definition 30.4 Material and spatial descriptions

Rests on

• depends_on definition 30.2 Representative volume element; continuum field ¶
  • 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 7.2 Absolute value ¶
        • depends_on definition 7.9 Real function ¶
      • 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 5.5 Linear combination ¶
        • depends_on definition 5.7 Vector subspace ¶
        • proves proof ch:03-linear-algebra-representations@proof-3 ¶
      • depends_on definition 5.14 Linear independence ¶
        • depends_on definition 5.5 Linear combination ¶ ↺
• 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 7.99 Differentiability at a point ¶
    • depends_on definition 7.16 Limit ¶ ↺
    • 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 ¶ ↺
  • proves proof ch:05-real-analysis@proof-63 ¶

Supports

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