Conclusion
Following completion of this free OpenLearn course, Introduction to the calculus of variations, you should find that your skills and confidence in finding solutions to variational problems are improving.
You should now be able to:
- understand what functionals are, and have some appreciation of their applications
- apply the formula that determines stationary paths of a functional to deduce the differential equations for stationary paths in simple cases
- use the Euler-Lagrange equation or its first integral to find differential equations for stationary paths
- solve differential equations for stationary paths, subject to boundary conditions, in straightforward cases.
This free OpenLearn course is an extract from the Open University course MS327 Deterministic and stochastic dynamics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .
If you feel you are ready to move on in your study of applied mathematics but don’t have time to study a full Open University course at this time, you might like to study the free OpenLearn courses Linear programming – the basic ideas and Kinematics of fluids.
If you are interested in pure mathematics, you might like to try the free OpenLearn courses Number theory, Group theory, Rings and polynomials and Metric spaces and continuity.
If you are interested in statistics, you might like to study the free OpenLearn courses Modelling events in time, Univariate continuous distribution theory and Point estimation.