example 10.38 The vibrating string
open in the book ·
parts/02-mathematical-methods/08-pdes.tex:1053
· p. 351
- example -- no derivation owed by its kind
Rests on
- depends_on equation 10.28 eq:pde-wave-separated ¶
-
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 ¶
-
depends_on
definition 10.1
Partial differential equation; order
¶
- proves proof ch:08-pdes@proof-9 ¶
-
depends_on
definition 10.2
Linear, semilinear, quasilinear
¶
- proves proof ch:08-pdes@proof-10 ¶
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cites
(history) |
→ | Réflexions et éclaircissemens sur les nouvelles vibrations des cordes exposées dans les mémoires de l'Académie de 1747 et 1748 | derived | parts/02-mathematical-methods/08-pdes.tex:1068 |
cites
(history) |
→ | Théorie analytique de la chaleur | derived | parts/02-mathematical-methods/08-pdes.tex:1069 |
depends_on |
→ | eq:pde-wave-separated | declared | parts/02-mathematical-methods/08-pdes.tex:1072 |
depends_on |
→ | Time separation reduces the canonical equations to Helmholtz | declared | parts/02-mathematical-methods/08-pdes.tex:1072 |