proposition 28.47 Modal solution of the initial-value problem
open in the book ·
parts/03-classical-mechanics/11-oscillations-waves.tex:1668
· p. 964
Rests on
- depends_on equation 28.50 eq:osc-string-modes ¶
-
depends_on
theorem 17.3
Euler–Fourier coefficient formulas
¶
- depends_on definition 17.1 Fourier coefficients and Fourier series ¶
-
depends_on
lemma 17.2
Orthogonality of the harmonics
¶
- depends_on definition 17.1 Fourier coefficients and Fourier series ¶ ↺
- proves proof ch:15-fourier-integral-transforms@proof-1 ¶
- proves proof ch:15-fourier-integral-transforms@proof-2 ¶
- proves proof ch:11-oscillations-waves@proof-26 ¶
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | eq:osc-string-modes | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:1684 |
depends_on |
→ | Euler–Fourier coefficient formulas | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:1684 |
proves |
← | ch:11-oscillations-waves@proof-26 | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:1687 |