TABL E O F C O N T E N T S Abstract vi 1. Introduction 1 2. The Variational Bicomplex for Ordinary Differential Equations . 12 3. First Integrals and the Inverse Problem for Second Order Ordinary Differential Equations 27 4. The Inverse Problem for Fourth Order Ordinary Differential Equations 35 5. Exterior Differential Systems and the Inverse Problem for Second Order Ordinary Differential Equations 50 6. Examples 64 7. The Inverse Problem for Two Dimensional Sprays 88 8. References 108

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