## In short

The course starts on
**Tuesday, Jan 16, 2018. **:

The schedule for this course can be found

here

## Thematic Schedule

Date | Lecture | Protocol |

2018-01-16 | **Lecture 1** Introduction and basic concepts, e.g. normed function spaces and setting up the approximation task
| Unit01a.pdf |

2018-01-18 | **Lecture 2** Introduction (Cont.): periodic functions, trigonometric polynomials, Weierstrass and Jackson theorems
| Unit01b.pdf |

2018-01-22 | **Lecture 3** Polynomial Interpolation
| Unit02a.pdf |

2018-01-25 | **Lecture 4** Polynomial Interpolation (Cont.)
| Unit02b.pdf |

2018-01-30 | **Lecture 5** More on divided differences, best choice of interpolation points, Tschebychev polynomials
| Unit2c.pdf |

2018-02-06 | **Lecture 6** More on optimal polynomials.
| Unit2d.pdf |

2018-02-13 | **Lecture 7** Best Approximations in normed linear spaces
| Unit3a.pdf |

2018-02-15 | **Lecture 8** Best Approximation in Euclidean spaces
| Unit3b.pdf |

2018-02-20 | **Lecture 9** Direct and Dual Characterization Theorems
| Unit4a.pdf |

2018-02-22 | **Lecture 10** Approximations in Euclidean Spaces
| --- |

2018-02-27 | **Lecture 11** Construction of best approximations in Euclidean spaces, the Gramean, orthogonal polygonials
| --- |

2018-03-01 | **Lecture 12** Characterization of the best approximation in the max-norm: Tschebychev approximation
| --- |

2018-03-06 | **Lecture 13** The Remez algorithm for computing the best Tchebychev approximation
| --- |

2018-03-08 | **Lecture 14** Weierstrass approximation theorem and its proof
| --- |