lemma A.735 Transfer of the flow

open in the book · appendices/A-long-proofs.tex:35680 · p. 3151

Rests on

depends_on definition A.734 The Joukowski map ¶
- depends_on theorem 8.6 Cauchy–Riemann equations ¶
  - 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 equation 8.4 eq:cpx-derivative ¶
  - proves proof ch:06-complex-analysis@proof-3 ¶
depends_on lemma A.733 The circle with incidence and circulation ¶
- depends_on equation 31.57 eq:fluid-complex-velocity ¶
- depends_on proposition 31.28 Potential flow reduces to Laplace's equation ¶
  - depends_on corollary 31.13 Incompressible flow ¶
    - depends_on theorem 31.12 Conservation of mass ¶
      - depends_on lemma 31.11 Transport theorem for a material volume ¶
      - proves proof ch:14-fluid-dynamics@proof-5 ¶
    - proves proof ch:14-fluid-dynamics@proof-6 ¶
  - depends_on equation 10.24 eq:pde-poisson-equation ¶
  - depends_on proposition 7.136 Properties of conservative fields ¶
    - depends_on definition 7.135 Conservative field ¶
      - depends_on equation 7.124 eq:ana-nabla-gradient ¶
    - depends_on proposition 7.104 Chain rule in several variables ¶
      - depends_on definition 7.13 Composite function ¶
      - depends_on definition 7.99 Differentiability at a point ¶
      - depends_on definition 7.102 Differential of a function ¶
      - proves proof ch:05-real-analysis@proof-63 ¶
    - depends_on theorem 7.132 Stokes ¶
      - depends_on proposition 7.104 Chain rule in several variables ¶ ↺
      - depends_on proposition 7.105 Clairaut–Schwarz ¶
      - depends_on theorem 7.131 Green ¶
      - proves proof ch:05-real-analysis@proof-78 ¶
    - proves proof ch:05-real-analysis@proof-80 ¶
  - proves proof ch:14-fluid-dynamics@proof-14 ¶
- proves proof app:A-long-proofs@proof-429 ¶
proves proof app:A-long-proofs@proof-430 ¶

Supports

depends_on theorem A.737 The lift-curve slope of the flat plate ¶

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`	→	The Joukowski map	declared	appendices/A-long-proofs.tex:35693
`depends_on`	→	The circle with incidence and circulation	declared	appendices/A-long-proofs.tex:35693
`depends_on`	←	The lift-curve slope of the flat plate	declared	appendices/A-long-proofs.tex:35762
`proves`	←	app:A-long-proofs@proof-430	declared	appendices/A-long-proofs.tex:35697