# Schedule

**This schedule is not yet final. Changes will be made during the semester. At the end of the course this page will constitute the curriculum of TMA4215.**

CK = Cheney and Kincaid, Numerical Analysis

N = Notes

Week | Date | CK | N | Subject | Links |
---|---|---|---|---|---|

34 | 26.08, 27.08 | Ch. 1 Ch. 2 Ch. 4.4 | Background. Floatingpoint numbers, rounding errors, stability of problems and algorithms. Condition numbers. | Floating point numbers. Interval arithmetic. Computer assisted proofs. Taylor's theorem. Big O notation. | |

35 | 02.09, 03.09 | Ch.1.1 and 1.2 Ch. 4.4. Ch. 3.0, 3.1, 3.2, 3.3 | Taylor's theorem and Big O notation. Condition number for linear systems. Numerical solution of nonlinear equations. | Cramer's rule. | |

36 | 09.09, 10.09 | Ch. 3.4, 4.0 4.1. | Nonlinear systems of equations. | Note about nonlinear equations. You should read ch 4.0, 4.1 on your own. | |

37 | 16.09, 17.09 | Ch. 4.2, 4.3, 4.5, 5.2. | LU- Cholesky and other factorizations. The Neumann series. In 5.2 only Gershgoring's theorem. | Note on linear algebra with some examples (with small matrices). | |

38 | 23.09, 24.09 | Ch. 6.1 | Interpolation. Lagrange interpolation polynomial. Chebishev points and optimality of the interpolation error. | ||

39 | 30.09, 01.10 | Supervision of the first project. | |||

40 | 07.10, 08.10 | Ch. 6.2. | Divided differences and Newton form of the interpolation polynomial. | Matlab codes interpolation.m and lk.m. Can be used for comparison of interpolation on equidistant and Chebyshev nodes. | |

41 | 14.10, 15.10 | Ch. 6.3, 6.4 (theorem 1 included), 7.1. | Hermite interpolation, splines, numerical differentiation. | der.pdf Error in the numerical approximation of the derivative of cos(x) for x=3,(-sin(3)=-0.14112000805987), by difference approximations (Taylor theorem) and for smaller and smaller values of h. When h is too small the rounding error starts propagating. | |

42 | 21.10, 22.10 | Ch. 7.1, 7.2, 7.4 | Numerical differentiation, quadrature, Romberg algorithm. | Note on Euler-Mclaurin formula and Bernoulli polynomials. | |

43 | 28.10, 29.10 | Ch. 7.3, 7.5, 8 | Gauss quadrature and Adaptive quadrature. | Note on orthogonal polynomials. Note on odes, introduction. | |

44 | 04.11, 05.11 | Ch. | odes | Note on odes, Euler method, convergence. Runge-Kutta methods. Implementation of explicit and implicit Euler. Checking the order of a method. | |

45 | 11.11, 12.11 | Ch. | odes | RK-methods order conditions. Supervision of the second project. | |

46 | 18.11, 19.11 | Ch. | odes | RK-methods step-size selection and linear stability. Linear multi-step methods. | |

47 | 25.11, 26.11 | Ch. | odes |