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

Rests on

• depends_on lemma A.735 Transfer of the flow ¶
  • 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 7.97 Partial derivative; gradient ¶
      • 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 ¶
        • 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 proposition 7.104 Chain rule in several variables ¶
        • depends_on theorem 7.132 Stokes ¶
        • 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 ¶
• depends_on theorem 31.68 Kutta–Joukowski ¶
  • depends_on lemma 31.67 Blasius' force formula ¶
    • depends_on theorem 8.6 Cauchy–Riemann equations ¶ ↺
    • depends_on theorem 31.24 Bernoulli ¶
      • depends_on equation 31.4 eq:fluid-lamb-identity ¶
      • depends_on theorem 31.22 Euler's equations of motion ¶
        • depends_on definition 31.21 Ideal fluid ¶
        • depends_on lemma 31.11 Transport theorem for a material volume ¶
        • depends_on theorem 30.21 Cauchy's equation of motion ¶
        • proves proof ch:14-fluid-dynamics@proof-11 ¶
      • proves proof ch:14-fluid-dynamics@proof-12 ¶
    • proves proof ch:14-fluid-dynamics@proof-31 ¶
  • depends_on theorem 8.24 Residue theorem ¶
    • depends_on corollary 8.15 Deformation of contours ¶
      • depends_on definition 6.17 Simply connected space ¶
        • depends_on definition 6.6 Continuous map ¶
        • depends_on definition 6.15 Path-connected space ¶
      • depends_on theorem 8.12 Cauchy ¶
        • depends_on equation 8.5 eq:cpx-cr ¶
        • depends_on theorem 7.131 Green ¶
        • proves proof ch:06-complex-analysis@proof-7 ¶
      • proves proof ch:06-complex-analysis@proof-9 ¶
    • depends_on definition 8.22 Isolated singularities; residue ¶
      • depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶
        • depends_on equation 8.6 eq:cpx-contour-integral ¶
        • depends_on proposition 8.4 Euler's formula ¶
        • proves proof ch:06-complex-analysis@proof-6 ¶
      • depends_on theorem 8.21 Laurent expansion ¶
        • depends_on corollary 8.15 Deformation of contours ¶ ↺
        • depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶ ↺
        • depends_on theorem 8.16 Cauchy integral formula ¶
        • depends_on theorem 8.20 Taylor expansion ¶
        • proves proof ch:06-complex-analysis@proof-15 ¶
    • depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶ ↺
    • depends_on theorem 8.21 Laurent expansion ¶ ↺
    • proves proof ch:06-complex-analysis@proof-17 ¶
  • proves proof ch:14-fluid-dynamics@proof-32 ¶
• proves proof app:A-long-proofs@proof-431 ¶

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