# Fremdriftsplan

**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), App. A3.2 and Chap. 9.6-9.7 | Changes of the period. Symmetries, cosine and sine series. Approximation by trigonometric polynomials, Parseval's identity. Partiell derivert og gradient. | 13, 14, 15, 16, 17 |

36 | 12.1-12.4 | Partial differential equations (PDEs). Wave equation. Separation of variables. D'Alembert's solution. | 24, 26, 27, 28, 29 |

37 | 12.5-12.6 (12.4-12.5), 11.3 | Heat equation and Laplace equation. Fourier series solution: LC-circuit (ODE) and heat equation (PDE). | 29, 30, 26, 27, 28, 31 |

38 | 11.7, 11.9, 12.7 (12.6) | Fourier transform and solution of the heat equation. Delta function. Other transforms including Laplace. | 19, 20, 21, 22, 23 |

39 | 6.1-6.6 | Laplace transform. Shift, Derivatives, Partial Fractions, Initial value problems. Convolution. | 31, 32, 2, 3, 4 |

40 | 6.1-6.6 | Laplace transform examples. Derivatives and discontinuities. Overview of all theory and methods covered so far, and plan for next weeks. | 4, 5, 6, 7, 8, 9 |

41 | 19.1-19.3,notat | Fixed point iteration, Newton's and secant method in one and several dimensions with least-squares. | 10, 33, 34 |

42 | 19.3-19.4, | Curve-fitting: Least-squares, Lagrange and Newton polynomials, Splines. slides | 35, 36, 37, 38, 39 |

43 | 19.5, 20.1-20.3 | Numerical differentiation. MC, Gauss, Trapezoidal, Simpson, adaptive, and Romberg integration. slides Numerical solution of linear equations: Gauss, LU, LL* slides | 39, 40; 41, 42 |

44 | 20.3-4, 21.1, 21.3 | Numerical solution of linear equations and fixed point iteration: Jacobi, Gauss-Seidel, and SOR method. Matrix norms.slides Runge-Kutta solution of differential equations. 3 Euler methods. The RK4 method.slides | 42,43; 44-47 |

45 | 21.6, 21.4 | Numerical solution of PDFs: heat equation slides, Laplace, and Poisson equations. Discretization, Crank-Nicholson, Liebmann, and ADI methods. | 48-51 |

46 | All above | Exam preparation: Repetition and case examples | 52-53 |

47 | Exam preparation: Repetition and case examples | 52-53 |