Universität des Saarlandes
FR Mathematik
Arbeitsgruppe Prof. S. Rjasanow

Institut für angewandte Mathematik

Calculus of Variations


There is no lecture on Tuesday 30.05.2017. Next lecture takes place on Friday 02.06.2017.


Register here.


- On Tuesdays 14-16 and Fridays, 8-10, in HS 1, Building E2.5. Begin 21.04.17.

  1. Lecturer: PD Dr. Darya Apushkinskaya ,
    Office hours: Thursdays 10:15-11:00 or by appointment (during semester break only by appointment)
  2. Tutor: Sumit Shekhar s8sushek@stud.uni-saarland.de

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
25.05.17 cv17-blatt2.pdf02.06.17


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

Date Topic Transparencies
21.04.17 Lecture 1. Introduction and Examples. Euler-Lagrange Equation.cv-17-lecture-1.pdf
25.04.17 Lecture 2. Remarks on the Euler-Lagrange Equation.cv-17-lecture-2.pdf
28.04.17 Lecture 3. Remarks on the Euler-Lagrange Equation (cont.). Undetermined End Points.cv-17-lecture-3.pdf
05.05.17 Lecture 4. Case of Several Variables. Examples of the Euler-Lagrange Equations. Introduction into Isoperimetric Problemscv-17-lecture-4.pdf
05.05.17 Lecture 5. Simple Dido's Problem. Catenary Problem. cv-17-lecture-5.pdf
09.05.17 Lecture 6. General Dido's Problem. Lagrange Multiplier Approach for Functionals. cv-17-lecture-6.pdf
12.05.17 Lecture 7. Problems with Non-Integral Constraints. cv-17-lecture-7.pdf
16.05.17 Lecture 8. Newton's Aerodynamic Problem. cv-17-lecture-8.pdf
19.05.17 Lecture 9. Classification of extrema. cv-17-lecture-9.pdf
23.05.17 Lecture 10. Inequality Constraints. cv-17-lecture-10.pdf
26.05.17 Lecture 11. Brocken Extremals. cv-17-lecture-11.pdf
02.06.17 Lecture 12. Numerical Solutions (Euler's Finite Difference Method. Ritz's Method). cv-17-lecture-12.pdf
06.06.17Lecture 13. Numerical Solutions (Ritz and Catenary, Kantorovich's Method). Introduction into Optimal Control Problems. Example of Dynamic Production.cv-17-lecture-13.pdf
09.06.17 Lecture 14. Aerospace Example (Part I). cv-17-lecture-14.pdf
13.06.17 Lecture 15. Aerospace Example (Part II). Hamiltonian's Formulation. cv-17-lecture-15.pdf
16.06.17 Lecture 16. Pontryagin's Maximum Principle. PMP Examples (Plant Growth).cv-17-lecture-16.pdf
20.06.17 Lecture 17. PMP examples. Introduction into Direct Methods.cv-17-lecture-17.pdf
23.06.17 Lecture 18. Direct Methods. Suitable Functional Spaces.cv-17-lecture-18.pdf
27.06.17 Lecture 19. Sobolev Spaces. Convexity and Lower Semicontinuity.cv-17-lecture-19.pdf
07.07.17 Lecture 20. Relaxation Theory. cv-17-lecture-20.pdf
10.08.17 Lecture 21. Variational Problems in Image Processing. cv-17-lecture-21.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/cv17.txt · Zuletzt geändert: 2017/08/10 13:19 von agrja
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