Wolfgang Ertel

Professor Dr. rer. nat.-
**Script (WS 16/17), latest version, now one script for IN, MM and EEM.** -
**Table of contents with marked parts not relevant for EEM students with old syllabus (before WS1617)** - Script (WS 15/16), with star-ratings for exercises.
- Script (WS 15/16) for Mechatronics and Computer Science
- Script (WS 15/16) for Electrical Engineering
- Script (WS 14/15) for Mechatronics and Computer Science
- Script (WS 14/15) for Electrical Engineering
- Script (WS 13/14)
- Script (WS 12/13)
- Script 2 (SS 12)
- Script 1 (WS 11/12)
- Script 1, latest release (PDF, extended by GNU Octave tutorial)
- Old German Script (PDF), incomplete!
- Weblinks relevant for this course (e.g. Mathematica, etc.)
- Weblinks on Random Numbers (at the end, label: "Zufallszahlen"
- Interactive Applet for Polynomial interpolation (student project, Toni Koller)
- Octave manual
- data file appraw1-15.m (Lexmed data, e.g. for PCA-exercise, Octave/Matlab format)

- Gilbert Strang - Introduction to Linear Algebra (978-0980232714)
- Linear Algebra Review and Reference (Zico Kolter)
- Matrix Identities (Sam Roweis)
- Schaum's Outline Lectures (e.g. for Calculus, Advanced Calculus, Linear Algebra, Differential Equations, Probability and Statistics, Numeriacl Analysis, ... are very good for repeating your bachelors maths by working on exercises and thus filling your gaps.

- Khan Academy offers very good videos on high school mathematics and also some undergraduate topics.
- videolectures.org offers all kinds of free academic videos.
- Youtube, Google, ...

# | Lecture Number, Part | Date | Content |
---|---|---|---|

01 | Lecture No 01 Part1 | 31.10.2011 | Computer Algebra |

02 | Lecture No 02 Part1 | 03.11.2011 | Sequences, Introduction to Mathematica |

03 | Lecture No 03 Part1 | 07.11.2011 | Introduction to Octave, Series |

04 | Lecture No 04 Part1 | 10.11.2011 | Power series, Continuity, Discontinuity |

05 | Lecture No 05 Part1 | 17.11.2011 | Continuity, Discontinuity, Taylor Series |

06 | Lecture No 06 Part1 | 21.11.2011 | Differential calculus in many variables |

07 | Lecture No 07 Part1 | 24.11.2011 | The total Differential, Extrema without / with constraints |

08 | Lecture No 08 Part1 | 01.12.2011 | Extrema, Statistics and Probability |

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

08 | Extrema, Statistics and Probability | 01.12.2011 |

09 | Discrete Distributions, Continuous Distributions | 05.12.2011 |

12 | Roots of Nonlinear Equations | 19.12.2011 |

13 | Roots of Nonlinear Equations | 22.12.2011 |

14 | Polynomial Interpolation, Spline interpolation | 09.01.2012 |

15 | Spline interpolation | 16.01.2012 |

16 | Method of Least Squares and Pseudoinverse | 19.01.2012 |

17 | Method of Least Squares and Pseudoinverse | 23.01.2012 |

18 | Method of Least Squares and Pseudoinverse | 26.01.2012 |

# | Lecture Number, Part | Date | Content |
---|---|---|---|

01 | Lecture No 01 Part1 | 04.10.2010 | Computer algebra, introduction to Mathematica |

02 | Lecture No 02 Part1 | 08.10.2010 | Mathematica introduction |

03 | Lecture No 03 Part1 | 11.10.2010 | Condition analysis, introduction |

04 | Lecture No 04 Part1 | 11.10.2010 | Gauss-Seidel Iteration for linear systems, matrix norm, condition analysis |

05 | Lecture No 05 Part1 | 18.10.2010 | Condition analysis (cont.), proof of triangle inequality for the p-norm |

06 | Lecture No 06 Part1 | 18.10.2010 | Roots of nonlinear equations, interval bisection |

07 | Lecture No 07 Part1 | 22.10.2010 | Fixed point iteration |

08 | Lecture No 08 Part1 | 25.10.2010 | Proof of the Banach fixed point theorem |

09 | Lecture No 09 Part1 | 29.10.2010 | Introduction to Matlab and convergence speed of fixed-point iteration. |

10 | Lecture No 10 Part1 | 08.11.2010 | Newton's method, polynomial interpolation. |

11 | Lecture No 11 Part1 | 08.11.2010 | Tschebychev interpolation, cubic splines. |

12 | Lecture No 12 Part1 | 12.11.2010 | Spline Interpolation, Method of Least Squares |

13 | Lecture No 13 Part1 | 15.11.2010 | Method of Least Squares and Pseudoinverse |

15 | Lecture No 15 Part1 | 22.11.2010 | Summary / Statistics and probability. |

16 | Lecture No 16 Part1 | 26.11.2010 | Solution of the midterm exam |

17 | Lecture No 17 Part1 | 29.11.2010 | Random Numbers |

18 | Lecture No 18 Part1 | 29.11.2010 | The Symmetry Test / BBS Generator |

19 | Lecture No 19 Part1 | 06.12.2010 | True Random Numbers / The Neumann Filter / Calculation of Means |

20 | Lecture No 20 Part1 | 06.12.2010 | Calculation of Means / Likelihood Function |

21 | Lecture No 21 Part1 | 13.12.2010 | Bayesian Linear Regression |

22 | Lecture No 22 Part1 | 20.12.2010 | Numerical Integration |

23 | Lecture No 23 Part1 | 20.12.2010 | Monte-Carlo-Simulation |

24 | Lecture No 24 Part1 | 10.01.2011 | Repeated Richardson Extrapolation, The Romberg Method, Nummerical Differentation |

25 | Lecture No 25 Part1 | 14.01.2011 | No description available |