变分学入门

Preiace Chapter 1.Introduction 1.1.The brachistochrone 1.2.The terrestrial brachistochrone 1.3.Geodesics 1.4.Minimal surfaces 1.5.Recommended reading 1.6.Exercises Chapter 2.The First Variation 2.1.The simplest problem 2.2.Euler's approach 2.3.Lagrange's approach 2.4.Recommended reading 2.5.Exercises Chapter 3.Cases and Examples 3.1.Special cases 3.2.Case study：Minimal surface of revolution 3.3.Case study：The brachistochrone 3.4.Geodesics 3.5.Recommended reading 3.6.Exercises Chapter 4.Basic Generalizations 4.1.Higher—order derivatives 4.2.Case study：The cantilever beam 4.3.Multiple unknown functions 4.4.Lagrangian mechanics 4.5.Case study：The spherical pendulum 4.6.Hamiltonian mechanics 4.7.Ray optics 4.8.Double integrals 4.9.Recommended reading 4.10.Exercises Chapter 5.Constraints 5.1.Types of constraints 5.2.Lagrange multipliers 5.3.Isoperimetric constraints 5.4.Case study：Queen Dido's problem 5.5.Case study：Euler's elastica 5.6.Holonomic constraints 5.7.Case study：A sliding rod 5.8.Recommended reading 5.9.Exercises Chapter 6.The Second Variation 6.1.Introduction 6.2.Legendre's condition 6.3.Jacobi's condition 6.4.Case study：The catenoid revisited 6.5.Recommended reading 6.6.Exercises Chapter 7.Review and Preview