Calculus of variations in mathematical physics

Description

Title page PREFACE CHAPTER I Maxima and minima of functions 1. Functions of a single variable 2. Functions of two and more variables 3. Subsidiary conditions CHAPTER II A concrete variational problem 4. Fundamental lemma's 5. The simplest variational problem 6. The brachistochrone problem 7. The catenary problem 8. The second variation CHAPTER III An abstract variational problem 9. Linear normed spaces 10. Functionals on a Banach space 11. The Hilbert space 12. Functionals on a Hilbert space CHAPTER IV Further variational problems 13. Several unknown functions 14. A functional depending on higher-order derivatives 15. Variable end point conditions 16. Several independent variables CHAPTER V Applications in mechanics 17. Hamilton's principle 18. Continuous mechanical systems 19. Equations of mathematical physics CHAPTER VI Advanced topics 20. Broken extremals 21. Noether's theorem CHAPTER VII Direct methods 22. Introduction 23. Minimizing sequences Recommended Reading Index