definition 7.135 Conservative field

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:4586 · p. 259

ground object -- no derivation owed

Rests on

depends_on equation 7.124 eq:ana-nabla-gradient ¶

Supports

depends_on proposition 7.136 Properties of conservative fields ¶
- depends_on example 31.15 The stream function of a plane flow ¶
  - depends_on definition A.715 Stokes stream function ¶
    - depends_on lemma A.716 The creeping-flow equation for $\psi$ ¶
      - depends_on lemma A.717 The radial solution ¶
- depends_on proposition 31.28 Potential flow reduces to Laplace's equation ¶
  - depends_on example 31.29 Flow past a sphere ¶
  - depends_on lemma A.777 The tangential field above a bending plate ¶
    - depends_on corollary A.778 The powder collects at the antinodes ¶
  - depends_on lemma A.733 The circle with incidence and circulation ¶
    - depends_on lemma A.735 Transfer of the flow ¶
      - depends_on theorem A.737 The lift-curve slope of the flat plate ¶
  - depends_on proposition A.797 The outer limit loses a boundary condition ¶
  - depends_on proposition 31.70 The lift-curve slope of a thin aerofoil ¶
  - depends_on theorem A.707 D'Alembert's paradox ¶
  - depends_on theorem 31.74 The interface dispersion relation ¶
    - depends_on corollary 31.76 Kelvin–Helmholtz instability ¶
    - depends_on corollary 31.75 Rayleigh–Taylor instability ¶
    - depends_on theorem 31.94 Gravity–capillary waves on a free surface ¶
      - depends_on phenomenon 31.96 The solitary wave ¶
      - depends_on phenomenon 31.95 The observed dispersion of water waves ¶
- depends_on theorem 16.63 Hilbert's invariant integral ¶
  - depends_on remark 23.8 The action as a function, not a functional ¶
  - depends_on theorem 16.64 Weierstrass' sufficient condition ¶
- depends_on theorem 30.15 Compatibility is sufficient on a simply connected body ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:ana-nabla-gradient	declared	parts/02-mathematical-methods/05-real-analysis.tex:4594
`depends_on`	←	Properties of conservative fields	declared	parts/02-mathematical-methods/05-real-analysis.tex:4614