Fachrichtung 6.1 Mathematik

Calculus of Variations - SS 2014

• Lecture.

  1. On Wednesdays, 12-14 and on Fridays, 10-12 in HS 001 in Building E1 3, Begin: 17.04.13

  2. Lecturer: PD Dr. Daria Apushkinskaya, Building E2 4, Room 433, Tel.: 302-2956,
     

  3. Tutor: Waqar Khan

• Assignments.
  

  
  
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  Date	Assignments
  30.04.	Assignment 1
  15.05.	Assignment 2
  23.05.	Assignment 3
  10.06.	Assignment 4
  26.06.	Assignment 5
  09.07.	Assignment 6
  14.08.	Exam (Part W)

• Script.
  The script in terms of transparencies will be available for download in the table below.
  
  

  Date	Transparencies
  30.04.	Lecture 1. Introduction and Examples.
  30.04.	Lecture 2. Remarks on the Euler-Lagrange Equation.
  02.05.	Lecture 3. Undetermined End Points.
  02.05.	Lecture 4. Case of Several Variables. Examples of the Euler-Lagrange Equations. Isoperimetric Problems. Dido's Problem.
  07.05.	Lecture 5. Integrals Constraints (continued) and General Dido's Problem.
  07.05.	Lecture 5. Appendix (Worksheet 1).
  23.05.	Lecture 6. Problems with Non-Integrals Constraints.
  23.05.	Lecture 7. Newton's aerodynamical problem.
  23.05.	Lecture 8. Classification of Extrema. Necessary and Sufficient Conditions. Legendre's Condition.
  23.05.	Lecture 9. Inequality Constraints.
  04.06.	Lecture 10. Inequality Constraints (continued).Proof of the General Result.
  06.06.	Lecture 11. Broken Extremals.
  26.06.	Lecture 12. Numerical Solutions (Euler's Finite Difference Method, Ritz's Method).
  26.06.	Lecture 13. Numerical Solutions (Ritz and the Catenary).
  26.06.	Lecture 14. Numerical Solutions (Kantorovich's Method).
  27.06.	Lecture 15. Introduction into Optimal Controls Probelms. Example of Dynamic Production.
  11.07.	Lecture 16. Aerospace Example (Part 1).
  11.07.	Lecture 17. Aerospace Example (Part 2). Hamilton's Formulation.
  11.07.	Lecture 18. Pontryagin's Maximum Principle.
  14.08.	Lecture 19. Direct Methods of the Calculus of Variations.
  14.08.	Lecture 20. Variational Problems in Image Processing.
  14.08.	Lecture 21. Suitable Functional Spaces.

  
  

• News.
  Attention!!! There is no lecture on 30.05.14. Next lecture will be given on 04.06.14!!!