, RK methods, systems and higher order equations. Numerical solution of PDEs. | 44, 45, 46, 47, 48 |

46 | 21.4, 21.6 | Numerical solution of PDEs. | 48, 49, 50, 51 |

47 | Repetition |