Differential equations from the group standpoint

Title page
1-3 Translations, rotations, transformations
4 Product of two translations
5 Inverse of a translation, identity transformation
6 Groups of transformations
7 Groups found by integrating differential equations
8 Infinitesimal transformations
9 Every one-parameter group is generated by an infinitesimal transformation
10 Equivalence of two one-parameter groups
11-12 Invariant points. Path curves
13 Corresponding ordinary and partial differential equations
14 First criterion for the invariance of a differential equation of the first order under a group
15-16 Finding an integrating factor, problems
17 Infinitude of groups leaving invariant a differential equation of the first order
18 Geometrical interpretation of Lie's integrating factor
19-20 Parallel curves, isothermal curves
21 Commutator
22 A second criterion for the invariance of a differential eqnation under an infinitesimal transformation
23 Group of extended transformations
24-26 Invariants, differential invariants
27 Invariant equations
28 A third criterion for the invariance of a differential equation of the first order under Uf
29 Introduction of new variables in a linear partial differential expression
30 Determination of all differential equations of the first order invariant under a given infinitesimal transformation, table
31-34 Complete system of linear partial differential equations
35 Standard methods of solving a complete system of two partial differential equations in three variables
36-38 Solution of one partial differential equation invariant under an infinitesimal transformation
39 Jacobi's identity
40-42 Solution of one partial differential equation invariant under two infinitesimal transformations
43 Second extension of an infinitesimal transformation
44 Differentiai invariants of the second order
45-46 Integration of differential equations of the second order invariant under one infinitesimal transformation, table
47-48 Number of linearly independent infinitesimal transformations leaving y"= ω(x,y,y') invariant
49 Integration of y" = w invariant under two infinitesimal transformations
50 First extension of a commutator
51-52 Closed system of infinitesimal transformations leaving y" = w invariant
58 Integra.tion of y" = ω
54 Differential invariants and the congruence of plane curves
55 Algebraic invariants and covariants