remark 7.124 The Laplacian of a vector field is a Cartesian notion

Rests on

• depends_on equation 7.133 eq:ana-nabla-sph-lap ¶
• depends_on proposition 7.123 Second-order identities of the nabla calculus ¶
  • depends_on equation 7.127 eq:ana-nabla-laplacian ¶
  • depends_on lemma 7.121 Contraction of two Levi-Civita symbols ¶
    • depends_on equation 7.134 eq:ana-epsilon-curl ¶
    • proves proof ch:05-real-analysis@proof-74 ¶
  • depends_on proposition 7.105 Clairaut–Schwarz ¶
    • depends_on definition 7.20 Continuity 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 equation 7.7 eq:ana-limit-left ¶
      • depends_on equation 7.5 eq:ana-limit-right ¶
    • depends_on theorem 7.35 Mean value theorem ¶
      • depends_on proposition 7.29 Linearity ¶
        • depends_on definition 7.11 Sum of functions ¶
        • depends_on equation 7.14 eq:ana-derivh ¶
        • depends_on proposition 7.6 Algebra of limits ¶
        • proves proof ch:05-real-analysis@proof-13 ¶
      • depends_on theorem 7.34 Rolle ¶
        • depends_on lemma 7.33 Fermat: interior extremum ¶
        • depends_on theorem 7.24 Extreme value theorem ¶
        • proves proof ch:05-real-analysis@proof-18 ¶
      • proves proof ch:05-real-analysis@proof-19 ¶
    • proves proof ch:05-real-analysis@proof-64 ¶
  • proves proof ch:05-real-analysis@proof-76 ¶

Supports

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