proposition 28.48 Modal energy

Rests on

• depends_on equation 28.52 eq:osc-modal-solution ¶
• depends_on theorem 17.34 Parseval's identity for 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 ¶
  • depends_on proposition 17.4 Least squares and Bessel's inequality ¶
    • depends_on definition 17.1 Fourier coefficients and Fourier series ¶ ↺
    • depends_on lemma 17.2 Orthogonality of the harmonics ¶ ↺
    • proves proof ch:15-fourier-integral-transforms@proof-3 ¶
  • depends_on theorem 17.22 Fejér ¶
    • depends_on lemma 17.6 Dirichlet kernel ¶
      • depends_on definition 17.1 Fourier coefficients and Fourier series ¶ ↺
      • depends_on lemma 17.2 Orthogonality of the harmonics ¶ ↺
      • proves proof ch:15-fourier-integral-transforms@proof-4 ¶
    • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      • depends_on proposition 7.22 Sequential characterization ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.4 Convergence ¶
        • proves proof ch:05-real-analysis@proof-7 ¶
      • depends_on theorem 7.7 Bolzano–Weierstrass ¶
        • depends_on corollary A.45 Archimedean property and density of $\Q$ ¶
        • depends_on corollary A.46 Monotone convergence ¶
        • proves proof ch:05-real-analysis@proof-4 ¶
      • proves proof ch:05-real-analysis@proof-10 ¶
    • proves proof ch:15-fourier-integral-transforms@proof-16 ¶
  • proves proof ch:15-fourier-integral-transforms@proof-22 ¶
• proves proof ch:11-oscillations-waves@proof-27 ¶

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