Selected Chapters in the Calculus of Variations Book

0.1	Introduction	1
0.2	On these lecture notes	2
1	One-dimensional variational problems	3
1.1	Regulatory of the minimals	3
1.2	Examples	9
1.3	The accessory variational problem	16
1.4	Extremal fields for n=1	20
1.5	The Hamiltonian formulation	25
1.6	Exercises to Chapter 1	30
2	Extremal fields and global minimals	33
2.1	Global extremal fields	33
2.2	An existence theorem	36
2.3	Properties of global minimals	42
2.4	A priori estimates and a compactness property	50
2.5	M[subscript [alpha]] for irrational [alpha], Mather sets	56
2.6	M[subscript [alpha]] for rational [alpha]	73
2.7	Exercises to chapter II	81
3	Discrete Systems, Applications	83
3.1	Monotone twist maps	83
3.2	A discrete variational problem	94
3.3	Three examples	98
3.4	A second variational problem	104
3.5	Minimal geodesics on T[superscript 2]	105
3.6	Hedlund's metric on T[superscript 3]	108
3.7	Exercises to chapter III	113
	Bibliography	115
A	Remarks on the literature	117
	Additional Bibliography	121
	Index	129