proposition 10.16 Cauchy's characteristic strips

Rests on

• 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 definition 3.43 Map ¶
    • 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 definition 7.9 Real function ¶ ↺
      • depends_on equation 7.14 eq:ana-derivh ¶
      • depends_on proposition 7.6 Algebra of limits ¶
        • depends_on definition 7.4 Convergence ¶
        • depends_on proposition 7.3 Triangle inequality ¶
        • proves proof ch:05-real-analysis@proof-3 ¶
      • proves proof ch:05-real-analysis@proof-13 ¶
    • depends_on theorem 7.34 Rolle ¶
      • depends_on lemma 7.33 Fermat: interior extremum ¶
        • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on proposition 7.18 Two-sided limit from one-sided limits ¶
        • proves proof ch:05-real-analysis@proof-17 ¶
      • 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 ¶
      • proves proof ch:05-real-analysis@proof-18 ¶
    • proves proof ch:05-real-analysis@proof-19 ¶
  • proves proof ch:05-real-analysis@proof-64 ¶
• depends_on proposition 10.15 Method of characteristics, first order ¶
  • depends_on definition 10.2 Linear, semilinear, quasilinear ¶
    • depends_on definition 10.1 Partial differential equation; order ¶
      • 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 definition 6.2 Open set ¶
        • depends_on definition 6.1 Topological space ¶
  • depends_on proposition 7.31 Chain rule ¶
    • depends_on definition 7.13 Composite function ¶
      • depends_on definition 7.9 Real function ¶ ↺
    • depends_on proposition 7.27 Differentiable implies continuous ¶
      • depends_on definition 7.20 Continuity at a point ¶ ↺
      • depends_on definition 7.26 Derivative of a function at a point ¶ ↺
      • depends_on proposition 7.6 Algebra of limits ¶ ↺
      • proves proof ch:05-real-analysis@proof-11 ¶
    • depends_on proposition 7.6 Algebra of limits ¶ ↺
    • proves proof ch:05-real-analysis@proof-15 ¶
  • proves proof ch:08-pdes@proof-5 ¶
• depends_on theorem 9.8 Picard–Lindelöf ¶
  • depends_on definition 9.4 Lipschitz condition ¶
  • depends_on equation 9.3 eq:slt-ode-system ¶
  • depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
    • depends_on definition 7.20 Continuity at a point ¶ ↺
    • depends_on proposition 7.47 Comparison; absolute convergence ¶
      • depends_on corollary A.46 Monotone convergence ¶
        • depends_on theorem A.40 Least-upper-bound property ¶
        • proves proof app:A-long-proofs@proof-33 ¶
      • depends_on definition 7.45 Series ¶
        • depends_on definition 7.2 Absolute value ¶ ↺
        • depends_on definition 7.4 Convergence ¶ ↺
      • depends_on theorem 7.8 Cauchy criterion ¶
        • depends_on corollary A.47 Cauchy completeness ¶
        • depends_on definition 7.4 Convergence ¶ ↺
        • proves proof ch:05-real-analysis@proof-5 ¶
      • proves proof ch:05-real-analysis@proof-28 ¶
    • proves proof ch:07-odes-sturm-liouville@proof-1 ¶
  • proves proof ch:07-odes-sturm-liouville@proof-2 ¶
• proves proof ch:08-pdes@proof-6 ¶

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