Modellierung I
Instructors: Univ.-Prof. Dr. Michael WandShortname: 08.079.314
Course No.: 08.079.314
Course Type: Vorlesung/Übung
Requirements / organisational issues
Requirements:- Basic Mathematics: Core mathematics lectures Calculus 1, Linear Algebra 1 ("for mathematicians"), basic probability theory. Mathematics for Physisists is also well-suited.
- Good programming skills („Einführung in die Programmierung“, „Einführung in die Softwareentwicklung“, „Datenstrukturen und Algorithmen“ or equivalent).
Useful:
- Basics of computer graphics are useful, but not required (plan for a bit of extra time, in case).
- Knowledge in Python & C++ (or an alternative environment simularly suited for data analysis, numerics and visualization).
Digital teaching
The course can be offered in-person and virtually, depending on circumstances.Details will be available on the course's web page at:
https://luna.informatik.uni-mainz.de/mod1-2122/
(online at the start of the semester)
Recommended reading list
Will be announced during the lecture.Contents
The lecture discusses basic concepts of how to model real-world phenomena with a computer. The goal is to give an overview of basic mathematical and theoretical tools for modeling, and (in particular) to bring these concepts into practical implementation and application.Modeling of real-world phenomena poses a number of questions:
- Representation: Which information is constitutes the state of the modeled phenomenon?
- Rules/dynamics: How does the phenomenon evolve/behave over time / space?
- Simulation: How can we simulate it?
- Inverse problems: Can we adjust the model parameter such that the simulation explains real-world measurement data?
- Variational modeling and optimization: How can we model problems implicitly through the use of objective functions and constraints?
Bottom Line: Modeling 1 = Linear Modelling
Modelling 1 focusses on linear models (model state is a vector in a linear space). It will discuss representations and sampling issues, and show a number of practical examples (such as global illumination or dynamics of objects). For optimization and inverse problems, we consider simple quadratic variational formulations that can be solved with the nice & easy to use linear algebra tools.
Dates
Date (Day of the week) | Time | Location |
---|---|---|
10/19/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
10/19/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
10/26/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
10/26/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
11/02/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
11/02/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
11/09/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
11/09/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
11/16/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
11/16/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
11/23/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
11/23/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
11/30/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
11/30/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
12/07/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
12/07/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
12/14/2021 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
12/14/2021 (Tuesday) | 16:00 - 18:00 | Newtonraum |
01/04/2022 (Tuesday) | 16:00 - 18:00 | Newtonraum |
01/04/2022 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
01/11/2022 (Tuesday) | 16:00 - 18:00 | Newtonraum |
01/11/2022 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
01/18/2022 (Tuesday) | 16:00 - 18:00 | Newtonraum |
01/18/2022 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
01/25/2022 (Tuesday) | 16:00 - 18:00 | Newtonraum |
01/25/2022 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |
02/01/2022 (Tuesday) | 16:00 - 18:00 | Newtonraum |
02/01/2022 (Tuesday) | 16:00 - 18:00 | 01 122 Newton-Raum 2413 - Neubau Physik/Mathematik |