|
Instructors: Univ.-Prof. Dr. Peter Spichtinger
Event type:
online: Lecture/practice class
Displayed in timetable as:
08.079.790
Hours per week:
4
Credits:
6,0
Language of instruction:
German
Min. | Max. participants:
- | -
Requirements / organisational issues:
The course will take place digitally, i.e. the lecture will be provided digitally, the exercises will take place via MSTeams.
Requirements:
Basic lectures from the bachelor's program in mathematics, i.e.
- Mathematics for Physicists
respectively
- Analysis & Linear Algebra
Contents:
In this lecture an overview of modeling with ordinary differential equations is given. Based on many examples from the natural sciences (physics, chemistry, biology), important approaches to modeling are presented, including the analysis of the underlying equations. Besides theory and examples, numerical methods for solving the differential equations are presented.
The following contents are treated:
- The role of models in the natural sciences (possibilities and limitations)
- Important examples from physics (cloud models), chemistry (cyclic reactions), biology (population dynamics, infection models)
- Important theorems from the theory of ordinary differential equations (existence/uniqueness)
- Analysis of dynamic systems (fixed points, limit cycles, bifurcations, stability)
- Asymptotic analysis (model reduction)
- Numerical methods for solving differential equations (finite differences, finite elements, spectral methods)
Digital teaching:
The course will take place digitally, i.e. the lecture will be provided digitally, the exercises will take place via MSTeams.
|
