Ordinary Differential Equations

Undergraduate / Graduate Course, Ruhr University Bochum, 2022

  • Lecturer: Prof. Dr. Heinzner
  • Language: German
  • Credits: 9 CP
  • Programs: B.A./B.Sc./M.Ed./M.Sc. Mathematics
  • Examination: 100 % Oral Exam (120 Minutes)

Course Description

In the simplest case, the solution of an ordinary differential equations is a differentiable curve whose derivative at each point is given by the differential equation. The areas of application of differential equations are extremely versatile. They include all natural sciences, economics, engineering, computer science, and linguistics. In all areas of pure mathematics, ordinary differential equations are used to solve a wide variety of problems. The lecture focuses on the qualitative properties of differential equations. Existence and uniqueness theorems are discussed, which, under suitable conditions, guarantee unambiguous solutions of differential equations. The following topics are included:

  • The causality principle and vector fields
  • solution approaches
  • linear vector fields and Jordan normal form
  • Vector fields and diffeomorphisms
  • existence and uniqueness of solutions
  • constants of motion
  • differential equations of higher order
  • stability of solutions