Module MA3400-KP05

Duration

1 Semester

Turnus of offer

each winter semester

Credit points

5

Course of studies, specific fields and terms:

• Bachelor CLS 2023, compulsory, mathematics
• Bachelor Computer Science 2019, optional subject, Extended optional subjects
• Bachelor Computer Science 2019, compulsory, Canonical Specialization Bioinformatics and Systems Biology
• Bachelor Medical Informatics 2019, optional subject, medical computer science
• Master MLS 2018, optional subject, interdisciplinary competence
• Bachelor Computer Science 2016, optional subject, advanced curriculum
• Bachelor Computer Science 2016, compulsory, Canonical Specialization Bioinformatics
• Master MLS 2016, optional subject, mathematics / computer science
• Bachelor CLS 2016, compulsory, mathematics
• Bachelor Biophysics 2016, compulsory, mathematics

Classes and lectures:

• Biomathematics (exercise, 2 SWS)
• Biomathematics (lecture, 2 SWS)

Workload:

• 20 hours exam preparation
• 60 hours in-classroom work
• 70 hours private studies and exercises

Contents of teaching:

• Examples and elementary solution methods for ordinary differential equations
• Existence and uniqueness theorems
• Dependence of solutions on initial conditions
• Linear systems (in particular with constant coefficients)
• Higher-Order linear differential equations
• Qualitative theory of nonlinear systems

Qualification-goals/Competencies:

• Students are able to explain basic notions from the theory of ordinary differential equations.
• Students can explain bad phenomena of solutions of differential equations using examples.
• Students can specify conditions under which good phenomena of solutions are guaranteed by applying theorems from the theory of ordinary differential equations.
• Students are able to find explicit solutions of simple differential equations.
• Students are able to explain how solutions of differential equations can be analysed qualitatively.
• Students are able to present important models of the natural sciences which can be analysed by differential equations.

Grading through:

• written exam

Requires:

• Linear Algebra and Discrete Structures 2 (MA1500-KP08, MA1500)
• Linear Algebra and Discrete Structures 1 (MA1000-KP08, MA1000)
• Analysis 2 (MA2500-KP04, MA2500)
• Analysis 1 (MA2000-KP08, MA2000)

Responsible for this module:

• PD Dr. rer. nat. Christian Bey

Teacher:

• Institute for Mathematics
• PD Dr. rer. nat. Christian Bey

Literature:

• G. Birkhoff, G.-C. Rota : Ordinary Differential Equations
• H. Heuser : Gewöhnliche Differentialgleichungen Teubner Verlag 2009 (6. Auflage)
• M.W. Hirsch, S. Smale : Differential Equations, Dynamical Systems, and Linear Algebra
• J. D. Murray : Mathematical Biology Springer
• J. Scheurle : Gewöhnliche Differentialgleichungen
• R. Schuster : Biomathematik Vieweg + Teubner Studienbücher 2009
• W. Walter : Gewöhnliche Differentialgleichungen

Language:

• offered only in German

Notes:

Last Updated:

22.02.2022