Chapter 1. Introduction
Chapter 2. The first variation
Chapter 3. Cases and examples
Chapter 4. Basic generalizations
Chapter 5. Constraints
Chapter 6. The second variation
Chapter 7. Review and preview
Chapter 8. The homogeneous problem
Chapter 9. Variable-endpoint conditions
Chapter 10. Broken extremals
Chapter 11. Strong variations
Chapter 12. Sufficient conditions

The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields.The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics.Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.---Summary provided by publisher