Universität des Saarlandes
FR Mathematik
Arbeitsgruppe Prof. S. Rjasanow

Institut für angewandte Mathematik

Calculus of Variations


Attention! There is no lecture on 12.07.16. Next lecture will be given on 15.07.16.

  1. On Tuesdays and Fridays, 8-10 in HS003, Building E1.3, Begin 26.04.16.
  2. Lecturer: PD Dr. Darya Apushkinskaya ,
    Office hours: Tuesdays 10:15-11:00 or by appointment (during semester break only by appointment)
  3. Tutor: Jón Arnar Tómasson jonarnar90@gmail.com
Target Group

The course is suitable for students specialising in applied mathematics, physics, computer science, visual computing, bioinformatics. The course language is English.

Date Assignments Due Date
14.06.16cv16-blatt4.pdf 21.06.16
29.06.16 cv16-blatt5.pdf05.07.16
26.07.16 cv-16-exam_w_.pdf30.09.16

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

Date Topic Transparencies
26.04.2016 Lecture 1. Introduction and Examples. Euler-Lagrange Equation.cv-16-lecture-1.pdf
29.04.2016 Lecture 2. Remarks on the Euler-Lagrange Equation. cv-16-lecture-2.pdf
03.05.2016Lecture 3. Remarks on the Euler-Lagrange Equation (cont.). Undetermined End Points. cv-16-lecture-3.pdf
06.05.2016Lecture 4. Case of Several Variables. Examples of the Euler-Lagrange Equations. cv-16-lecture-4.pdf
10.05.2016Lecture 5. Isoperimetric Problems. Dido's Problem.cv-16-lecture-5.pdf
17.05.2016Lecture 6. Catenary Problem and General Dido's Problem. cv-16-lecture-6.pdf
17.05.2016 Lecture 6. Appendix (Worksheet 1).cv16-l6-worksheet1.pdf
20.05.2016 Lecture 7. Problems with Non-Integral Constraints. cv-16-lecture-7.pdf
31.05.2016 Lecture 8. Newton's Aerodynamic Problem.cv-16-lecture-8.pdf
03.06.2016 Lecture 9. Classification of Extrema. Necessary and Sufficient Conditions. Legendre's Condition.cv-16-lecture-9.pdf
07.06.2016 Lecture 10. Inequality Constraints. Proof of the General Result. cv-16-lecture-10.pdf
14.06.2016 Lecture 11. Proof of General Result (cont.). Broken Extremals. cv-16-lecture-11.pdf
17.06.2016 Lecture 12. Numerical Solutions (Euler's Finite Difference Method. Ritz's Method).cv-16-lecture-12.pdf
21.06.2016 Lecture 13. Numerical Solutions (Ritz and Catenary, Kantorovich's Method). Introduction into Optimal Control Problems. Example of Dynamic Production. cv-16-lecture-13.pdf
01.07.2016 Lecture 14. Aerospace Example. cv-16-lecture-14.pdf
01.07.2016 Lecture 15. Hamiltonian's Formulation. Pontryagin's Maximum Principle.cv-16-lecture-15.pdf
05.07.2016 Lecture 16. PMP examples. Introduction into Direct Methods. cv-16-lecture-16.pdf
15.07.2016 Lecture 17. Direct Methods. Suitable Functional Spaces.cv-16-lecture-17.pdf
19.07.2016 Lecture 18. Sobolev Spaces. Convexity and Lower Semicontinuity. cv-16-lecture-18.pdf
26.07.2016 Lecture 19. Relaxation. Variational Problems in Image Processing. cv-16-lecture-19.pdf
  • G.Buttazzo, M.Giaquinta, S.Hildebrandt. One-dimensional Variational Problems. An Introduction. Clarendon Press, Oxford, 1998.
  • B. Dacorogna. Introduction to the Calculus of Variations. 2nd edition, Imperial College Press, 2009.
  • R. Weinstock. Calculus of Variations with Applications to Physics & Engineering. Dover Publications Inc., 1974.
  • G. Aubert, P. Kornprobst. Mathematical Problems in Image Processing. Partial Differential Equations and the Calculus of Variations. 2nd edition, Applied Mathematical Sciences, 147, Springer, 2006.
lehre/vorlesung/cv16.txt · Zuletzt geändert: 2016/08/31 07:20 von agrja
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