Contents

• Contents
• Derivation of the Euler Equation
• Getting the Euler Equation from the Pontryagin Maximum Principle
• The Growth-Reproduction Trade-off
• The Growth-Defense Trade-off
• The Arabidopsis Problem of Zeno
• The Brachystochrone Problem
• A Biological problem of optimal growth

Herein I would like to walk you through some of the basic derivations of the calculus of variations. These include the simple but elegant Euler-Legrange equation, the derivation of the same using the Pontryagin maximum principle, and a number of basic applications that should give hardy devotees a place to start.