phenomenon 28.53 Chladni's figures

open in the book · parts/03-classical-mechanics/11-oscillations-waves.tex:1925 · p. 967

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depends_on proposition 10.29 Time separation reduces the canonical equations to Helmholtz ¶
- depends_on equation 10.25 eq:pde-helmholtz-equation ¶
- depends_on lemma 10.28 The separation constant ¶
  - 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 6.2 Open set ¶
  - proves proof ch:08-pdes@proof-9 ¶
- proves proof ch:08-pdes@proof-10 ¶
depends_on theorem 9.57 Orthogonality of Sturm–Liouville eigenfunctions ¶
- depends_on equation 9.55 eq:slt-eigenproblem ¶
- depends_on lemma 9.56 Lagrange identity ¶
  - depends_on definition 9.54 Sturm–Liouville differential operator ¶
  - proves proof ch:07-odes-sturm-liouville@proof-28 ¶
- proves proof ch:07-odes-sturm-liouville@proof-29 ¶
proves proof ch:11-oscillations-waves@proof-29 ¶

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type	direction	node	provenance	where
`cites`	→	Entdeckungen über die Theorie des Klanges	derived	parts/03-classical-mechanics/11-oscillations-waves.tex:1930
`depends_on`	→	Time separation reduces the canonical equations to Helmholtz	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:1932
`depends_on`	→	Orthogonality of Sturm–Liouville eigenfunctions	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:1932
`proves`	←	ch:11-oscillations-waves@proof-29	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:1935