proposition 28.44 Superposition

open in the book · parts/03-classical-mechanics/11-oscillations-waves.tex:1528 · p. 962

Rests on

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 7.16 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 definition 6.2 Open set ¶
    - depends_on definition 6.1 Topological space ¶
      - depends_on definition 3.31 Empty set ¶
      - depends_on definition 3.35 Union, intersection, difference ¶
      - depends_on definition 3.30 Subset ¶
      - depends_on equation 3.51 eq:set-indexed ¶
depends_on equation 28.46 eq:osc-wave-eq ¶
proves proof ch:11-oscillations-waves@proof-23 ¶

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type	direction	node	provenance	where
`depends_on`	→	Linear, semilinear, quasilinear	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:1533
`depends_on`	→	eq:osc-wave-eq	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:1533
`proves`	←	ch:11-oscillations-waves@proof-23	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:1536