remark 22.13 Euler's theorem on homogeneous functions is owed

Rests on

• depends_on proposition 7.104 Chain rule in several variables ¶
  • depends_on definition 7.13 Composite function ¶
    • depends_on definition 7.9 Real function ¶
      • depends_on definition 3.43 Map ¶
        • depends_on definition 3.24 Quantifiers ¶
        • depends_on definition 3.28 Set ¶
  • depends_on definition 7.99 Differentiability at a point ¶
    • depends_on definition 7.16 Limit ¶
      • depends_on definition 7.2 Absolute value ¶
      • depends_on definition 7.9 Real function ¶ ↺
    • depends_on definition 5.37 Linear transformation ¶
      • depends_on definition 4.33 Vector space ¶
        • depends_on definition 4.8 Commutativity; abelian structure ¶
        • depends_on definition 4.32 Field ¶
        • depends_on definition 4.31 Module ¶
    • depends_on equation 6.12 eq:top-euclidean-metric ¶
  • depends_on definition 7.102 Differential of a function ¶
    • depends_on definition 7.99 Differentiability at a point ¶ ↺
    • depends_on definition 7.97 Partial derivative; gradient ¶
      • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on definition 7.16 Limit ¶ ↺
        • depends_on definition 7.9 Real function ¶ ↺
      • depends_on definition 5.15 Basis ¶
        • depends_on definition 5.12 Subspace generated by a set of vectors ¶
        • depends_on definition 5.14 Linear independence ¶
  • proves proof ch:05-real-analysis@proof-63 ¶
• depends_on proposition 22.11 Hamiltonian and total energy ¶
  • depends_on equation 22.1 eq:ham-hamiltonian ¶
  • depends_on proposition 21.38 Energy in generalized coordinates ¶
    • depends_on equation 21.44 eq:lag-energy ¶
    • depends_on equation 21.7 eq:lag-gct ¶
    • depends_on equation 21.45 eq:lag-jacobi-integral ¶
    • proves proof ch:04-lagrangian-mechanics@proof-9 ¶
  • proves proof ch:05-hamiltonian-mechanics@proof-5 ¶

Supports

Nothing declares a dependency on this node yet.