Contents
Foreword i
Acknowledgments xi
Lecture 1. The Brachistochrone
Lecture 2. The Fundamental Problem. Extremals
Appendix 2: The Fundamental Lemma 1
Lecture 3. The Insufficiency of Extremality 1
Appendix 3: The Principle of Least Action 2
Lecture 4. Important First Integrals 2
Lecture 5. The du Bois-Reymond Equation 3
Appendix 5: Another Fundamental Lemma 4
Lecture 6. The Corner Conditions 4
Lecture 7. Legendre’s Necessary Condition 5
Appendix 7: Yet Another Lemma 5
Lecture 8. Jacobi’s Necessary Condition 5
Appendix 8: On Solving Jacobi’s Equation 6
v
Foreword i
Acknowledgments xi
Lecture 1. The Brachistochrone
Lecture 2. The Fundamental Problem. Extremals
Appendix 2: The Fundamental Lemma 1
Lecture 3. The Insufficiency of Extremality 1
Appendix 3: The Principle of Least Action 2
Lecture 4. Important First Integrals 2
Lecture 5. The du Bois-Reymond Equation 3
Appendix 5: Another Fundamental Lemma 4
Lecture 6. The Corner Conditions 4
Lecture 7. Legendre’s Necessary Condition 5
Appendix 7: Yet Another Lemma 5
Lecture 8. Jacobi’s Necessary Condition 5
Appendix 8: On Solving Jacobi’s Equation 6
v
