Wolfgang Ertel

Professor Dr. rer. nat.Courses of studies | Master IN, MM, EI |

Professor | Ertel, Schneider, Bou Ammar |

Requirements | Basics in mathematics, programming |

Evidence of academic achievement | 24. Sep. 16:30 - 17:30, 1. Oct. 17:00 - 17:30 (90 min.) |

This is a preparatory course for master students. The goal is
to close gaps in the required bachelor mathematics in order to
prepare the students for the lecture "Advanced mathematics for
Engineers". In 28 hours
of lectures we provide the essentials of Linear Algebra and
multidimensional Analysis and in another 28 hours these subjects
will be practiced by solving exercises.

Most of the lectures will be given through videos from the MIT open course
ware platform. This means you will be getting excellent lectures from one of
the best Professors in the world! Additionally, during the course a lecturer who
can interrupt the videos at any time to answer questions will be present.

The course takes seven days with eight hours per day. On all seven
days the first four hours, in the
morning (9:00 to 12:30), will include lectures and the second four hours, in
the afternoon (14:00 to 17:30), will be dedicated to the practical solution of
exercises and asking questions. We strongly recommend all students to
attend this preparatory course.

Day 1: |
LU-decomposition, Inverses and Transposes, Column Spaces and NullSpaces |

Day 2: |
Ax = 0 and Pivot Variables, Solving Ax = b, The Four Fundamental Subspaces |

Day 3: |
Orthogonality, Gram Schmidt technique, Determinants, Properties of Determinants |

Day 4: |
Eigenvalues and Eigenvectors, Diagonalization of Matrices |

Day 5: |
Symmetric and Positive Semi-Definite Matrices, Similar Matrices and Jordan Form, Linear Transformation |

Day 6: |
Taylor-Series, Basics of multidimensional Analysis |

Day 7: |
Multidimensional Nonlinear Optimization |

Lec # | Topics | Date |
---|---|---|

1 | The geometry of linear equations | day 1 |

2 | Factorization into A = LU | day 1 |

3 | Transposes, Permutations, Spaces R^n | day 1 |

4 | Column Space and Nullspace | day 1 |

5 | Solving Ax = 0: Pivot Variables, Special Solutions | day 2 |

6 | Solving Ax = b: Row Reduced Form R | day 2 |

7 | Independence, Basis, and Dimension | day 2 |

8 | The Four Fundamental Subspaces | day 2 |

9 | Orthogonal Vectors and Subspaces | day 3 |

10 | Projections onto subspaces | day 3 |

11 | Orthogonal Matrices and Gram-Schmidt | day 3 |

12 | Properties of Determinants | day 3 |

13 | Determinant Formulas and Cofactors | day 4 |

14 | Cramer's rule, inverse matrix, and volume | day 4 |

15 | Eigenvalues and Eigenvectors | day 4 |

16 | Diagonalization and Powers of A | day 4 |

17 | Symmetric Matrices and Positive Definiteness | day 5 |

18 | Similar Matrices and Jordan Form | day 5 |

19 | Linear Transformations and Their Matrices | day 5 |

20 | Change of basis; image compression | day 5 |

- Gilbert Strang - Introduction to Linear Algebra (978-0980232714)
- Linear Algebra Review and Reference (Zico Kolter)
- Matrix Identities (Sam Roweis)

** Solutions : **
Linear Algebra,
Analysis
Part 1