Information on individual educational components (ECTS-Course descriptions) per semester

Functional Analysis and Partial Differential Equations

Course unit title Functional Analysis and Partial Differential Equations
Course unit code 024613031001
Language of instruction German, English
Type of course unit (compulsory, optional) Compulsory
Teaching hours per week 30
Year of study 2026
Number of ECTS credits allocated 3
Name of lecturer(s) Thomas STEINBERGER
courseEvent.detail.semester
Degree programme Mechatronics
Subject area Engineering Technology
Type of degree Master full-time
Type of course unit (compulsory, optional) Compulsory
Course unit code 024613031001
Teaching units 30
Year of study 2026
Name of lecturer(s) Thomas STEINBERGER
Requirements and Prerequisites

Mathematical background at Bachelor level in technical studies.

Linear Algebra and Numerical Optimaziation

Course content
  • Partial Differential Equations
    • Linear Partial Differential Equations, Method of Characteristics
    • Laplace, heat conduction and wave equation
    • Boundary and initial value problems
  • Functional analytical methods
    • Hilbert space
    • Weak form 
    • Existence of solutions
    • Ritz-Galerkin method for numerical approximation
Learning outcomes

The students

  • can interpret function spaces as vector spaces.
  • are able to classify partial differential equations (PDE) (order, linearity, type)
  • can create the weak form of simple PDEs with suitable boundary or initial values.
  • understand the idea of the Ritz-Garlerkin method for numerical solution.
  • can solve simple PDEs numerically using a suitable software tool.
Planned learning activities and teaching methods

Integrated course: Besides the lectures the participants work on many exercises at home asynchronously and during the course.

Assessment methods and criteria

Oral Exam

Comment

None

Recommended or required reading
  • Evans, L. C. (2010). Partial Differential Equations (2nd ed.). AMS.
  • Burg, K., Haf, H., Wille, F., & Meister, A. (2010). Partielle Differentialgleichungen und funktionalanalytische Grundlagen (5. Aufl.). Vieweg+Teubner.
Mode of delivery (face-to-face, distance learning)

Attandance