SMAT5308 Calculus of Variations (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Grading scale:
0-5
Description
Calculus of variations is a field of mathematical analysis that deals with maximizing or minimizing functionals, which are mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. The interest is in extremal functions that make the functional attain a maximum or minimum value; or stationary functions; those where the rate of change of the functional is zero.
1 EXTREME VALUES OF FUNCTIONALS
2 THE THEORY OF THE FIRST VARIATION
3 THEORY OF FIELDS AND SUFFICIENT CONDITIONS FOR A STRONG RELATIVE EXTREMUM
4 THE HOMOGENEOUS PROBLEM
5 THE PROBLEM OF LAGRANGE AND THE ISOPERIMETRIC PROBLEM
6. THE MINIMUM PRINCIPLE OF PONTRYAGIN
Learning outcomes
The course provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations and prepares students for the study of modern optimal control theory. The treatment is limited to extensive coverage of single integral problems in one and more unknown functions.
Additional information
Course will be given on autumn 2026.
Description of prerequisites
Recommended preceding studies: Differential Equations and Partial Differential Equations