definition 16.83 One-parameter transformation group; variational symmetry

Rests on

• depends_on definition 16.15 Variation; the first variation ¶
  • depends_on definition 16.11 Admissible class; functional ¶
    • depends_on definition 7.98 Functions of class $C^{1}$ ¶
      • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on equation 7.7 eq:ana-limit-left ¶
        • depends_on equation 7.5 eq:ana-limit-right ¶
      • depends_on definition 7.97 Partial derivative; gradient ¶
        • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on definition 5.15 Basis ¶
    • depends_on theorem 7.40 Continuous functions are integrable ¶
      • depends_on definition 7.39 Darboux sums and the definite integral ¶
        • depends_on axiom 7.1 Completeness of $\R$ ¶
      • depends_on theorem 7.24 Extreme value theorem ¶
        • depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
        • depends_on proposition 7.22 Sequential characterization ¶
        • depends_on theorem 7.7 Bolzano–Weierstrass ¶
        • proves proof ch:05-real-analysis@proof-9 ¶
      • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
        • depends_on proposition 7.22 Sequential characterization ¶ ↺
        • depends_on theorem 7.7 Bolzano–Weierstrass ¶ ↺
        • proves proof ch:05-real-analysis@proof-10 ¶
      • proves proof ch:05-real-analysis@proof-23 ¶
  • depends_on equation 7.177 eq:ana-functional-derivative ¶
• depends_on equation 16.11 eq:calcvar-basic-functional ¶

Supports

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