Dozent*in: Dr.-Ing. Ulrich Hoppe
Semesterwochenstunden: 2V + 1Ü
Leistungspunkte: 5
Studiengänge: MSc-CE, MSc-SE, BSc-MB, MSc-BI
Häufigkeit des Angebots: jedes Wintersemester
Prüfung: Schriftliche Prüfung 90 Minuten

Inhalt:

1. Vectors and operation with vectors
   • Definition
   • Addition
   • Multiplication with scalar
   • Scalar product
   • Vector product
      
2. Tensors and operations with tensors
   • Definition
   • Addition
   • Multiplication with scalar
   • Contraction
   • Product of tensors and vectors
   • Tensor product
   • Examples from continuum mechanics
      
3. Vector and tensor fields
   • Definition
   • Nabla operator
   • Divergence of vector field
   • Gradient of vector field
   • Divergence of tensor field
   • Curl of vector field
   • Gradient of tensor field
   • Examples from continuum mechanics
      
4. Integral theorems
   • Line integral
   • Gauss theorem
   • Stokes theorem
      
5. Curvilinear coordinates
   • Cylindrical coordinates
   • Spherical coordinates
   • Examples from continuum mechanics
      
6. One-dimensional variational problem
   • Functional
   • Variational problem
   • First variation
   • Necessary condition and Euler equation
   • Examples from mechanics
      
7. Extended 1-D variational problems
   • Variable end-point
   • n unknown functions
   • Functional depending on higher order derivatives
   • Variational problems with constraints
   • Examples from continuum mechanics
      
8. Sufficient conditions
   • Second variation
   • Necessary condition
   • Sufficient condition
      
9. Multi-dimensional variational problems
   • 2-dimensional variational problems
   • 3-dimensional variational problems
   • 4-dimensional variational problems
   • Examples from continuum mechanics
      
10. Direct methods in the calculus of variation
    • Rayleigh-Ritz method
    • Method of finite differences and finite elements
    • Dual variational principles
    • Variational-asymptotic method

Weitere Informationen finden Sie auf der E-Learning-Plattfrom Moodle.