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[ 281MANAMA3U20 ] UE Mathematics 3
Versionsauswahl
(*) Unfortunately this information is not available in english.
Workload Education level Study areas Responsible person Hours per week Coordinating university
1,5 ECTS B2 - Bachelor's programme 2. year Mathematics Markus Passenbrunner 1 hpw Johannes Kepler University Linz
Detailed information
Original study plan Bachelor's programme Mechatronics 2025W
Learning Outcomes
Competences
Students know the types of ordinary and partial differential equations and can apply various solution strategies to them. Furthermore, they understand the significance of ordinary and partial differential equations in natural sciences and are able to apply numerical methods for solving ordinary differential equations.
Skills Knowledge
  • Classify ordinary differential equations (ODEs) (k3)
  • Geometric interpretation of solutions of ODEs (k4)
  • Apply criteria for the existence and uniqueness of initial value problems (k3)
  • Apply elementary explicit solution methods to ODEs (k3)
  • Perform error estimates for solutions of ODEs in terms of initial values (k4)
  • Determine fundamental matrices of systems of linear ODEs (k4)
  • Explicitly solve systems of linear ODEs with constant coefficients (k3)
  • Explicitly solve linear ODEs with constant coefficients (k3)
  • Draw phase portraits of autonomous ODEs (k4)
  • Apply the Laplace transformation to solve ODEs (k3)
  • Solve elementary boundary or eigenvalue problems (k3)
  • Analyze the long-term stability of solutions of ODEs (k4)
  • Apply various numerical methods (explicit and implicit single and multistep methods) to approximate solutions of ODEs (k6)
  • Classify partial differential equations (k3)
  • Apply the method of separation of variables to elementary partial differential equations (k3)
  • Ordinary differential equations
  • systems of differential equations
  • examples from the natural sciences
  • separable differential equations
  • Peano's theorem
  • Picard-Lindelöf theorem
  • successive approximation
  • generalized eigenvectors of matrices
  • phase portraits
  • Laplace transformation
  • eigenvalue problems
  • Lyapunov function
  • explicit and implicit single and multistep methods
  • method of separation of variables for partial differential equations
  • maximum principle for partial differential equations
Criteria for evaluation exercises and written exam
Methods students present the exercises, discussion
Language German
Changing subject? No
Further information none
Corresponding lecture (*)MEBPAUEMAT3: UE Mathematik 3 (1,25 ECTS)
On-site course
Maximum number of participants 35
Assignment procedure Assignment according to sequence