Calculus of Variations with Applications in Mathematics (UMAP)

A unit that involves calculus of variations with applications in mathematics. With completion of this module students will be able to: 1) explain the concept of the definite integral as a functional; 2) find Euler equations for various definite integral forms; 3) describe Hamilton's principle; and 4) apply Hamilton's principle to conservative dynamical systems using Euler equations.

Table of Contents:

1. INTRODUCTION

2. SOME USEFUL NOTATION

3. INTEGRALS AS FUNCTIONALS

4. AN ILLUSTRATIVE EXAMPLE

5. EULER EQUATIONS: THE SIMPLEST CASE

6. SOLUTION OF THE BRACHISTOCHRONE PROBLEM

7. EULER EQUATIONS AND OTHER FUNCTIONALS

8. APPLCIATIONS IN MECHANICS

9. WHAT WE DIDN'T SAY

10. MODEL EXAMINATION

11. ANSWERS TO EXERCISES

12. ANSWERS TO MODEL EXAM

13. APPENDIX: DERIVATION OF EULER EQUATIONS