2 | Introduction to MATLAB (exercise sheet), ill-conditioned problems and rounding errors, floating point numbers, loss of significance (cancellation errors), Taylor series and O(h) notation. | Ch. 1.1, 1.2, 1.3, 1.4 | |

3 | Linear systems, Gaussian elimination, the necessity of row exchanges and scaled partial pivoting, analysis of the numerical complexity. | Ch. 2.1, 2.2 | |

4 | Gaussian elimination for tridiagonal linear systems, matrix factorizations: connection between LU factorization and Gaussian elimination, LDL^{T} factorization for symmetric matrices, Cholesky factorization. | Ch. 2.2, 2.3 (not pentadiagonal systems), 8.1 | |

5 | Cholesky factorization. Non-linear equations: bisection method, method of false position, fixed-point iterations. | Ch. 8.1, 3.1 | Cholesky |

6 | Fixed-point iterations for the solution of non-linear equations, a short excursion to matrix norms, Newton's method, the secant method. | Ch. 3.2, 3.3 | Fixed Points |

7 | Eigenvalues, power method (including inverse and shifted power methods), iterative solvers for linear systems (meaning: (damped) Richardson, Jacobi, Gauss-Seidel, and SOR), a short discussion on their convergence properties. | Ch. 8.2 (only first 4 pages), 8.3, 8.4 (not conjugate gradient) | |

8 | Polynomial interpolation (Lagrangian interpolation, Newton interpolation and divided differences), interpolation errors. | Ch. 4.1, 4.2 | |

9 | Minimization of interpolation errors: Chebyshev points, estimation of derivatives, Richardson extrapolation. | Ch. 4.2, 4.3 | |

10 | Numerical integration: Trapezoid rule, Romberg integration, Simpson rule. | Ch. 5.1, 5.2, 5.3 | |

11 | Numerical integration: Newton-Cotes rules, approximation errors and convergence rates, Gaussian quadrature. | Ch. 5.3, 5.4 | |

12 | Numerical integration: Gaussian quadrature & Legendre polynomials. Splines: linear splines, natural cubic splines | Ch. 5.4, 6.1, 6.2 | |

13 | Least squares, linear regression, and normal equations. Initial value problems: Euler's method. | Ch. 9.1, 9.3, 7.1 | |

14 | Initial value problems: Runge-Kutta methods, multi-step methods. | Ch. 7.2, 7.3, 7.5 | |

15 | Implicit methods and stiff ODEs. Summary and questions. | Ch. 7.5 | |