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Consortium for Mathematics and its Applications

Product ID: 99468
Supplementary Print
Undergraduate

Calculus of Variations with Applications in Mathematics (UMAP)

Author: Carroll O. Wilde


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

©1980 by COMAP, Inc.
UMAP Module
40 pages

Mathematics Topics:

Calculus

Application Areas:

Engineering & Construction , Physical Sciences , Mechanical Engineering & Physics

Prerequisites:

Basic physics (kinetic and potential energy); multivariate calculus (chain rule); ordinary differential equations

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